Download - Artificial Neural Networksvasighi/courses/ann96fall/ann15.pdf · Artificial Neural Networks Part16. Self Organizing Maps Design a SOM network selforgmap(dim,cover,initNeighb,topol,distFcn)

Artificial Neural Networks

Part 16

Self Organizing Maps

Design a SOM network

selforgmap(dim,cover,initNeighb,topol,distFcn)

dim Row vector of dimension sizes (default = [8 8])cover Number of training steps (default = 100)initNeighb Initial neighborhood size (default = 3)topol Layer topology function (default = 'hextop')distFcn Neuron distance function (default = 'linkdist')

x = simplecluster_dataset;net = selforgmap([8 8]);net = train(net,x);view(net)y = net(x);classes = vec2ind(y);


plotsompos(net,x)


plotsomhits(net,x)

plotsomplanes(net)



plotsomnd(net)


http://michem.disat.unimib.it/chm/

http://michem.disat.unimib.it/chm/download/kohoneninfo.htm


settings = som_settings(‘Kohonen’);

settings.nsize = 8;settings.epochs = 100;

settings.bound = 'normal';setting.training= 'sequential';settings.topol = 'hexagonal';

model = model_kohonen(X,settings);pred_koh = pred_kohonen(Xnew,model);


settings = som_settings(‘cpann’);settings.nsize = 8;settings.epochs = 100;Model_cp = model_cpann(X,class,settings);visualize_model(model_cp);pred_cp = pred_cpann(Xnew,model_cp);

cv = cv_cpann(X,class,settings,1,5);

cv.class_param.accuracycv.class_param.ner

cv.class_param.conf_mat

50 0 00 45 50 4 46C

lass

Predicted


i

j

k

Patterns

k

j feature vectors

attributes

k

j feature vectors

attributes

• Feature based sensor fusion• Brain-inspired computing• It is possible to obtain a feature matrix (several feature

vectors) per pattern.

Self Organizing Maps MOLMAP

Classification of multiway analytical data was carried out by means of amethod for the calculation of molecular descriptors, called:

MOLMAP (MOLecular Map of Atom-level Properties)

The input of the MOLMAP approach is a three-way data matrix: molecules on thefirst mode, molecule bonds on the second mode and bond properties on the lastmode. The data array is unfolded and used to train a Kohonen map

i

j

k

molecules

k

j molecule bonds

bond properties


The MOLMAP approach requires two major steps:

(a) Generation of MOLMAP scores by means of Kohonen maps and

(b) development of predictive classification models which use MOLMAP scores as independent variables.

Data pretreatment

Data need to be processed by Kohonen networks in order to make themcomparable with the Kohonen weights, multiway data are always range scaledbetween 0 and 1 when MOLMAP classification models are applied, in thefollowing way:

range scaled value of the ijk-th element of X maximum value of X

minimum value of X


After scaling, the data are arranged into a bi-dimensional matrix Xarr with I*Jrows (input vectors) and K columns

i

j

k

i*j

k

The MOLMAP approach requires the Kohonen map to be trained with the bi-dimensional matrix, i.e. I*J input vectors (each composed by K values) arepresented to the map

k

i*j

Molecular bonds Molecule 1

Molecule 2

Molecule 3


A trained Kohonen map showssimilarities between input vectorsin the sense that similar vectorsare mapped into the same orclosely adjacent neurons.

The pattern of activated neuronscan be seen as a fingerprint ofthe object and constitutes itsMOLMAP score.

K × ijKohonen

map

N × N

a representation of the objects of the original multiway dataset can be obtainedby projecting them onto the trained map, one at a time, and by mapping the Jinput vectors of each multiway object.

Winner(Activated)


MOLMAP scores

Trained Kohonen Map

1.3 0.6 0.3 0.3 1.0V1 V3

V2

V4 V5

0.6 1.3 0.3 0.3 0.3

0.3 0.3 0.3 0.0 0.0

0.3 0.3 0.0 0.3 0.3

1.0 0.3 0.0 0.3 1.0

MOLMAP score for molecule i

For each molecule a score vector can be obtained using this procedure



k

i*j

Molecule 1

Molecule 2

Molecule 3

Kohonen map

N × N

The MOLMAP score matrix M is constituted by i object fingerprintscalculated by means of Kohonen maps.

ClassificationRegression

MOLMAP score matrix

i

N × N

X Y


The MOLMAP score matrix M is constituted by i object fingerprintscalculated by means of Kohonen maps.

ClassificationRegression

MOLMAP score matrix

i

N × N

X Y

One of the major advantages of this approach is related to the factthat MOLMAP descriptors are able to represent properties of bonds ina molecular structure by a fixed-length code and allow the comparisonof molecules that have different numbers of bonds.

Learning Vector Quantization (LVQ) is asupervised method which has been introducedby Kohonen as a simple, universal and efficientlearning classifier.

LVQ represents a family of algorithms that arewidely used in the classification of potentiallyhigh-dimensional data.

Their popularity and success in numerousapplications is closely related to their easyimplementation and their intuitively clearapproach.

A

B

Learning Vector Quantization

Class AClass B

A complex boundary should be used for discrimination between classes

LVQ1



Class AClass B

Codebook ACodebook B

B

B

A

A

LVQ1


Class AClass B


wi(t+l) = wi(t) - α(t) (x(t) – wi(t)), where α(t) is a monotonically decreasing function of time.

B

B

A

A

If the closest referencevector (Codebook) wi

belongs to a class otherthan that of the point x(t), itis moved away in proportionto the distance between thetwo vectors

LVQ1

x w


Class AClass B


B

B

A

A

LVQ1

If the closest referencevector (Codebook) wi

belongs to a class otherthan that of the point x(t), itis moved away in proportionto the distance between thetwo vectors

wi(t+l) = wi(t) - α(t) (x(t) – wi(t)), where α(t) is a monotonically decreasing function of time.


Class AClass B


B

B

A

A

LVQ1

wi(t+l) = wi(t) + α(t) (x(t) – wi(t)), where α(t) is a monotonically decreasing function of time.

If this reference vector(Codebook) wi belongs tothe same class as thetraining point x(t), it ismoved closer to the point, inproportion to the distancebetween the two vectors


Class AClass B


B

B

A

A

LVQ1

When all points were used intraining process once, one epochis completed.Training will continue untilmaximum number of epochs hasbeen reached or codebooks havestabilized.


Class AClass B


B

B

A

A

LVQ1


Class AClass B


B

B

A

A

LVQ1

Voronoi region


LVQ Issues Initialization of the prototypes

Dead neurons – too far away from the training examples, never move in proper direction.

Number of codebooks for each class Depends on class structure in data space and number of input

vectors. Performance of classification can be checked at different

number of codebooks

Number of epochs Depends on the complexity of the data and learning rate.