Research Article Application of Machine Learning in Postural...

Research ArticleApplication of Machine Learning in Postural ControlKinematics for the Diagnosis of Alzheimerrsquos Disease

Luiacutes Costa1 Miguel F Gago23 Darya Yelshyna1 Jaime Ferreira1

Heacutelder David Silva1 Luiacutes Rocha1 Nuno Sousa34 and Estela Bicho1

1Algoritmi Center Department of Industrial Electronics School of Engineering University of Minho Braga Portugal2Neurology Department Hospital da Senhora da Oliveira Guimaraes Portugal3Life and Health Sciences Research Institute (ICVS) School of Health Sciences University of Minho Braga Portugal4ICVS-3Brsquos-PT Government Associate Laboratory Braga Portugal

Correspondence should be addressed to Miguel F Gago miguelfgagoyahoocom

Received 21 July 2016 Accepted 9 October 2016

Academic Editor Silvia Conforto

Copyright copy 2016 Luıs Costa et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The use of wearable devices to study gait and postural control is a growing field on neurodegenerative disorders such as Alzheimerrsquosdisease (AD) In this paper we investigate if machine-learning classifiers offer the discriminative power for the diagnosis of ADbased on postural control kinematics We compared Support Vector Machines (SVMs) Multiple Layer Perceptrons (MLPs) RadialBasis Function Neural Networks (RBNs) and Deep Belief Networks (DBNs) on 72 participants (36 AD patients and 36 healthysubjects) exposed to seven increasingly difficult postural tasks The decisional space was composed of 18 kinematic variables(adjusted for age education height and weight) with or without neuropsychological evaluation (Montreal cognitive assessment(MoCA) score) top ranked in an error incremental analysis Classification results were based on threefold cross validation of 50independent and randomized runs sets training (50) test (40) and validation (10) Having a decisional space relying solelyon postural kinematics accuracy of AD diagnosis ranged from 717 to 861 Adding the MoCA variable the accuracy rangedbetween 91 and 966MLP classifier achieved top performance in both decisional spaces Having comprehended the interdynamicinteraction between postural stability and cognitive performance our results endorse machine-learning models as a useful tool forcomputer-aided diagnosis of AD based on postural control kinematics

1 Introduction

Around 30 of the people aged more than 65 living in thecommunity and more than 50 of those living in residentialcare facilities or nursing homes fall every year Moreoverabout half of those who fall do so repeatedly [1] With theincrease in the elderly population the number of falls in thisgroup has been rising constituting an important public healthproblem [2] Postural instability characterized by excessiveand uncontrolled sway degrades with ageing and is a riskfactor for the occurrence of falls especially in neurodegen-erative diseases such as Alzheimerrsquos disease (AD) [3] AD isa neurodegenerative cortical disorder that besides memorydeficits also displays disturbances of posture and gait whichtriggers more serious falls compared to nondemented elderly

people In that regard diagnostic tools that allow an early andnoninvasive detection of AD pathology are highly required

To this end many researchers have devoted their effortsto find appropriate datafeatures and have applied differentmachine-learning methods for computer-aided diagnosis ofAD Most of the works reported in the literature make use ofSupport Vector Machines (SVMs) and Artificial Neural Net-works (ANNs) such as Multiple Layer Perceptrons (MLPs)Radial Basis Function Networks (RBNs) and Deep BeliefNetworks (DBNs) We provide a brief review next in thiscontext

SVMs are a particular type of supervised machine-learning method that classifies data points by maximizingthe margin between classes in a high-dimensional space [4]They are the most widely used classifiers and have shown

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2016 Article ID 3891253 15 pageshttpdxdoiorg10115520163891253

2 Computational Intelligence and Neuroscience

promising results on problems of pattern recognition inneurology and psychiatry diseases [5] including detection ofADbased on electrical brain activity Electroencephalography(EEG) [6] neuroimaging data from Magnetic ResonanceImaging (MRI) and Positron Emission Tomography (PET)brain images [7ndash10] Several works have applied MLPs inthe diagnosis of AD combining different variables suchas demographic neurological and psychiatric evaluationneuropsychological tests and even more complex clinicaldiagnostic tools (eg neuropathology EEG and MRIPETbrain imaging) where hundreds of variables of recordeddata are potentially clinically relevant on one single patient[7 11 12] RBNs have successfully been applied to the dis-crimination of plasma signalling proteins for the predictionof this disease [13] and classification of MRI features ofAD [7] DBNs are a recent machine-learning model thatis exhibiting performance records on classification accuracyalso on medical fields such as AD based on MRIPETneuroimaging data [14 15]

The survey of the above literature shows that the majorityof the studies have relied on neuroimaging data from MRIandor PET images which though widely available arerelatively expensive In contrast inertial measurement units(IMUs) with integrated accelerometers and gyroscopes areinexpensive and small fully portable devices opening a newfield of research on AD In fact IMUs have been used toportrait different postural kinematic profiles inAD includinga higher risk of falling [16] These devices are independent ofinclination in space having proved to be equivalent to forceplatforms in the evaluation of the center ofmass (COM) kine-maticsHowever althoughhundreds of kinematic parametershave been used to represent postural body sway [17] whichparameters provide the most relevant information aboutnormal postural control and which kinematic parametersbetter identify neurodegenerative diseases such asAD are stillyet undetermined We advocate that a complementary toolthat makes use of kinematic postural data for the diagnosis ofAD would be extremely helpful and valuable for clinicians

To the best of our knowledge the use ofmachine-learningclassifiers for the diagnosis of AD based on kinematicpostural sway data has not yet been investigated With thisin mind our study has two main goals First to validate thefeasibility of the application of machine-learning models inthe diagnosis of AD based on postural kinematic data col-lected on different and increasingly difficult postural balancetasks Second to compare different classifier modelsmdashSVMMLP RBN and DBNmdashwith respect to their discriminativeperformance

The remainder of the paper is structured as follows InSection 2 we explain the materials and methodology usedfor collecting the data feature reduction and implementationof the three dataset models subsequently used for trainingtesting and comparing the different classifiers models Sec-tion 3 gives a brief description on how we implemented theclassifiersrsquo models Section 4 presents results of performancefor the different classifiers in the different dataset models InSection 5 a detailed discussion ismade such that in Section 6some conclusions can be drawn about the potential use of the

tested classifiers in future automatic diagnostic tools for ADbased on kinematic postural sway data

2 Materials and Methodologyfor Data Collection

21 Study Population The study population was recruitedfrom our hospital outpatient neurology department Patientswith probable AD according to Diagnostic and StatisticalManual of Mental Disorders- IV (DSM-IV) and NationalInstitute of Neurological and Communicative Disorders andStrokeAlzheimerrsquos Disease and Related Disorders Associa-tion (NINCDSADRDA) criteria [18] on a stage of 1 on theClinical Dementia Rating Scale were consecutively recruitedfor the study The control group included age-matched care-givers of patients that had no history of falls or of neurologicalor psychiatric disease Patients or controls were excluded ifthere was a history of orthopedic musculoskeletal vestibulardisorder or alcohol abuse Demographic anthropometricand MoCA data normalized to the Portuguese population[19] were collected in both groups Local hospital ethicscommittee approved the protocol of the study submitted byICVSUM and Center AlgoritmiUM Written consent wasobtained from all subjects or their guardians

We included 36 AD patients (24 females12 males witha mean age of 76 plusmn 7 years) and 36 healthy controls (15females21 males with a mean age of 70plusmn8 years) (AD versusC119901 = 0003) Concerning demographic and anthropometricdata the two groups displayed the following education (AD1 plusmn 058 control 2 plusmn 119 119901 = 0008) MoCA (AD 11 plusmn 510control 25 plusmn 387 119901 lt 0001) weight (kg) (AD 6560 plusmn1028 control 7524 plusmn 1211 119901 = 0001) height (m) (AD154plusmn008 control 163plusmn0106 119901 lt 0001) bodymass index(kgm2) (AD 2758 plusmn 412 control 2824 plusmn 379 119901 = 044)These significant differences between the two groups justifiedthe adjustment of the kinematic variables to age educationheight and weight (please see below)

22 Kinematic Acquisition and Assessment System Five kine-tic sensing modules harboring 8051 microprocessor embed-ded in CC2530 Texas Instrument SoC (System on Chip)[20] and an inertial measurement unit MPU6000 (triaxialaccelerometer and gyroscope) operating with a sample ratefrequency of 113Hz on SD card were attached to five bodysegments trunk (on the COM located at 55 of a personrsquosheight [21]) both legs (middle of ankle-knee) and boththighs (middle of knee-iliac crest) by Velcro bands One ofthe normal human mechanisms of maintaining balance isto vary the height of the COM Therefore final kinematicinformation derived from the IMU on the COM was con-stantly adjusted to the angle and length of the IMU locatedon the thigh and shank A more detailed description ofour methodology and mathematical formulas for kinematicacquisition procedure can be consulted at [16]

23 Clinical Postural Tasks Subjects were instructed to per-form seven different postural tasks with increasing stabilitystress normal stance standing with the medial aspects of

Computational Intelligence and Neuroscience 3

(a) (b)

Figure 1 Representation of a patient wearing the safety trunk belt with the IMUplaced on the center ofmass (55 height) while performingthe tasks eyes closed with feet together on flat surface (a) and on frontwards platform (b) (other tasks were performed as further detailed onthe Materials and Methodology for Data Collection)

the feet touching each other with eyes open (EO) and eyesclosed (EC) and standing with the medial aspects of the feettouching each other with EO and EC on a ramp with 15degreesrsquo inclination in a backwards position (EOBP ECBP)and frontwards position (EOFP ECFP) [22] A representationof a patient wearing the safety trunk belt with the IMUplaced on the center of mass while performing the tasksmentioned can be seen in Figure 1 Tasks with kinematiccapture were performed for 30 seconds [23] with subjectsstanding quiet their arms hanging at their sides and theirhead in a normal forward-looking position to a visual eyetarget height approximately 2 meters away Balance is acomplex process of coordination of multiple body systemsmdashincluding the vestibular auditory visual motor and higherlevel premotor systemsmdashthat generates appropriate synergicpostural muscle movements of the head eye trunk andlimbs tomaintain posture [24]This is achieved by sustainingachieving or restoring the body COM relative to the baseof support or more generally within the limits of stabilitywithminimal sway [25] Visual suppressionmakes the humanbody more dependent on vestibular and proprioceptivesystems consequently increasing sway [26] On an inclinedor tilting support surface postural control is mainly achievedwith the help of visual vestibular and proprioceptive affer-ents The investigation of postural stability under dynamicconditions either continuous or predictable perturbations ofthe supporting platform has been used to study anticipatoryadjustments and sensory feedback [24]Thiswas the rationalein our study to use different and increasing difficulty posturalstability tasks changing kinematic variables in order toobtain more information for machine-learning analysis anddiscrimination between patients and healthy subjects

24 Kinematic Collected Variables We focused on demo-graphic and biometric data (age weight height and bodymass index) and kinematic parameters (extracted from theIMU placed at the COM) that emerged from a systematicreview as predictors of falls among older people and ADpatients [26ndash30] Kinematic parameters are as follows total

displacement on the transverse plane (cm) maximal dis-placement (cm) with respect to the origin mean distance(cm) with respect to origin on transverse plane dispersionradius (average distances relative to average point) maximaland mean linear velocity (cms) positioning (cm) on 119909-axis(maximal mean and range) and 119910-axis (maximal mean andrange) roll angle (degrees) (maximal minimum and mean)and pitch angle (degrees) (maximal minimum and mean)These 18 kinematic measurements captured on each taskwere further averaged summarizing the patientrsquos behaviorthroughout the seven different postural tasks The overlapbetween the different kinematic postural features between thetwo groups and the different tasks can be seen in Figure 2

25 Feature Extraction and Statistical Significance There isstill little information about the value of each singular kine-matic variable and even less information exists on how thesevariables interact among themselves during postural balanceDuring data collection on the different postural tasks thereis substantial overlap of kinematic information even if weonly consider one particular variable like displacement onthe 119909 and 119910-axis (Figure 2) Therefore the objective of thefeature extraction process is to assess which of the kinematicvariables are statistically significant features that contribute toan accurate classification of AD patients

As in [31] all kinematic variables were adjusted for ageeducation height and weight (as these were found to besignificant factors with a significance value of 005 using theMannndashWhitney U test and Chi-Square test)

119870a = 119870ua minus 119866age (119870sAge minus 119870mAge)minus 119866wght (119870sWght minus 119870mWght)minus 119866hght (119870sHght minus 119870mHght)minus 119866Edu (119870sEdu minus 119870mEdu)

(1)

where 119870a is the adjusted kinematic feature 119870ua is the unad-justed kinematic feature119870sAge 119870sWght 119870sHght and119870sEdu are


8

6

4

2

0

minus2

minus4

minus6

Ydi

stan

ce (c

m)

X distance (cm)86420minus2minus4

ADControls

(a)

8

6

4

2

0

minus2

minus4

minus6

Ydi

stan

ce (c

m)


ADControls

minus8

10

(b)

6

4

2

0

minus2

minus4

minus6

Ydi

stan

ce (c

m)


ADControls

(c)

8

6

4

2

0

minus2

minus4

minus6

Ydi

stan

ce (c

m)


ADControls

(d)


ADControls

8

6

4

2

0

minus2

minus4

minus6

Ydi

stan

ce (c

m)

minus8

minus6

(e)

6

4

2

0

minus2

minus4

minus6

Ydi

stanc

e (cm

)


ADControls

(f)

Figure 2 Representation of the substantial overlap on the different kinematic postural features on an orthogonal projection between thetwo groups and the different tasks (a) EO (b) EOFW (c) EOBW (d) EC (e) ECFW and (f) ECBW with increasing difficulty of posturalstability


Data collection

Kinematic

variables (n = 18)

Adjust for ageheight weight and

education

MoCA

Rank variables using


Select variables by error

incremental analysis

Classify using several

machine-learning classifiers




incremental analysis19 datasets

18 datasetsMannndashWhitney U test

MannndashWhitney U test

Figure 3 Methodological flowchart of the classification approach

the subjectrsquos age weight height and years of education resp-ectively 119870mAge 119870mWght 119870mHght and 119870mEdu are the corre-sponding means for all subjects The gradients 119866age 119866wght119866hght and 119866Edu are the slopes of a region specific regressionline against subject age weight height and education ofall participants This process of adjustment guarantees thatthe regression is not influenced by the classification of eachvariable in particular

Data is then preprocessed by a minndashmax normalizationmethod (see eg [32])

1199091015840 = (119909 minusmin (119892)) lowast (new max (119892) minus new min (119892))(max (119892) minusmin (119892))

+ new min (119892)(2)

and that in our case transformed data into a range of val-ues between minus1 and 1 Thus new max(119892) and new min(119892)were set to 1 and minus1 respectively and max(119892) and min(119892)are the maximum and minimum values of the attributerespectively Afterwards a nonparametric statistical analysis(MannndashWhitney U test) is implemented to determine therank and significance of each variable in the classificationoutcome of the two groups following one branch consideringsolely the 18 kinematic variables and the second branchincluding the MoCA score as to form a 19-variable vector foreach subject

26 Variable Selection Using Error Incremental Analysis Asper [10] the ranking of the statistically significant variablesprovides an insight on the discriminative power of eachvariable for each classifier Selecting the optimal numberof top-ranked variables can be considered a dimensionalityreduction problem which is performed using error incre-mental analysis starting from the top-ranked variable and

incrementally adding the next best ranked variable until allsignificant variables are includedThemethodology followedin this study is presented in Figure 3

3 Machine-Learning Classifiers

The selection of the best classifier for diagnosis is an openproblem In addition the advantage of usingmultiple classifi-cation models over a single model has been suggested [32]Hence we compare four different classifier models SVMMLP RBN and DBN With the purpose of facilitating andstreamlining the work we developed a custom-made soft-ware application on MATLAB (version R2014a) whichimplements an automatic grid-search (ie automatically andsystematically tests different configurations and performanceof the different machine-learning models)

All the experiments were based on a threefold cross vali-dationmeaning that the subjects were divided into three setstraining (50) test (40) and validation (10) [33] To limitthe potential data partitioning error induced by random dataassignment and cross validation the same experiment wasrepeated 50 times and the average performancewas recordedWe opted for an output layer composed of two neuronsone representing AD patients and the other healthycontrolsubjects as thismodel would better replicate clinical practice

31 Support Vector Machines (SVMs) The learning mechan-ism of a SVM considers distinct classes of examples as beingdivided by geometrical surfaces separating hyperplaneswhose optimal behavior is determined by an extension ofthe method of Lagrange multipliers The support vectorclassifier chooses the classifier that separates the classes withmaximal margin [34] Our implementation of SVM followsthe MATLAB Documentation and [35]


We provide a brief description but for more detailedinformation refer to the respective references

Let us assume that the dataset is of the form

119863 = x119896 119900119896119896=119898119896=1 (3)

where x119896 isin R119898 is the 119896th input vector of dimension119898 and 119900119896is the corresponding binary category 119900119896 isin minus1 1

The equation that defines the hyperplane is

⟨V x119896⟩ + 119887 = 0 (4)

where v isin R119898 is the vector normal to the hyperplane ⟨sdot⟩represents the inner product and b a real number is the bias

In order to define the best separating hyperplane oneneeds to find v and 119887 that minimize v subject to

119900119896 (⟨V x119896⟩ + 119887) ge 1 (5)

In order to simplify themath the problem is usually givenas the equivalent of minimizing ⟨V v⟩2

Once the optimal v and 119887 are found one can classify agiven vector z as follows

119910119911 = ⟨V z⟩ + 119887 (6)

where 119910119911 is the binary category in which z is inserted Thisis considered to be the primal form of the classificationproblem

In order to attain the dual form of the classificationproblem one needs to take the Lagrange multipliers 120572119896multiplied by each constraint and subtract from the objectivefunction

119871119901 = 12 ⟨v v⟩ minus 119873sum119896=1

120572119896 (119900119896 (⟨V x119896⟩ + 119887) minus 1) (7)

where119873 is the size of the training dataThe first-order optimal conditions of the primal problem

are obtained by taking partial derivatives of 119871119901 with respectto the primal variables and then setting them to zero

120597119871119901120597v = 0 997888rarr v = 119873sum119896=1

120572119896119900119896x119896 (8)

The dual form of the classification problem is obtained asfollows

119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895 ⟨x119896x119895⟩ (9)

subject to constraints

119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (10)

where 119888 is considered a constraint value that keeps theallowable values of the Lagrangemultipliers 120572119896 in a boundedregion

Some classification problems cannot be solved with thelinear methods explained above because they do not havea simple hyperplane as a separating criterion For thoseproblems one needs to use a nonlinear transformation andthat is achievable through the use of kernels [34]

Assuming119865 is a high-dimensional feature space and120593 is afunction that maps x119896 to 119865 the kernel has the following form

119870(x119896x119895) = ⟨120593 (x119896) 120593 (x119895)⟩ (11)

In our implementation we used the Gaussian kernelfunction defined as follows

119870(x119896x119895) = ⟨120593 (x119896) 120593 (x119895)⟩ = 119890minus⟨(x119896minusx119895)(x119896minusx119895)⟩21205902 (12)

where 120590 is a positive numberApplying the kernel to the dual form of the classification

problem one obtains

119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895119870(x119896x119895) (13)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (14)

32 Multiple Layer Perceptrons (MLPs) We have previouslydetailed our MLP model [36] where computation of theoutput of neuron 119910119895 was based on the following

119910119895 = 119892( 119873sum119894=0

119908(119897)119895119894 (119899) 119910(119897minus1)119894 (119899)) 119892 (V119895) = 11 + 119890minusV119895

(15)

where 119910(119897minus1)119894 (119899) is the output of neuron 119894 in the previous layer119897 minus1 at iteration 119899 and119908(119897)119895119894 is the synaptic weight from neuron119894 in layer 119897 minus 1 to neuron 119895 in layer 119897 The synaptic weight119908(119897)1198950 equals the bias 119887119895 applied to neuron 119895 [34] We used asigmoidal logistic activation function 119892(V119895) to represent thenonlinear behavior between the inputs and outputs where V119895is the net internal activity level of neuron 119895 (ie the weightedsum of all synaptic inputs plus bias)

We used MLP backpropagation (MLP-BP) and MLPScaled Conjugate Gradient (MLP-SCG) training algorithms[35] Our custom-made software application automaticallycreated trained and tested different configurations of MLPsaccording to number of hidden layers and number of neuronsin each hidden layer and best performance The applicationbegins testing the ANN with the minimum number ofneurons chosen for the first hidden layer (1st hidden layer)incrementing until it reaches the maximum number ofneurons (100) When this happens a second hidden layer(2nd hidden layer) is included first with one neuron and afirst hidden layer is set to its initial setup incrementing once


again till best performance is rendered This autonomousprocess is cyclically repeated with a hypothetical maximumnumber of neurons of 100 on 1st hidden layer and 100 on2nd hidden layer On each training cycle the performance ofeach neural network is evaluated and storedThe autonomouscreation of networks MLP-BP or MLP-SCG was tried withdifferent error functions (Mean Absolute Error (MAE)MeanSquared Error (MSE) Sum Absolute Error (SAE) and Sum-Squared Error (SSE)) until best performance was reachedIn the training process the best performance is measuredby two parameters that control the terminus of the trainingthe number of error checks and the error gradient The latteris associated with the training performance the lower itsvalue the better the training performance and the first isincremented each time the error value in the validation setrises These parameters were defined through an initial testwith a limited number of neurons in each layer where theperformance was evaluated with different gradient and errorcheck values

33 Radial Basis Function Neural Networks (RBNs) RBNsare a subtype of an artificial neural network that uses radialbasis functions as activation functions [37] They consist ofthree layers an input layer a hidden radial basis neuronlayer and a linear neuron output layer The output unitsimplement a weighted sum of hidden-unit outputs In RBNsthe transformation from the input space to the hidden-unit space is nonlinear whereas the transformation from thehidden-unit space to the output space is linearWhen an inputvector x is presented to such a network each neuronrsquos outputin the hidden layer is defined by

120593119894 (x) = 119890minusxminusc119894221205902119894 (16)

where c119894 = [1198881198941 1198881198942 119888119894119898] 119879 isin R119898 is the center vector ofneuron 119894 and 120590119894 is the width of the 119894th node The response ofeach neuron in the output layer is computed according to

119910119895 = 119873sum119894=1

119908119894119895120593119894 (x) + 119887119895 with 119895 = 1 2 (17)

where 119908119894119895 represents the synaptic weight between neuron 119894in the hidden layer and neuron 119895 in the output layer and 119887119895represents the bias applied to the output neuron 119895 For moredetails refer to the relevant MATLAB Documentation

In the training process in each iteration two parameterswere changed the Sum-Squared Error goal and the spreadvalue (or neuron radius) until a designated maximum valueis achieved (the error goal from 1119890minus8 to 1 and the spread valuefrom 001 to 10)

34 Deep Belief Networks (DBNs) A DBN is a generativegraphical model with many layers of hidden causal variablesalong with a greedy layer-wise unsupervised learning algo-rithm These networks are built in two separate stages Inthe first stage the DBN is formed by a number of layers ofRestricted Boltzmann Machines (RBMs) which are trainedin a greedy layer-wise fashion In order to use the DBN

for classification the second stage uses the synaptic weightsobtained in the RBM stage to train the whole model in asupervised way as a feed-forward-backpropagation neuralnetwork For the implementation of DBNs we used a MAT-LAB Toolbox developed by Palm [38]

RBMs have binary-valued hidden and visible units If onedefines the visible input layer as x the hidden layer as hand weights between them as W the model that defines theprobability distribution according to [39] is

119875 (x h) = 119890minus119864(xh)119885 (x h) (18)

where 119885(x h) is a partition function given by summing overall possible pairs of visible and hidden vectors

119885 (x h) = sumxh119890minus119864(xh) (19)

119864(x h) is the energy function analogous to the one usedon a Hopfield network [40] defined as

119864 (x h) = minus sum119894isinvisible

119887(1)119894 119909119894 minus sum119895isinhidden

119887(2)119895 ℎ119895 minussum119894119895

119909119894ℎ119895119908119894119895 (20)

where 119909119894 and ℎ119895 are the binary states of visible unit 119894 andhidden unit 119895 and 119887(1)119894 and 119887(2)119895 are the bias values of the visibleand hidden layer units respectively

Taking into account (18) and given that there are no directconnections between hidden units in a RBM the probabilityof a single neuron state in the hidden layer ℎ119895 to be set to onegiven the visible vector x can be defined as

119875 (ℎ119895 = 1 | x) = 11 + 119890minus(119887(2)119895 +sum119894 119909119894119908119894119895) (21)

In the same way one can infer the probability of a singleneuron 119909119894 in the visible layer binary state being set to onegiven the hidden vector h

119875 (119909119894 = 1 | h) = 11 + 119890minus(119887(1)119894 +sum119895 119909119895119908119894119895) (22)

In the training process the goal is to maximize the logprobability of the training data or minimize the negative logprobability of the training data

Palmrsquos algorithm [38] instead of initializing the modelat some arbitrary state and iterating it 119899 times initializes itwith contrastive divergence algorithm introduced in [39] Forcomputational efficiency reasons this training algorithmusesstochastic gradient descent instead of a batch update ruleTheRestricted Boltzmann Machines (RBM) learning algorithmas defined in [38] can be seen as follows (see [39])

for all training samples as 119905 do119909(0) larr 119905ℎ(0) larr sigm(119909(0)119882+ 119888) gt rand()119909(1) larr sigm(ℎ(0)119882+ 119861) gt rand()


ℎ(1) larr sigm(119909(1)119882+ 119888) gt rand()119882 larr 119882 + 120572 sigm(119909(0)ℎ(0) minus 119909(1)ℎ(1))119887 larr 119887 + 120572(119909(0) minus 119909(1))119888 larr 119888 + 120572(ℎ(0) minus ℎ(1))end for

where 120572 is a learning rate and rand() produces randomuniform numbers between 0 and 1

Our algorithm which uses the implementation abovetrains several DBNs consecutively varying the number ofhidden neurons of the RBM and of the feed-forward neuralnetwork to a maximum of 100 hidden neurons in each of thetwo layers Each RBM is trained in a layer-wise greedy man-ner with a learning rate of 1 for the duration of 100 epochsAfter this training the synapticweights are subsequently usedto initialize and train a backpropagation feed-forward neuralnetwork with optimal tangency activation function (11) forthe hidden layers and sigmoid logistic activation function (12)for the output layer

119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)

where V119894 in (23) is the weighted sum of all synaptic inputsof neuron 119894 plus its bias and V119895 is the weighted sum of allsynaptic inputs of the output neuron 119895 plus its bias In eachtraining cycle the performance of each network is evaluatedand stored

35 Quantitative Measurements for Performance EvaluationTo evaluate the performance of the different classifiers wecalculated accuracy sensitivity and specificity A true positive(TP) was considered when the classifier output agreed withthe clinical diagnosis of AD A true negative (TN) wasconsidered when the classifier output correctly excludedAD Meanwhile a false positive (FP) indicated that theclassifier output incorrectly classified a healthy person withADThe last case was a false negative (FN) when the classifieroutput missed AD and incorrectly classified an AD patientas a healthy person Classification accuracy is calculated asfollows

Accuracy = TP + TNTCT

(25)

where TCT (= TP + TN + FP + FN) is the total number ofclassification tests

Sensitivity (true positive rate) and specificity (true nega-tive rate) are calculated as follows

Sensitivity = TPTP + FN

Specificity = TN

TN + FP

(26)

4 Results

In this work classifiersrsquo performance is evaluated using thequantitative measures presented in Section 35

Table 1 Ranking of the 19 variables in the input vector Alzheimerrsquosdisease versus controls groups

Variable RankMoCA 1Distance covered 2Y range 3X range 4Maximum distance 5Y maximum 6Maximum Pitch 7Mean distance 8Y mean 9X maximum 10Radius of dispersion 11Mean velocity 12X mean 13Maximum Roll 14Mean pitch angle 15Maximum velocity 16Mean roll angle 17Minimum Roll 18Minimum Pitch 19

41 Rank of Variables Based on the methodology describedin Section 26 variables found with significance level below005 are ranked as shown in Table 1 In this step only thetraining data was used to assert the statistical significance ofeach feature A box-plot is presented in Figure 4 in order toshow that even when data was normalized and adjusted forbiometric data with the exception of MoCA score there issubstantial overlap This highlights the challenge for diseaseclassification based onmachine learning In order to evaluatethe rank reliability of the features which might be dependenton the dataset size a test was conducted by randomlyreducing the dataset to 80 and 50 of its original sizeThe rank of variables was then conducted in 100 randomrepetitions and the ranks were summed and averaged to getthe rank expectationThe final rank was calculated by sortingthe rank expectation of all features from low to high andthe top three variables were recorded and shown in Table 2demonstrating that the rank does not change even whenthe dataset size is reduced 80 and 50 This is a goodindication that the set of variables found and used in thisstudy is reliable reproducible and statistically meaningfuleven under a smaller subset of the data

42 Error Incremental Analysis Results The objective of theincremental error analysis is to determine the number oftop-ranked variables one should use in order to produce thebest classification results As in [10] the classification of ADwas performed starting from the top-ranked variable andincrementally adding the next best ranked variable until allsignificant variables were included The results are depictedin Figure 5 In this step the test dataset was used to estimatethe accuracy values As one can observe all the classifiers


50

40

30

20

10

0

Controls AD Controls AD

10

05

00

minus05

minus10

MoCADistance covered

Raw data Normalized and adjusted data

∘56

∘56

∘26

∘62

∘42

∘46

∘46∘

62

y-axis range

Figure 4 Box-plot representation of raw versus adjusted and normalized data of MoCA total distance covered and range of sway on 119910-axisin controls and Alzheimerrsquos disease (AD) groups There were significant differences between the two groups in raw data (MoCA 119901 lt 0001distance covered 119901 lt 0001 119910-axis range 119901 = 0022) and after data was adjusted for age education height and weight followed by anormalization process (MoCA 119901 lt 0001 distance covered 119901 = 0002 119910-axis range 119901 = 005) Despite these statistical differences especiallyin unadjusted raw data it is important to note the significant overlap between the different individuals in the kinematic postural variableshighlighting the challenge of classification based on machine learning

Table 2 Summary of top-ranked variables with varying dataset size

Dataset size Rank of variables

100MoCA

Distance coveredY range

80MoCA


50MoCA


benefited from the addition of kinematic variables having in-creasingly higher accuracy values until the maximum accu-racy values were achieved These values are displayed inTable 3 Figures 6 and 7 allow inferring that AD and CNgroups are generally separable as they tend to form two dis-tinct clusters

43 General Classification Performance Overall MLP ach-ieved the highest scores with accuracy ranging from 861without MoCA to 966 when kinematic postural variableswere combined with MoCA When trained with datasetscombining the MoCA variable and kinematic variablesall machine-learning models showed a good classificationperformance with superiority for MLP (achieving accuracyof 966) followed by DBN (accuracy of 965) RBN(accuracy of 925) and SVM classifiers (accuracy of 91)MLP also achieved higher sensitivity which is also beneficialreducing the cost ofmisdiagnosing anADpatient as a healthysubject [41 42] MLP was also less susceptible to the differenttraining iterations presenting lower standard deviation when

compared to the other classifiers Withdrawing the MoCAvariable the machine-learning classifiers also displayed areasonably good accuracy with results above 71 with MLPachieving an 861 of accuracy rating These results werefollowed by the DBN classifier with 78 accuracy rating theRBN model with 74 accuracy and lastly the SVM modelachieving 717 accuracy rating

5 Discussion

Postural control and sensory organization are known to becritical for moving safely and adapting to the environmentThe investigation of postural stability under dynamic con-ditions either continuous or on predictable perturbationsof the supporting platform has been used to study thecomplexity of balance process which coordinates visualvestibular proprioceptive auditory andmotor systems infor-mation [24 27] Visual suppression makes the human bodymore dependent on vestibular and proprioceptive systemsconsequently increasing postural sway [27 Moreover thereis growing evidence that executive function and attentionhave an important role in the control of balance duringstanding and walking as other higher cognitive processingshares brain resources with postural control [43] Therebyindividuals who have limited cognitive processing due toneurological impairments such as in AD when using moreof their available cognitive resources on postural control mayinadvertently increase their susceptibility to falls [44]

Having the above in context it is not surprising thathundreds of kinematic parameters can be extracted from theIMU and each parameter can individually or in correlationrepresent postural body sway While the discriminatory roleof each kinematic postural variable per se is not clear therationale in our study was to use different and increasing


Number of top-ranked variables included191715131197531

100

95

90

85

80

75

70

65

60

Accu

racy

()

(a)

100

95

90

85

80

75

70

65

Accu

racy

()


(b)


100

95

90

85

80

75

70

65

60

Accu

racy

()

(c)

100

95

90

85

80

75

70

65

60

Accu

racy

()


(d)

Figure 5 Incremental error analysis performance of accuracy with standard deviation indicated as error bar for SVM (a) MLP-BP (b) RBN(c) and DBN (d) The orange curve represents the datasets with the MoCA variable and the blue curve the datasets with only kinematicvariables

difficulty balance tasks (manipulating vision and inclination)so as to increase discriminative kinematic information

In our studywehave shown that there is high intercorrela-tion between the different proposed kinematic variables andeven when data was normalized and adjusted for biometriccharacteristics there is substantial overlap between healthysubjects andADpatients (Figures 2 and 4) which highlightedthe challenge and added value on using machine-learningclassifiers As the problem being handled in this study is aclassification problem three important questions have arisenthe sample size the number of variables per patient andwhich variables compose the ideal dataset that yields the bestaccuracy A small size sample has been proved to limit theperformance ofmachine-learning accuracy [45 46] Also toomany variables relative to the number of patients potentiallyleads to overfitting a consequence of the classifier learningwith the data instead of learning the trend that underliesthe data [47] As a rule of thumb more than 10 ldquoeventsrdquoare needed for each attribute to result in a classifier withreasonable predictive value [48] Ideally similar numbersof ldquohealthyrdquo and ldquounhealthyrdquo subjects would be used in atraining set resulting in a training set that is more than 20times the number of attributes Since most medical studiestypically involve a small number of subjects and there areessentially unlimited numbers of parameters that can beused the possibility of overfitting has to be acquainted [49]On one neuroimaging study with a relatively small sample14 AD patients versus 20 healthy subjects SVM reached adiscriminating power of 882 [50] In another study a com-bined approach of a genetic algorithmwithANNonEEG and

neuropsychological examination of 43 AD patients versus 5healthy subjects returned an accuracy of 85 [51]

Feature reduction can be a viable solution to tackle thisproblem Besides speeding up the process of classification italso reduces the required sizes of the training sets thereforeavoiding overfitting Moreover it is a way to avoid the so-called curse of dimensionality which is the difficulty forthe classifiers to learn effective models in spaces of high-dimensionality (many features) when the number of samplesis limitedHigh dimensionality leads to overparameterization(the complexity is too high to identify all the coefficientsof the model) or to poor performance of the classifiers[52] Feature reduction can be accomplished by combininglinear with nonlinear statistical analyses andor by reducingthe number of attributes In this regard it may contributeto simplifying the medical interpretation of the machine-learning process by directing attention to practical clinicallyrelevant attributes However choosing attributes in this ret-rospective manner introduces a post hoc subjective elementinto analyses [53] Previous works have shown that featurereductionselection methods have a positive effect on theclassifiersrsquo performance [10 54ndash57]

Using the error incremental analysis method one wasable to determine the optimal decisional space in which theclassification of AD versus controls is carried out By testingthe variablersquos ranks with reduced datasets (80 and 50) oneverified that the rank of the top variables did not changeindicating that the combination of features suggested in thisstudy is reliable and statistically relevant As also indicatedin [10] it can be argued that incremental error analysis does


Table 3 Best results obtained with each classifier trained with datasets with and without the MoCA variable Between parentheses are theminimum and maximum values obtained All results are in percentage

Accuracy Sensitivity Specificity Best decisional spaceSVM with MoCA 91 (75ndash964) 893 (643ndash100) 927 (714ndash100) Top 10 featuresSVM without MoCA 717 (536ndash929) 65 (357ndash929) 784 (357ndash100)MLP with MoCA 966 (965ndash100) 100 (100ndash100) 949 (947ndash100) Top 11 features and top 15

featuresMLP without MoCA 861 (793ndash862) 785 (778ndash786) 931 (818ndash933)RBN with MoCA 925 (75ndash100) 904 (714ndash100) 945 (786ndash100) Top 15 featuresRBN without MoCA 740 (536ndash821) 713 (50ndash100) 767 (429ndash100)DBN with MoCA 965 (893ndash100) 953 (857ndash100) 977 (857ndash100) Top 15 featuresDBN without MoCA 780 (571ndash929) 79 (143ndash100) 77 (214ndash100)

not cover all the possible combinations of features Assessingall the combinations of variables besides being exhaustingand extremely time-consuming is unnecessary due to theranking of variables done in the beginning of the study

Several biomarkers such as demographic neuropsycho-logical assessment MRI imaging and genetic and fluidbiomarkers have been used in the diagnosis of AD [58]Even though neuroimaging biomarkers such as normalizedhippocampus volume have reachedhigh accuracy rates in thediagnosis of AD they are a structural anatomical evaluationof the brain and not its function Patients with highercognitive reserve due to education and occupational attain-ment can compensate their deficits and be more resilientto structural pathological brain changes [59] As such neu-ropsychological test a functional cognitive assessment canoutperform MRI imaging in the diagnosis of AD or evenin the differential diagnosis with other dementias [60] Inour study in general all classifiersmdashSVM MLP RBN andDBNmdashhave presented very satisfying results MLP classifiermodel had the highest performances being more consistentbetween the different training iterations As expected addingMoCA scores yielded higher accuracy rates with above 90accuracy rates for all classifiers As the diagnosis of AD issupported on cognitive evaluation including theMoCA eval-uation score into the dimensional space has to be consideredwith caution as it can result in biased accuracy estimatesNevertheless relying solely on kinematic data we achievedperformance rates ranging from 717 to 861 Interestinglyour results are in contrast to other studies where the combi-nation of biomarkers MRI imaging and neuropsychologicalassessment had a detrimental effect of classification accuracyrates probably as a consequence of redundancy betweenthese variables that represent the same dysfunction [60] Eventhough further studies are needed to elucidate the correlationbetween postural control and cognition we have shownthat the combination of neuropsychological assessment andpostural control analysis are complementary in the diagnosisof AD Our results are consistent with other studies whereperformances within 88 [6 61] and 92 [12] were achievedusing neural networks DBNs have also displayed very goodperformances which are compatible to the performancerecords of classifying AD based on neuroimaging data [1441 62] SVM is considered useful for handling high-dimen-

sional data [53] as it efficiently deals with a very large numberof features due to the exploitation of kernel functions Thisis particularly useful in applications where the number ofattributes is much larger than the number of training objects[63] However we did not find SVM to be the superiorclassifier A drawback of SVM is that the problem complexityis not of the order of the dimension of the samples but of theorder of the samples

6 Conclusion

Our work shows that postural kinematic analysis has thepotential to be used as complementary biomarker in thediagnosis of ADMachine-learning classification systems canbe a helpful tool for the diagnosis of AD based on posturalkinematics age height weight education and MoCA Wehave shown that MLPs followed by DBN RBN and SVMare useful statistical tools for pattern recognition on clinicaldata and neuropsychological and kinematic postural evalua-tion Specifically in the datasets relying solely on kinematicpostural data (i) MLP achieved a diagnostic accuracy of 86(sensitivity 79 specificity 93) (ii) DBN achieved a diag-nostic accuracy of 78 (sensitivity 79 specificity 77)(iii) RBN achieved a diagnostic accuracy of 74 (sensitivity713 specificity 767) and finally (iv) SVM achieved adiagnostic accuracy of 717 (sensitivity 65 specificity784)

These results are competitive in comparison to resultsreported in other recent studies that make use of other typesof data such as MRI PET EEG and other biomarkers (see[10] for a list of performances) These results are also com-petitive when compared to [10] which also used a neuropsy-chological variable (minimental state examination) (MMSE)in combination with MRI obtaining results of 782 and924 accuracy when the SVM is trained with datasetswithout and with the MMSE variable respectively Crossinga statistical model (nonparametric MannndashWhitneyU test) toreduce the number of input variables with machine-learningmodels has proved to be an advantageous preprocessing toolto a certain extent This is corroborated by observing that thebest results were obtained by the classifiers when trained withreduced datasets


60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040

403020100minus10minus20

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040


60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040


60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040


ADCNMisclassified as ADMisclassified as CN




SVM MLP

RBN DBN

Figure 6 Four specific cases displaying the distribution of the subject population of the testing sets of Support Vector Machines (SVMs)Multiple Layer Perceptrons (MLPs) Radial Basis Function Neural Networks (RBNs) and Deep Belief Networks (DBNs) in the context of thetop three features This is a typical case of classification approach for Alzheimerrsquos disease (AD) versus controls (CN)

Future perspectives of our work are to collect a largerdataset of AD patients and healthy subjects so as to bettercomprehend the discriminatory role of each kinematic pos-tural variable per se as well as its interdynamic interaction inthe process of maintaining balance within the limits of stabil-ity Other future step would be to evolve from a nonstatic toa dynamic paradigm that is to say simultaneously studyingthe constant dynamics of postural control and cognition

(eg attention) on nonstationary increasingly difficult levelsof balance and cognition tasks

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


60

70

60

50

50

6050

40

30

20

10

0

Dist

ance

cove

red 60

70

80

90

50

40

30

20

10

0

Dist

ance

cove

red

X range

X range

Y rangeminus20minus100

1020

3040


6050

Y range403020100minus10minus20minus30

SVM

minus30minus20

minus10

minus10

010

2030

4050

60



MLP

60

70

60

50

50

6050

40

30

20

10

0

Dist

ance

cove

red

X rangeY rangeminus20

minus100

1020

3040




RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040


Figure 7 One specific case displaying the distribution of the same subject population of the testing of Support Vector Machines (SVMs)Multiple Layer Perceptrons (MLPs) Radial Basis Function Neural Networks (RBNs) and Deep Belief Networks (DBNs) in the context of thetop three features This is a typical case of classification approach for Alzheimerrsquos disease (AD) versus controls (CN)

Acknowledgments

The Algoritmi Center was funded by the FP7 ITN MarieCurie Neural Engineering Transformative Technologies(NETT) project

References

[1] P Kannus H Sievanen M Palvanen T Jarvinen and JParkkari ldquoPrevention of falls and consequent injuries in elderlypeoplerdquoThe Lancet vol 366 no 9500 pp 1885ndash1893 2005

[2] A Etman G J Wijlhuizen M J G van heuvelen A ChorusandM Hopman-Rock ldquoFalls incidence underestimates the riskof fall-related injuries in older age groups a comparison withthe FARE (Falls risk by exposure)rdquo Age and Ageing vol 41 no2 Article ID afr178 pp 190ndash195 2012

[3] A Shumway-Cook and M Woollacott ldquoAttentional demandsand postural control the effect of sensory contextrdquo Journals ofGerontologymdashSeries A Biological Sciences and Medical Sciencesvol 55 no 1 pp M10ndashM16 2000

[4] G Orru W Pettersson-Yeo A F Marquand G Sartori and AMechelli ldquoUsing support vector machine to identify imaging


biomarkers of neurological and psychiatric disease a criticalreviewrdquo Neuroscience and Biobehavioral Reviews vol 36 no 4pp 1140ndash1152 2012

[5] A Subasi and M I Gursoy ldquoEEG signal classification usingPCA ICA LDA and support vector machinesrdquo Expert Systemswith Applications vol 37 no 12 pp 8659ndash8666 2010

[6] C Lehmann T Koenig V Jelic et al ldquoApplication and compar-ison of classification algorithms for recognition of Alzheimerrsquosdisease in electrical brain activity (EEG)rdquo Journal of Neuro-science Methods vol 161 no 2 pp 342ndash350 2007

[7] C Aguilar E Westman J-S Muehlboeck et al ldquoDifferentmultivariate techniques for automated classification of MRIdata in Alzheimerrsquos disease and mild cognitive impairmentrdquoPsychiatry ResearchmdashNeuroimaging vol 212 no 2 pp 89ndash982013

[8] J Guan and W Yang ldquoIndependent component analysis-basedmultimodal classification of Alzheimerrsquos disease versus healthycontrolsrdquo in Proceedings of the 9th International Conference onNatural Computation (ICNC rsquo13) pp 75ndash79 Shenyang ChinaJuly 2013

[9] F Rodrigues and M Silveira ldquoLongitudinal FDG-PET featuresfor the classification of Alzheimers diseaserdquo in Proceedings ofthe Annual International Conference of the IEEE Engineering inMedicine and Biology Society vol 2014 pp 1941ndash1944 August2014

[10] Q Zhou M Goryawala M Cabrerizo et al ldquoAn optimaldecisional space for the classification of alzheimerrsquos disease andmild cognitive impairmentrdquo IEEE Transactions on BiomedicalEngineering vol 61 no 8 pp 2245ndash2253 2014

[11] J Escudero J P Zajicek and E Ifeachor ldquoMachine Learningclassification of MRI features of Alzheimers disease and mildcognitive impairment subjects to reduce the sample size in clin-ical trialsrdquo in Proceedings of the Annual International Conferenceof the IEEE Engineering in Medicine and Biology Society vol2011 pp 7957ndash7960 2011

[12] W S Pritchard D W Duke K L Coburn et al ldquoEEG-basedneural-net predictive classification of Alzheimerrsquos disease ver-sus control subjects is augmented by non-linear EEGmeasuresrdquoElectroencephalography and Clinical Neurophysiology vol 91no 2 pp 118ndash130 1994

[13] S Agarwal P Ghanty and N R Pal ldquoIdentification of a smallset of plasma signalling proteins using neural network forprediction of Alzheimerrsquos diseaserdquo Bioinformatics vol 31 no 15pp 2505ndash2513 2015

[14] H-I Suk S-W Lee and D Shen ldquoHierarchical feature rep-resentation and multimodal fusion with deep learning forADMCI diagnosisrdquo NeuroImage vol 101 pp 569ndash582 2014

[15] S Liu S Liu W Cai et al ldquoMultimodal Neuroimaging FeatureLearning forMulticlass Diagnosis of Alzheimerrsquos Diseaserdquo IEEETransactions on Biomedical Engineering vol 62 no 4 pp 1132ndash1140 2015

[16] M F Gago V Fernandes J Ferreira et al ldquoPostural stabilityanalysis with inertial measurement units in Alzheimerrsquos dis-easerdquo Dementia and Geriatric Cognitive Disorders Extra vol 4no 1 pp 22ndash30 2014

[17] D Lafond H Corriveau R Hebert and F Prince ldquoIntrasessionreliability of center of pressure measures of postural steadinessin healthy elderly peoplerdquo Archives of Physical Medicine andRehabilitation vol 85 no 6 pp 896ndash901 2004

[18] GMMcKhann D S Knopman H Chertkow et al ldquoThe diag-nosis of dementia due toAlzheimerrsquos disease recommendations

from the National Institute on Aging-Alzheimerrsquos Associationworkgroups on diagnostic guidelines for Alzheimerrsquos diseaserdquoAlzheimerrsquos and Dementia vol 7 no 3 pp 263ndash269 2011

[19] S Freitas M R Simoes L Alves and I Santana ldquoMon-treal Cognitive Assessment (MoCA) normative study for thePortuguese populationrdquo Journal of Clinical and ExperimentalNeuropsychology vol 33 no 9 pp 989ndash996 2011

[20] J A Afonso H D Silva P Macedo and L A Rocha ldquoAn en-hanced reservation-based MAC protocol for IEEE 802154networksrdquo Sensors vol 11 no 4 pp 3852ndash3873 2011

[21] D AWinter A E Patla and J S Frank ldquoAssessment of balancecontrol in humansrdquo Medical Progress through Technology vol16 no 1-2 pp 31ndash51 1990

[22] M Piirtola and P Era ldquoForce platform measurements aspredictors of falls among older peoplemdasha reviewrdquo Gerontologyvol 52 no 1 pp 1ndash16 2006

[23] M G Carpenter J S Frank D A Winter and G W PeysarldquoSampling duration effects on centre of pressure summarymeasuresrdquo Gait amp Posture vol 13 no 1 pp 35ndash40 2001

[24] F B Horak S M Henry and A Shumway-Cook ldquoPosturalperturbations new insights for treatment of balance disordersrdquoPhysical Therapy vol 77 no 5 pp 517ndash533 1997

[25] A S Pollock B R Durward P J Rowe and J P Paul ldquoWhatis balancerdquo Clinical Rehabilitation vol 14 no 4 pp 402ndash4062000

[26] M Leandri S Cammisuli S Cammarata et al ldquoBalancefeatures in Alzheimerrsquos disease and amnestic mild cognitiveimpairmentrdquo Journal of Alzheimerrsquos Disease vol 16 no 1 pp113ndash120 2009

[27] A Nardone and M Schieppati ldquoBalance in Parkinsonrsquos diseaseunder static and dynamic conditionsrdquoMovement Disorders vol21 no 9 pp 1515ndash1520 2006

[28] A Merlo D Zemp E Zanda et al ldquoPostural stability andhistory of falls in cognitively able older adults The CantonTicino StudyrdquoGait and Posture vol 36 no 4 pp 662ndash666 2012

[29] Y Maeda T Tanaka Y Nakajima and K Shimizu ldquoAnalysisof postural adjustment responses to perturbation stimulus bysurface tilts in the feet-together positionrdquo Journal ofMedical andBiological Engineering vol 31 no 4 pp 301ndash305 2011

[30] D A Winter Biomechanics and Motor Control of HumanMovement JohnWiley amp Sons Hoboken NJ USA 4th edition2009

[31] C R Jack Jr CK TwomeyA R Zinsmeister FW SharbroughR C Petersen and G D Cascino ldquoAnterior temporal lobes andhippocampal formations normative volumetric measurementsfromMR images in young adultsrdquo Radiology vol 172 no 2 pp549ndash554 1989

[32] J Han M Kamber and J Pei Data Mining Concepts and Tech-niques MorganKaufmann BurlingtonMass USA 3rd edition2011

[33] G J Bowden H R Maier and G C Dandy ldquoOptimaldivision of data for neural network models in water resourcesapplicationsrdquo Water Resources Research vol 38 no 2 pp 2-1ndash2-11 2002

[34] V N Vapnik The Nature of Statistical Learning Theory Sprin-ger-Verlag New York NY USA 1995

[35] N Cristianini and J Shawe-Taylor An Introduction to SupportVector Machines and Other Kernel-Based Learning MethodsCambridge University Press Cambridge UK 2000

[36] J Ferreira M F Gago V Fernandes et al ldquoAnalysis of posturalkinetics data using artificial neural networks in Alzheimerrsquos


diseaserdquo in Proceedings of the 9th IEEE International Symposiumon Medical Measurements and Applications (MeMeA rsquo14) pp 1ndash6 IEEE Lisbon Portugal June 2014

[37] JMoody andC J Darken ldquoFast learning in networks of locally-tuned processing unitsrdquo Neural Computation vol 1 no 2 pp281ndash294 1989

[38] R B Palm Prediction as a candidate for learning deep hierar-chical models of data [MS thesis] DTU Informatics KongensLyngby Technical University of Denmark 2012

[39] G E Hinton S Osindero and Y-W Teh ldquoA fast learning alg-orithm for deep belief netsrdquo Neural Computation vol 18 no 7pp 1527ndash1554 2006

[40] J J Hopfield ldquoNeural networks and physical systemswith emer-gent collective computational abilitiesrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 79 no 8 pp 2554ndash2558 1982

[41] S Liu S Liu W Cai S Pujol R Kikinis and D FengldquoEarly diagnosis of Alzheimerrsquos disease with deep learningrdquoin Proceedings of the in IEEE 11th International Symposium onBiomedical Imaging (ISBI rsquo14) pp 1015ndash1018 Beijing ChinaApril-May 2014

[42] D Zhang YWang L ZhouH Yuan andD Shen ldquoMultimodalclassification of Alzheimerrsquos disease and mild cognitive impair-mentrdquo NeuroImage vol 55 no 3 pp 856ndash867 2011

[43] M Woollacott and A Shumway-Cook ldquoAttention and thecontrol of posture and gait a review of an emerging area ofresearchrdquo Gait amp Posture vol 16 no 1 pp 1ndash14 2002

[44] M F Gago D Yelshyna E Bicho et al ldquoCompensatory posturaladjustments in an oculus virtual reality environment and therisk of falling in Alzheimerrsquos diseaserdquo Dementia and GeriatricCognitive Disorders Extra vol 6 no 2 pp 252ndash267 2016

[45] K Fukunaga and R R Hayes ldquoEffects of sample size in classifierdesignrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 8 pp 873ndash885 1989

[46] S J Raudys and A K Jain ldquoSmall sample size effects in statis-tical pattern recognition recommendations for practitionersrdquoIEEE Transactions on Pattern Analysis andMachine Intelligencevol 13 no 3 pp 252ndash264 1991

[47] G P Zhang ldquoNeural networks for classification a surveyrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 30 no 4 pp 451ndash462 2000

[48] P Peduzzi J Concato E Kemper T R Holford and A R Fein-stem ldquoA simulation study of the number of events per variablein logistic regression analysisrdquo Journal of Clinical Epidemiologyvol 49 no 12 pp 1373ndash1379 1996

[49] K R Foster R Koprowski and J D Skufca ldquoMachine learn-ing medical diagnosis and biomedical engineering researchmdashcommentaryrdquo BioMedical Engineering Online vol 13 no 1article no 94 2014

[50] P POliveira RNitrini G Busatto C Buchpiguel J R Sato andE Amaro ldquoUse of SVM methods with surface-based corticaland volumetric subcortical measurements to detect Alzheimerrsquosdiseaserdquo Journal of Alzheimerrsquos Disease vol 19 no 4 pp 1263ndash1272 2010

[51] F Berte G Lamponi R S Calabro and P Bramanti ldquoElmanneural network for the early identification of cognitive impair-ment in Alzheimerrsquos diseaserdquo Functional Neurology vol 29 no1 pp 57ndash65 2014

[52] L Palmerini L Rocchi S Mellone F Valzania and L ChiarildquoFeature selection for accelerometer-based posture analysis inParkinsons diseaserdquo IEEE Transactions on Information Technol-ogy in Biomedicine vol 15 no 3 pp 481ndash490 2011

[53] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Neural Networks vol 61 pp 85ndash117 2015

[54] MTorabi RDArdekani andE Fatemizadeh ldquoDiscriminationbetween Alzheimerrsquos disease and control group in MR-imagesbased on texture analysis using artificial neural networkrdquo inPro-ceedings of the 2006 International Conference on Biomedical andPharmaceutical Engineering (ICBPErsquo06) pp 79ndash83 December2006

[55] T Howley M G Madden M-L OrsquoConnell and A G RyderldquoThe effect of principal component analysis on machine learn-ing accuracy with high-dimensional spectral datardquo Knowledge-Based Systems vol 19 no 5 pp 363ndash370 2006

[56] M Ahmadlou H Adeli and A Adeli ldquoNew diagnostic EEGmarkers of the Alzheimerrsquos disease using visibility graphrdquoJournal of Neural Transmission vol 117 no 9 pp 1099ndash11092010

[57] S I Pan S Iplikci K Warwick and T Z Aziz ldquoParkinsonrsquosdisease tremor classificationmdasha comparison between SupportVector Machines and neural networksrdquo Expert Systems withApplications vol 39 no 12 pp 10764ndash10771 2012

[58] Y Jin Y Su X Zhou and S Huang ldquoHeterogeneous multi-modal biomarkers analysis for Alzheimerrsquos disease via Bayesiannetworkrdquo EURASIP Journal on Bioinformatics and SystemsBiology vol 12 2016

[59] Y Stern ldquoCognitive reserve in ageing and Alzheimerrsquos diseaserdquoThe Lancet Neurology vol 11 no 11 pp 1006ndash1012 2012

[60] JWang S J RedmondM Bertoux J R Hodges andMHorn-berger ldquoA comparison of magnetic resonance imaging andneuropsychological examination in the diagnostic distinctionof Alzheimerrsquos disease and behavioral variant frontotemporaldementiardquo Frontiers in Aging Neuroscience vol 8 article 1192016

[61] P Anderer B Saletu B Kloppel H V Semlitsch and H Wer-ner ldquoDiscrimination between demented patients and normalsbased on topographic EEG slow wave activity comparisonbetween z statistics discriminant analysis and artificial neuralnetwork classifiersrdquo Electroencephalography and Clinical Neuro-physiology vol 91 no 2 pp 108ndash117 1994

[62] S Liu S Liu W Cai et al ldquoMultimodal neuroimaging featurelearning for multiclass diagnosis of Alzheimerrsquos diseaserdquo IEEETransactions on Biomedical Engineering vol 62 no 4 pp 1132ndash1140 2015

[63] M G Simon RogersA First Course inMachine Learning Chap-man and HallCRC 2011

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Advances in

Computer EngineeringAdvances in



promising results on problems of pattern recognition inneurology and psychiatry diseases [5] including detection ofADbased on electrical brain activity Electroencephalography(EEG) [6] neuroimaging data from Magnetic ResonanceImaging (MRI) and Positron Emission Tomography (PET)brain images [7ndash10] Several works have applied MLPs inthe diagnosis of AD combining different variables suchas demographic neurological and psychiatric evaluationneuropsychological tests and even more complex clinicaldiagnostic tools (eg neuropathology EEG and MRIPETbrain imaging) where hundreds of variables of recordeddata are potentially clinically relevant on one single patient[7 11 12] RBNs have successfully been applied to the dis-crimination of plasma signalling proteins for the predictionof this disease [13] and classification of MRI features ofAD [7] DBNs are a recent machine-learning model thatis exhibiting performance records on classification accuracyalso on medical fields such as AD based on MRIPETneuroimaging data [14 15]

The survey of the above literature shows that the majorityof the studies have relied on neuroimaging data from MRIandor PET images which though widely available arerelatively expensive In contrast inertial measurement units(IMUs) with integrated accelerometers and gyroscopes areinexpensive and small fully portable devices opening a newfield of research on AD In fact IMUs have been used toportrait different postural kinematic profiles inAD includinga higher risk of falling [16] These devices are independent ofinclination in space having proved to be equivalent to forceplatforms in the evaluation of the center ofmass (COM) kine-maticsHowever althoughhundreds of kinematic parametershave been used to represent postural body sway [17] whichparameters provide the most relevant information aboutnormal postural control and which kinematic parametersbetter identify neurodegenerative diseases such asAD are stillyet undetermined We advocate that a complementary toolthat makes use of kinematic postural data for the diagnosis ofAD would be extremely helpful and valuable for clinicians

To the best of our knowledge the use ofmachine-learningclassifiers for the diagnosis of AD based on kinematicpostural sway data has not yet been investigated With thisin mind our study has two main goals First to validate thefeasibility of the application of machine-learning models inthe diagnosis of AD based on postural kinematic data col-lected on different and increasingly difficult postural balancetasks Second to compare different classifier modelsmdashSVMMLP RBN and DBNmdashwith respect to their discriminativeperformance

The remainder of the paper is structured as follows InSection 2 we explain the materials and methodology usedfor collecting the data feature reduction and implementationof the three dataset models subsequently used for trainingtesting and comparing the different classifiers models Sec-tion 3 gives a brief description on how we implemented theclassifiersrsquo models Section 4 presents results of performancefor the different classifiers in the different dataset models InSection 5 a detailed discussion ismade such that in Section 6some conclusions can be drawn about the potential use of the

tested classifiers in future automatic diagnostic tools for ADbased on kinematic postural sway data

2 Materials and Methodologyfor Data Collection

21 Study Population The study population was recruitedfrom our hospital outpatient neurology department Patientswith probable AD according to Diagnostic and StatisticalManual of Mental Disorders- IV (DSM-IV) and NationalInstitute of Neurological and Communicative Disorders andStrokeAlzheimerrsquos Disease and Related Disorders Associa-tion (NINCDSADRDA) criteria [18] on a stage of 1 on theClinical Dementia Rating Scale were consecutively recruitedfor the study The control group included age-matched care-givers of patients that had no history of falls or of neurologicalor psychiatric disease Patients or controls were excluded ifthere was a history of orthopedic musculoskeletal vestibulardisorder or alcohol abuse Demographic anthropometricand MoCA data normalized to the Portuguese population[19] were collected in both groups Local hospital ethicscommittee approved the protocol of the study submitted byICVSUM and Center AlgoritmiUM Written consent wasobtained from all subjects or their guardians

We included 36 AD patients (24 females12 males witha mean age of 76 plusmn 7 years) and 36 healthy controls (15females21 males with a mean age of 70plusmn8 years) (AD versusC119901 = 0003) Concerning demographic and anthropometricdata the two groups displayed the following education (AD1 plusmn 058 control 2 plusmn 119 119901 = 0008) MoCA (AD 11 plusmn 510control 25 plusmn 387 119901 lt 0001) weight (kg) (AD 6560 plusmn1028 control 7524 plusmn 1211 119901 = 0001) height (m) (AD154plusmn008 control 163plusmn0106 119901 lt 0001) bodymass index(kgm2) (AD 2758 plusmn 412 control 2824 plusmn 379 119901 = 044)These significant differences between the two groups justifiedthe adjustment of the kinematic variables to age educationheight and weight (please see below)

22 Kinematic Acquisition and Assessment System Five kine-tic sensing modules harboring 8051 microprocessor embed-ded in CC2530 Texas Instrument SoC (System on Chip)[20] and an inertial measurement unit MPU6000 (triaxialaccelerometer and gyroscope) operating with a sample ratefrequency of 113Hz on SD card were attached to five bodysegments trunk (on the COM located at 55 of a personrsquosheight [21]) both legs (middle of ankle-knee) and boththighs (middle of knee-iliac crest) by Velcro bands One ofthe normal human mechanisms of maintaining balance isto vary the height of the COM Therefore final kinematicinformation derived from the IMU on the COM was con-stantly adjusted to the angle and length of the IMU locatedon the thigh and shank A more detailed description ofour methodology and mathematical formulas for kinematicacquisition procedure can be consulted at [16]

23 Clinical Postural Tasks Subjects were instructed to per-form seven different postural tasks with increasing stabilitystress normal stance standing with the medial aspects of


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Data collection

Kinematic

variables (n = 18)


education

MoCA

















+ new min (119892)(2)











119863 = x119896 119900119896119896=119898119896=1 (3)



⟨V x119896⟩ + 119887 = 0 (4)



119900119896 (⟨V x119896⟩ + 119887) ge 1 (5)



119910119911 = ⟨V z⟩ + 119887 (6)



119871119901 = 12 ⟨v v⟩ minus 119873sum119896=1

120572119896 (119900119896 (⟨V x119896⟩ + 119887) minus 1) (7)



120597119871119901120597v = 0 997888rarr v = 119873sum119896=1

120572119896119900119896x119896 (8)


119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895 ⟨x119896x119895⟩ (9)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (10)




119870(x119896x119895) = ⟨120593 (x119896) 120593 (x119895)⟩ (11)




problem one obtains

119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895119870(x119896x119895) (13)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (14)


119910119895 = 119892( 119873sum119894=0

119908(119897)119895119894 (119899) 119910(119897minus1)119894 (119899)) 119892 (V119895) = 11 + 119890minusV119895

(15)






120593119894 (x) = 119890minusxminusc119894221205902119894 (16)


119910119895 = 119873sum119894=1

119908119894119895120593119894 (x) + 119887119895 with 119895 = 1 2 (17)






119875 (x h) = 119890minus119864(xh)119885 (x h) (18)


119885 (x h) = sumxh119890minus119864(xh) (19)




119887(2)119895 ℎ119895 minussum119894119895

119909119894ℎ119895119908119894119895 (20)



119875 (ℎ119895 = 1 | x) = 11 + 119890minus(119887(2)119895 +sum119894 119909119894119908119894119895) (21)


119875 (119909119894 = 1 | h) = 11 + 119890minus(119887(1)119894 +sum119895 119909119895119908119894119895) (22)








119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)




(25)




Specificity = TN

TN + FP

(26)

4 Results







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5 Discussion





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6 Conclusion




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SVM MLP

RBN DBN




Competing Interests



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Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




(a) (b)








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stanc

e (cm

)


ADControls

(f)



Data collection

Kinematic

variables (n = 18)


education

MoCA

















+ new min (119892)(2)











119863 = x119896 119900119896119896=119898119896=1 (3)



⟨V x119896⟩ + 119887 = 0 (4)



119900119896 (⟨V x119896⟩ + 119887) ge 1 (5)



119910119911 = ⟨V z⟩ + 119887 (6)



119871119901 = 12 ⟨v v⟩ minus 119873sum119896=1

120572119896 (119900119896 (⟨V x119896⟩ + 119887) minus 1) (7)



120597119871119901120597v = 0 997888rarr v = 119873sum119896=1

120572119896119900119896x119896 (8)


119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895 ⟨x119896x119895⟩ (9)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (10)




119870(x119896x119895) = ⟨120593 (x119896) 120593 (x119895)⟩ (11)




problem one obtains

119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895119870(x119896x119895) (13)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (14)


119910119895 = 119892( 119873sum119894=0

119908(119897)119895119894 (119899) 119910(119897minus1)119894 (119899)) 119892 (V119895) = 11 + 119890minusV119895

(15)






120593119894 (x) = 119890minusxminusc119894221205902119894 (16)


119910119895 = 119873sum119894=1

119908119894119895120593119894 (x) + 119887119895 with 119895 = 1 2 (17)






119875 (x h) = 119890minus119864(xh)119885 (x h) (18)


119885 (x h) = sumxh119890minus119864(xh) (19)




119887(2)119895 ℎ119895 minussum119894119895

119909119894ℎ119895119908119894119895 (20)



119875 (ℎ119895 = 1 | x) = 11 + 119890minus(119887(2)119895 +sum119894 119909119894119908119894119895) (21)


119875 (119909119894 = 1 | h) = 11 + 119890minus(119887(1)119894 +sum119895 119909119895119908119894119895) (22)








119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)




(25)




Specificity = TN

TN + FP

(26)

4 Results







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6 Conclusion




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Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




8

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stanc

e (cm

)


ADControls

(f)



Data collection

Kinematic

variables (n = 18)


education

MoCA

















+ new min (119892)(2)











119863 = x119896 119900119896119896=119898119896=1 (3)



⟨V x119896⟩ + 119887 = 0 (4)



119900119896 (⟨V x119896⟩ + 119887) ge 1 (5)



119910119911 = ⟨V z⟩ + 119887 (6)



119871119901 = 12 ⟨v v⟩ minus 119873sum119896=1

120572119896 (119900119896 (⟨V x119896⟩ + 119887) minus 1) (7)



120597119871119901120597v = 0 997888rarr v = 119873sum119896=1

120572119896119900119896x119896 (8)


119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895 ⟨x119896x119895⟩ (9)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (10)




119870(x119896x119895) = ⟨120593 (x119896) 120593 (x119895)⟩ (11)




problem one obtains

119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895119870(x119896x119895) (13)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (14)


119910119895 = 119892( 119873sum119894=0

119908(119897)119895119894 (119899) 119910(119897minus1)119894 (119899)) 119892 (V119895) = 11 + 119890minusV119895

(15)






120593119894 (x) = 119890minusxminusc119894221205902119894 (16)


119910119895 = 119873sum119894=1

119908119894119895120593119894 (x) + 119887119895 with 119895 = 1 2 (17)






119875 (x h) = 119890minus119864(xh)119885 (x h) (18)


119885 (x h) = sumxh119890minus119864(xh) (19)




119887(2)119895 ℎ119895 minussum119894119895

119909119894ℎ119895119908119894119895 (20)



119875 (ℎ119895 = 1 | x) = 11 + 119890minus(119887(2)119895 +sum119894 119909119894119908119894119895) (21)


119875 (119909119894 = 1 | h) = 11 + 119890minus(119887(1)119894 +sum119895 119909119895119908119894119895) (22)








119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)




(25)




Specificity = TN

TN + FP

(26)

4 Results







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5 Discussion





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6 Conclusion




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SVM MLP

RBN DBN




Competing Interests



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Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Data collection

Kinematic

variables (n = 18)


education

MoCA

















+ new min (119892)(2)











119863 = x119896 119900119896119896=119898119896=1 (3)



⟨V x119896⟩ + 119887 = 0 (4)



119900119896 (⟨V x119896⟩ + 119887) ge 1 (5)



119910119911 = ⟨V z⟩ + 119887 (6)



119871119901 = 12 ⟨v v⟩ minus 119873sum119896=1

120572119896 (119900119896 (⟨V x119896⟩ + 119887) minus 1) (7)



120597119871119901120597v = 0 997888rarr v = 119873sum119896=1

120572119896119900119896x119896 (8)


119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895 ⟨x119896x119895⟩ (9)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (10)




119870(x119896x119895) = ⟨120593 (x119896) 120593 (x119895)⟩ (11)




problem one obtains

119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895119870(x119896x119895) (13)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (14)


119910119895 = 119892( 119873sum119894=0

119908(119897)119895119894 (119899) 119910(119897minus1)119894 (119899)) 119892 (V119895) = 11 + 119890minusV119895

(15)






120593119894 (x) = 119890minusxminusc119894221205902119894 (16)


119910119895 = 119873sum119894=1

119908119894119895120593119894 (x) + 119887119895 with 119895 = 1 2 (17)






119875 (x h) = 119890minus119864(xh)119885 (x h) (18)


119885 (x h) = sumxh119890minus119864(xh) (19)




119887(2)119895 ℎ119895 minussum119894119895

119909119894ℎ119895119908119894119895 (20)



119875 (ℎ119895 = 1 | x) = 11 + 119890minus(119887(2)119895 +sum119894 119909119894119908119894119895) (21)


119875 (119909119894 = 1 | h) = 11 + 119890minus(119887(1)119894 +sum119895 119909119895119908119894119895) (22)








119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)




(25)




Specificity = TN

TN + FP

(26)

4 Results







50

40

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∘56

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5 Discussion





100

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65

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Accu

racy

()

(a)

100

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Accu

racy

()


(b)


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Accu

racy

()

(c)

100

95

90

85

80

75

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65

60

Accu

racy

()


(d)














6 Conclusion




60

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ance

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60

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Dist

ance

cove

red

X range

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SVM MLP

RBN DBN




Competing Interests



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ance

cove

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70

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90

50

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ance

cove

red

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X range


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minus30minus20

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MLP

60

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50

6050

40

30

20

10

0

Dist

ance

cove

red


minus100

1020

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RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119863 = x119896 119900119896119896=119898119896=1 (3)



⟨V x119896⟩ + 119887 = 0 (4)



119900119896 (⟨V x119896⟩ + 119887) ge 1 (5)



119910119911 = ⟨V z⟩ + 119887 (6)



119871119901 = 12 ⟨v v⟩ minus 119873sum119896=1

120572119896 (119900119896 (⟨V x119896⟩ + 119887) minus 1) (7)



120597119871119901120597v = 0 997888rarr v = 119873sum119896=1

120572119896119900119896x119896 (8)


119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895 ⟨x119896x119895⟩ (9)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (10)




119870(x119896x119895) = ⟨120593 (x119896) 120593 (x119895)⟩ (11)




problem one obtains

119871119863 = 119873sum119896=1

120572119896 minus 12119873sum119896=1

119873sum119895=1

120572119896120572119895119900119896119900119895119870(x119896x119895) (13)


119873sum119895=1

120572119896119900119896 = 0 0 le 120572119896 le 119888 (14)


119910119895 = 119892( 119873sum119894=0

119908(119897)119895119894 (119899) 119910(119897minus1)119894 (119899)) 119892 (V119895) = 11 + 119890minusV119895

(15)






120593119894 (x) = 119890minusxminusc119894221205902119894 (16)


119910119895 = 119873sum119894=1

119908119894119895120593119894 (x) + 119887119895 with 119895 = 1 2 (17)






119875 (x h) = 119890minus119864(xh)119885 (x h) (18)


119885 (x h) = sumxh119890minus119864(xh) (19)




119887(2)119895 ℎ119895 minussum119894119895

119909119894ℎ119895119908119894119895 (20)



119875 (ℎ119895 = 1 | x) = 11 + 119890minus(119887(2)119895 +sum119894 119909119894119908119894119895) (21)


119875 (119909119894 = 1 | h) = 11 + 119890minus(119887(1)119894 +sum119895 119909119895119908119894119895) (22)








119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)




(25)




Specificity = TN

TN + FP

(26)

4 Results







50

40

30

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minus05

minus10



∘56

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5 Discussion





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Accu

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(a)

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Accu

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(b)


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Accu

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()

(c)

100

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Accu

racy

()


(d)














6 Conclusion




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ance

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SVM MLP

RBN DBN




Competing Interests



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ance

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ance

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MLP

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0

Dist

ance

cove

red


minus100

1020

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RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






120593119894 (x) = 119890minusxminusc119894221205902119894 (16)


119910119895 = 119873sum119894=1

119908119894119895120593119894 (x) + 119887119895 with 119895 = 1 2 (17)






119875 (x h) = 119890minus119864(xh)119885 (x h) (18)


119885 (x h) = sumxh119890minus119864(xh) (19)




119887(2)119895 ℎ119895 minussum119894119895

119909119894ℎ119895119908119894119895 (20)



119875 (ℎ119895 = 1 | x) = 11 + 119890minus(119887(2)119895 +sum119894 119909119894119908119894119895) (21)


119875 (119909119894 = 1 | h) = 11 + 119890minus(119887(1)119894 +sum119895 119909119895119908119894119895) (22)








119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)




(25)




Specificity = TN

TN + FP

(26)

4 Results







50

40

30

20

10

0


10

05

00

minus05

minus10



∘56

∘56

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100MoCA


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5 Discussion





100

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Accu

racy

()

(a)

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Accu

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()


(b)


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Accu

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()

(c)

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Accu

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()


(d)














6 Conclusion




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ance

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SVM MLP

RBN DBN




Competing Interests



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6050

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Dist

ance

cove

red 60

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ance

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MLP

60

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50

6050

40

30

20

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0

Dist

ance

cove

red


minus100

1020

3040




RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







119892 (V119894) = tanh (V119894) (23)

119892 (V119895) = 11 + 119890minusV119895 (24)




(25)




Specificity = TN

TN + FP

(26)

4 Results







50

40

30

20

10

0


10

05

00

minus05

minus10



∘56

∘56

∘26

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∘42

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y-axis range




100MoCA


80MoCA


50MoCA





5 Discussion





100

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Accu

racy

()

(a)

100

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Accu

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()


(b)


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Accu

racy

()

(c)

100

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Accu

racy

()


(d)














6 Conclusion




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ance

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Dist

ance

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SVM MLP

RBN DBN




Competing Interests



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6050

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20

10

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Dist

ance

cove

red 60

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10

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ance

cove

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MLP

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6050

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30

20

10

0

Dist

ance

cove

red


minus100

1020

3040




RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




50

40

30

20

10

0


10

05

00

minus05

minus10



∘56

∘56

∘26

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y-axis range




100MoCA


80MoCA


50MoCA





5 Discussion





100

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75

70

65

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Accu

racy

()

(a)

100

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Accu

racy

()


(b)


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Accu

racy

()

(c)

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Accu

racy

()


(d)














6 Conclusion




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ance

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RBN DBN




Competing Interests



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6050

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20

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Dist

ance

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red 60

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Dist

ance

cove

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SVM

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Dist

ance

cove

red


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RBN DBN

60

50

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20

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Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





100

95

90

85

80

75

70

65

60

Accu

racy

()

(a)

100

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Accu

racy

()


(b)


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Accu

racy

()

(c)

100

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Accu

racy

()


(d)














6 Conclusion




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ance

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ance

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SVM MLP

RBN DBN




Competing Interests



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ance

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red 60

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ance

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X range


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MLP

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20

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Dist

ance

cove

red


minus100

1020

3040




RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










6 Conclusion




60

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ance

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ance

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Dist

ance

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X range

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10

0

Dist

ance

cove

red

X range

Y rangeminus20

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1020

3040






SVM MLP

RBN DBN




Competing Interests



60

70

60

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50

6050

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30

20

10

0

Dist

ance

cove

red 60

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90

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20

10

0

Dist

ance

cove

red

X range

X range


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6050


SVM

minus30minus20

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minus10

010

2030

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MLP

60

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50

6050

40

30

20

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0

Dist

ance

cove

red


minus100

1020

3040




RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




60

50

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10

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Dist

ance

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ance

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ance

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Dist

ance

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X range

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SVM MLP

RBN DBN




Competing Interests



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6050

40

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20

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0

Dist

ance

cove

red 60

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10

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Dist

ance

cove

red

X range

X range


1020

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6050


SVM

minus30minus20

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010

2030

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MLP

60

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50

6050

40

30

20

10

0

Dist

ance

cove

red


minus100

1020

3040




RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

red

X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




60

70

60

50

50

6050

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Dist

ance

cove

red 60

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Dist

ance

cove

red

X range

X range


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MLP

60

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Dist

ance

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RBN DBN

60

50

40

30

20

10

0

Dist

ance

cove

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X range

Y rangeminus20

minus100

1020

3040



Acknowledgments


References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article Application of Machine Learning in Postural...

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