Information Fusion Dr. B. K. Panigrahi
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1 Information Fusion By Dr. B. K. Panigrahi Asst. Professor Department of Electrical Engineering IIT Delhi, New Delhi /12/2007 1
2 Introduction Classification OUTLINE K-fold cross Validation Feature selection by GA Multiple Classifiers System Information Fusion Methods 2
3 Introduction Information Fusion refers to the field of study of techniques attempting to merge information from disparate sources despite differing conceptual, contextual and typographical representations. Pattern recognition aims to classify data patterns based on either a prior knowledge or on statistical information extracted from the patterns. The patterns to be classified are usually groups of measurements or observations, defining points in an appropriate multidimensional space. 3
4 Introduction Classification OUTLINE K-fold cross Validation Feature selection by GA Multiple Classifiers System Information Fusion Methods 4
5 Classification Classification is regarded as one of the most important fields of machine intelligence Aim in this process is to build a model that can recognize the samples The model must be able to classify a given pattern in one or more classes Methods used as classifier: Neural Networks LVQ, PNN, MLP,etc. Decision trees Support vector Machines Data Modeling Feature Extraction Classification Visualization & Interpretation 5
6 Classification: Definitions A classifier is any mapping from the space of features (measurements) to a space of class labels (names, tags, distances, probabilities) A classifier is a hypothesis about the real relation between features and class labels A learning algorithm is a method to construct hypotheses A learning algorithm applied to a set of samples (training set) outputs a classifier 6
7 Classification Error on the training data is not a good indicator of performance on future data Q: Why? A: Because new data will probably not be exactly the same as the training data! Over fitting fitting the training data too precisely - usually leads to poor results on new data 7
8 Classification Natural performance measure for classification problems: Error Rate: Success: instance s class is predicted correctly Error: instance s class is predicted incorrectly Error rate: proportion of errors made over the whole set of instances Training set Error Rate: is way too optimistic! you can find patterns even in random data 8
9 Classification Step 1 Split data into train and test sets Training set Data + Testing set 9
10 Classification Step 2 Build a model on a training set Training set Data + Model Builder Y N Testing set 10
11 Classification Step 3 Evaluate on test set Training set Data + Model Builder Testing set Y N Predictions 11
12 Introduction Classification OUTLINE K-fold cross Validation Feature selection by GA Multiple Classifiers System Information Fusion Methods 12
13 Simple Classification Process: (Large data set) 1. Split data in to Train and test set 2. Build a model on a training set 3. Evaluate on test set K-fold cross validation: (small data set) 1. Data is split into k subsets of equal size. 2. Each subset in turn is used for testing and the remainder for training. The accuracy estimates are averaged to yield an overall accuracy estimate 13
14 K-fold cross validation: Break up data into groups of the same size Keep the first one for Testing and others for training the model Repeat the procedure for all the folds 14
15 Classification with K-fold cross validation Data 10-fold validation Classification algorithm Test Data Model Algorithm evaluation Y N Prediction of Targets 15
16 Introduction Classification OUTLINE K-fold cross Validation Feature selection by GA Multiple Classifiers System Information Fusion Methods 16
17 Feature selection by GA Feature vector spaces are HUGE Many algorithms are sensitive to the number of parameters Feature selection is defined as the selection of a subset of features to describe a phenomenon from a larger set that may contain irrelevant or redundant features 17
18 Advantages Feature selection by GA Reducing dimensionality Improving learning efficiency Increasing predictive accuracy Reducing complexity of learned results Mutual Information Iteratively eliminate features with least mutual information with other remaining features Genetic Algorithms Try lots of subsets and choose the best 18
19 Genetic Algorithms Genetic Algorithms - Adaptive search and optimisation techniques based on the principles of survival of the fittest (C. Darwin) and genetics (G.J. Mendel) structure of a living being, i.e,, a creature is "built decoding a set of chromosomes, organism which are well-adapted to the environment are allowed to reproduce more often than those which are not. Holland, 1975 (American biologist) - GAs as an attempt to explain algorithmically diversity of species and individuals in the nature. C. Darwin 19
20 Genetic Algorithms contin. Stochastic search algorithms based on principle of natural selection Chromosomes represent potential solutions Binary or integer coding Population based search Crossover and mutation operations for selection of new individuals Mutation introduces genetic diversity (New Information) Computationally intense 20
21 Genetic Algorithms contin. Process: Encoding and Decoding Cross Over - Single point, two point, multi point and uniform cross over Mutation - Single bit mutation Selection - Roulette Wheel selection and Tournament selection 21
22 Genetic Algorithms contin. Encoding Each 0/1 bit represents exclusion/inclusion of corresponding feature 22
23 GA Operational diagram P P2 Source Encoding P P P P4 Mating Pool C C2 Cross Over P C3 Mutation Roulette Wheel Selection Off Spring C C C3 Decoding Solution Fitness Computation 23
24 Genetic Algorithm Flowchart 24
25 Cross Over Genetic Algorithms contin. Is a recombination operator Off springs are created by changing information among parent stringss Mutation Produces spontaneous random changes Responsible for injection of new information This prevents premature convergence to local optima. Fitness Function Computation GA works on Maximization problem, Here in our case The old cross validation is done, so that average of 10 accuracies considered as fitness function to be maximized. 25
26 Selection Procedure: (Implementation) Roulette wheel Selection: Genetic Algorithms contin. Sum the fitness of all chromosomes, call it T Generate a random number N between 1 and T Return chromosome whose fitness added to the running total is equal to or larger than N Chance to be selected is exactly proportional to fitness Chromosome : Fitness: Running total: N(1 N 49): 23 Selected: 3 Tournament selection: Randomly choose a group of T individuals from the population. Select the best fittest one among them. 26
27 Genetic Algorithms contin. How to guarantee that the best member of a population will survive? Elitist model: the best member of the current population is set to be a member of the next population always. 27
28 Feature selection by GA Data GA Feature Selection Classifier Rely on a predetermined classification algorithm Use 10 fold average as goodness measure High accuracy, but computationally expensive 28
29 GA Feature selection for Wavelet Packet The 4 th level of wavelet packet contains 16 nodes, from each node among 6 features only one is selected by GA. Optimally Selected features by GA Node Selected Feature Node Selected Feature Node Selected Feature 0 Mean 4 Kurtosis 8 Energy 1 Kurtosis 5 Standard Deviation 9 Kurtosis Node Selected Feature 12 Standard Deviation 13 Energy 14 Standard 2 Skewness 6 Entropy 10 Energy Deviation 3 Mean 7 Kurtosis 11 Mean 15 Kurtosis 29
30 Results: GA Feature selection for Wavelet Packet The accuracy obtained by FkNN classifier Case Energy(16) Entropy(16) Energy & Entropy(32) All (96) GA selected Feature (16) Pure signal (10 fold avg)
31 Introduction Classification OUTLINE K-fold cross Validation Feature selection by GA Multiple Classifiers System Information Fusion Methods 31
32 Multiple classifiers System Named as Multiple experts, Mixture of experts, co operative agents, classifier ensembles, multiple classifier systems, etc. by different authors. A multiple classifier system (MCS) is a structured way to combine (exploit) the outputs of individual classifiers The Final decision is taken by decision fusion techniques called Combiners. 32
33 Multiple classifiers System CLASSIFIER 1 D1 CLASSIFIER 2 D2 Data CLASSIFIER 3 D3 Dn COMBINER D CLASSIFIER n Parallel architecture of MCS 33
34 Multiple classifiers System Architecture of MCS with sensor fusion (data itself grouped and given to different classifier) 34
35 Introduction Classification OUTLINE K-fold cross Validation Feature selection by GA Multiple Classifiers System Information Fusion Methods 35
36 Information Fusion Methods Abstract level Rank level Measurement level ANN Agent Based fusion 36
37 Fusion Methods Based on classifier outputs Different information levels merit different fusion schemes Abstract Level : A classifier only outputs a unique label Rank Level: A classifier ranks all labels or a subset of the labels in a queue with the label at the top being the first choice Measurement Level: Each classifier attributes to each label a measurement value to address the degree that the sample has the label 01/12/2007 IIT Delhi 37
38 Abstract-level Fusion Methods Voting methods Behaviour Knowledge space (BKS) Bayes belief method 01/12/2007 IIT Delhi 38
39 Abstract-level Fusion Methods Majority Voting method: The final decision is the most frequent class in the each classifiers output. CLASSIFIER 1 D1 CLASSIFIER 2 D2 Data CLASSIFIER 3 D3 Dn Majority Voting D CLASSIFIER n 01/12/2007 IIT Delhi 39
40 Abstract-level Fusion Methods Behaviour Knowledge space (BKS): Every combination of classifier output is regarded as a cell in Look up Table Each cell contains the number of samples of the validation set characterized by a particular value of class labels Class Pc ( = 0 D1= 0,D2= 1,D3= 0) = = 0.82 Threshold /12/2007 IIT Delhi 40
41 Abstract-level Fusion Methods Bayes belief method: It assumes the mutual independency of classifiers and considers the error matrix called Confusion Matrix is known. C(x) A(m) 1 2 M 1 n 11 n 12 n 1M 2 n 21 n 22 n 2M. M n M1 n M2 n MM n ij = number of events from C(i) classified as C(j) 01/12/2007 IIT Delhi 41
42 Abstract-level Fusion Methods Bayes belief method: Sample x is assigned to class i if its probability becomes more than other classes. P( Ci D1,D2,...,Dn ) > P( Cj D1,D2,...,Dn ) j i 01/12/2007 IIT Delhi 42
43 Rank-level Fusion Methods Based on democratic Election strategies Some classifiers provide class scores,, or some sort of class probabilities This information can be used to rank each class Pc1=0.20 Rc1=1 Classifier N-> N > Pc2=0.69 -> > Rc2=3 Pc3=0.34 Rc3=2 In general if Ω={c1, ={c1, ck} ck} is the set of classes, the classifiers can provide an ordered (ranked) list of class labels 01/12/2007 IIT Delhi 43
44 The Borda Count Method Let no. of classifiers N=3 and no. of classes k=4, class lables Ω={a,b,c,d} For a given pattern, the ranked outputs of the three classifiers are as follows Rank value Classifier1 Classifer2 Classifier3 4 c a b 3 b b a 2 d d c 1 a c d 01/12/2007 IIT Delhi 44
45 The Borda Count Methods So we have r a = r a1 +r a2 + r 3 a = 1+4+3=8 r b = r b1 +r b2 + r 3 b = 3+3+4=10 r c = r c1 +r c2 + r 3 c = 4+1+2=7 r d = r d1 +r d2 + r 3 d = 2+2+1=5 The winner-class is b because it has the maximum overall rank 01/12/2007 IIT Delhi 45
46 Measurement-level Fusion Methods Linear combiners: -Simple and weighted averaging of classifiers output. - Weighted averaging is required for imbalanced classifiers, i.e. classifier with different accuracy and / or different pair wise correlations P avg i N k ( x) W P ( x) = k= 1 Where P ik is the probability measure of k th classifier for i th class k i 01/12/2007 IIT Delhi 46
47 Artificial Neural Network in Decision Fusion - Simple and weighted averaging of classifiers output. - Weighted averaging is required for imbalanced classifiers, i.e. classifier with different accuracy and / or different pair wise correlations CLASSIFIER 1 D1 CLASSIFIER 2 D2 Data CLASSIFIER 3 D3 Dn ANN D CLASSIFIER n 01/12/2007 IIT Delhi 47
48 Multi Agent Based Decision Fusion Wooldridge and Jennings have defined an agent, as "a computer system that is situated in some environment and that is capable of autonomous action in this environment in order to meet its design objectives." 48
49 In addition to being autonomous, an intelligent agent is expected to have the following capabilities Reactivity: Intelligent agents are not only able to perceive their environment, but are also able to respond in a timely fashion to changes that occur in it in order to satisfy their design objectives. Proactive ness: Intelligent agents are able to exhibit goal directed behavior by taking the initiative in order to satisfy their design objectives. Social ability: Intelligent agents are capable of interacting with other agents (and possibly humans) in order to satisfy their design objectives. 49
50 Multi-agent systems, unlike centralized systems or client server systems, are typically distributed systems in which several distinct components, each of which is an independent problem solving agent, come together to form a coherent whole MAS is any system that contains * Two or more agents * At least one autonomous agent and * At least one relationship between two agents where one satisfies the goal of the other." 50
51 MAS based architecture has the following advantages over client-server systems: Lower network bandwidth: being a distributed system, lesser volumes of data are exchanged between the agents as compared to traditional client-server architecture. Lesser computation time: in MAS, agents process data in parallel, thus decreasing the overall computation time. No single point failure: a centralized system without redundancy leads to single point failures that may collapse the entire system. However, in MAS the single point failure is alleviated due to its distributed architecture. Ease in addition of new resources or interconnections and extensibility. 51
52 Multi Agent based Decision Fusion 52
53 Conclusion Intelligent computational methods are more suitable for Improving the accuracy of classification. Selection of a method is based on the nature of the problem. 53
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