Post on 20-Dec-2015
A Technique for Advanced Dynamic Integration of Multiple Classifiers
Alexey Tsymbal*, Seppo Puuronen**, Vagan Terziyan*
*Department of Artificial Intelligence and Information Systems, Kharkov State Technical University of Radioelectronics, UKRAINE
e-mail: vagan@kture.cit-ua.net, vagan@jytko.jyu.fi
**Department of Computer Science and Information Systems, University of Jyvaskyla, FINLAND, e-mail: sepi@jytko.jyu.fi
STeP’98 - Finnish AI Conference, 7-9 September, 1998
Finland and UkraineFinland and Ukraine
University of JyväskyläFinland
State Technical University of Radioelectronics
KharkovUkraine
Metaintelligence Laboratory: Research Topics
• Knowledge and metaknowledge engineering;
• Multiple experts;
• Context in Artificial Intelligence;
• Data Mining and Knowledge Discovery;
• Temporal Reasoning;
• Metamathematics;
• Semantic Balance and Medical Applications;
• Distance Education and Virtual Universities.
Contents
• What is Knowledge Discovery ?
• The Multiple Classifiers Problem
• A Sample (Training) Set
• A Sliding Exam of Classifiers as Learning Technique
• A locality Principle
• Nearest Neighbours and Distance Measure
• Weighting Neighbours, Predicting Errors and Selecting Classifiers
• Data Preprocessing
• Some Examples
What is Knowledge Discovery ?
• Knowledge discovery in databases (KDD) is a combination of data warehousing, decision support, and data mining and it is an innovative new approach to information management.
• KDD is an emerging area that considers the process of finding previously unknown and potentially interesting patterns and relations in large databases*.
• __________________________________________________________________________________________________________________________________________
• * Fayyad, U., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R., Advances in Knowledge Discovery and Data Mining, AAAI/MIT Press, 1996.
The Research Problem
During the past several years, in a variety of application domains, researchers in machine learning, computational learning theory, pattern recognition and statistics have tried to combine
efforts to learn how to create and combine an ensemble of classifiers.
The primary goal of combining several classifiers is to obtain a more accurate prediction than can be obtained from any single classifier alone.
Approaches to Integrate Multiple Classifiers
Integrating Multiple Classifiers
Selection Combination
Global (Static)
Local (Dynamic)
Local (“Virtual” Classifier)
Global (Voting-Type)
Decontextualization
Classification Problem
Given: n training pairs (xi, yi)
with xiRp and yi{1,…,J}
denoting class membership
Goal: given: new x0
select classifier for x0
predict class y0
J classes, n training observations,p object features
ClassificationClassifiers
Training set Vectorclassified
Classmembership
A Sample (Training) Set
X1
X2
Cixi2
xi1
P x x C
P x x C
P x x Cnn n
n
1 11
21
1
2 12
22
2
1 2
:( , ) ;
:( , ) ;
...
:( , ) .
Classifiers Used in Example
• Classifier 1: LDA - Linear Discriminant Analysis;
• Classifier 2: k-NN - Nearest Neighbour
Classification;
• Classifier 3: DANN - Discriminant Adaptive Nearest Neighbour
Classification
A Sliding Exam of Classifiers (Jackknife Method):
We apply all the classifiers to the Training Set
points and check correctness of classification
X1
X2
(0;0;1)
(1;0;0)
(0;0;0)
(0;0;0)
(0;0;0)(1;1;0)
(0;1;0)
(0;0;0)
(0;1;0)(0;0;0)
(0;0;0)
(0;0;0)
LDA - incorrect classification
k-NN - incorrect classification
DANN - correct classification
A Locality Principle
X1
X2
(0;0;1)
(1;0;0)
(0;0;0)
(0;0;0)
(0;0;0)
(0;1;0)
(0;0;0)
(0;1;0)(0;0;0)
(0;0;0)
(0;0;0)
We assume that also in neighbourhood of a pointwe may expect the sameclassification result:
LDA - incorrect classificationk-NN - incorrect classification
DANN - correct classification
Selecting Amount of Nearest Neighbours
• A suitable amount l of nearest neighbours for a training set point should be selected, which will be used to classify case related to this point.
• We have used l = max(3, n div 50) for all training set points in the example, where n is the amount of cases in a training set.
• ? ? Should we locally select an appropriate l value ?
Brief Review of Distance Functions According to D. Wilson and T. Martinez (1997)
Weighting Neighbours
X1
X2
(0;0;1)
(1;0;0)
(0;0;0)
(0;0;0)
(0;0;0)(1;1;0)
(0;1;0)
(0;0;0)
(0;1;0)(0;0;0)
(0;0;0)
(0;0;0)
d1
d2d3
NN3
NN1
NN2
Pidmax
T h e v a l u e s o f d i s t a n c e m e a s u r e a r e u s e d t o d e r i v e t h e w e i g h t w k f o re a c h o f s e l e c t e d n e i g h b o u r s k = 1 , … , l u s i n g f o r e x a m p l e a c u b i cf u n c t i o n :
w d dk k ( ( / ) )m a x1 3 3
Nearest Neighbours’ Weights in the Example
X1
X2
(0;0;1)
(1;0;0)
(0;0;0)
(0;0;0)
(0;0;0)(1;1;0)
(0;1;0)
(0;0;0)
(0;1;0)(0;0;0)
(0;0;0)
(0;0;0)
d1
d2d3
NN3
NN1
NN2
Pidmax
k=3; d1=2,1; d2=3,2; d3=4,3; dmax=6w1=0,88; w2=0,61; w3=0,25
Selection of a Classifier
X1
X2
(0;0;1)
(0,3;0,6;0)
(1;0;0)
(0;0;0)
(0;0;0)
(0;0;0)(1;1;0)
(0;1;0)
(0;0;0)
(0;1;0)(0;0;0)
(0;0;0)
(0;0;0)
d1
d2d3
NN3
NN1
NN2
Pi
dmax
Predicted classification errors:
q w q k j mj ii
k
ij* ( ) / , , .
11
q*=(0,3; 0,6; 0). DANN should be selected
Compenetnce Map of Classifiers
X1
X2
(0;0;0)
(1;0;0)
(0;0;0)
(0;0;0)
(0;0;0)
(0;1;0)
(1;1;0)(0;0;1)
(0;0;0)
(0;1;0)(0;0;0)
(0;0;0)
DANN
k-NN
LDA
k-NN
LDA
DANN
Data Preprocessing: Selecting Set of Features
p'i - subsystems of features
PCM AFS+LDA
AFS+s-by-sDA
AFS+LDAby optimalscoring
AFS+FDA
AFS+PDA
p '1
p '2 p '
3 p '4 p '
5p '
6
Classification errorsaccountF1 F2 F3
F4 F5 F6
F*
Fi
i
min1
6
- the best subsystem of featuresp *
Conclusion:methodi - the best
Fi - classification errors
Features Used in Dystonia Diagnostics
• AF (x1) - attack frequency;
• AM0 (x2) - the mode, the index of sympathetic tone;
• dX (x3) - the index of parasympathetic tone;
• IVR (x4) - the index of autonomous reactance;
• V (x5) - the velocity of brain blood circulation;
• GPVR (x6) - the general peripheral blood-vessels’ resistance;
• RP (x7) - the index of brain vessels’ resistance.
Training Set for a Dystonia Diagnostics
Visualizing Training Set for the Dystonia Example
Evaluation of Classifiers
Diagnostics of the Test Vector
Experiments with Heart Disease Database
• Database contains 270 instances. Each instance has 13 attributes which have been extracted from a larger set of 75 attributes.
The average cross-validation errors for the three classification methods were the following:
DANN 0.196,
K-NN 0.352,
LDA 0.156,
Dynamic Classifier Selection Method 0.08
Experiments with Liver Disorders Database
• Database contains 345 instances. Each instance has 7 numerical attributes.
The average cross-validation errors for the three classification methods were the following:
DANN 0.333,
K-NN 0.365,
LDA 0.351,
Dynamic Classifier Selection Method 0.134
Liver learning curves
0.5
0.55
0.6
0.65
0.7
50 75 100
125
150
175
200
225
250
Training Set Size
Acc
urac
y
Voting
CVM
DCS
Heart learning curves
0,77
0,79
0,81
0,83
0,85
100 120 140 160 180 200
Training Set Size
Acc
urac
y
Voting
CVM
DCS
Local (Dynamic) Classifier Selection (DCS) is compared with Voting and static Cross-Validation Majority
Experimental Comparison of Three Integration Techniques
Conclusion and Future Work• Classifiers can be effectively selected or integrated due
to the locality principle
• The same principle can be used when preprocessing data
• The amount of nearest neighbours and the way of distance measure it is reasonable decided in every separate case
• The difference between classification results obtained in different contexts can be used to improve classification due to possible trends