Extending a Hybrid CBR-ANN Model by Modeling Predictive Attributes using Fuzzy Sets

Transcription

1 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets Yanet Rodríguez 1, Maria M. García 1, Bernard De Baets 2, Rafael Bello 1, Carlos Morell 1 1 Universidad Central de Las Villas 2 Ghent University 1

2 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. Content

3 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. ANN and CBR are two approaches of Artificial Intelligence that use the notion of similarity in an etensive way. The massively parallel methods are preferred to CBR for their computational cost An ANN is a black bo and usually we can not check whether its solution is plausible. These approaches to build a hybrid system were combined in a model proposed by Garcia, M. and Bello, R 1 1 García, M.M., Bello, P.R.: A model and its different applications to case-based reasoning. Knowledge-based systems 9 (1996):

4 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. This hybrid system is a variant of the model proposed by Stanfill and Waltz 2. It takes advantage of the learning power of the ANNs and their capability to solve several types of problems. CBR enables us to overcome the null eplanation capacity of ANN by presenting the most similar cases of the problem solved Stanfill, C., Waltz, D.: Toward memory-based reasoning. Comm. of ACM, 29 (1986):

5 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. (Overview) A simple implementation of Interactive and Competition neural net (SIAC), proposed by Rumelhart 3. There is a group of neurons for each attribute, representing each value in the domain D ai of attribute a i by a single neuron. A Hebbian-like learning mechanism is used to calculate the weights The representative value T j corresponding with the node of greatest activation will be the value given to this attribute. The CBR allows justifying the solution given by ANN with most similar eperiences stored in the case base. 3 McClelland, David E. Rumelhart: Eplorations in parallel distributed processing. MIT Press (1989) 5

6 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. (limitations) When a numeric attribute is used many different values for it in the case base should appear The quantity of neurons in the ANN of the previous model very rapidly will be increased 6

7 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. Neuro-Fuzzy computing constitutes one of the best-known visible hybridizations capturing the merits of fuzzy set theory and ANN. Measurements are crisp whereas perceptions are fuzzy. Fuzzy set theory enables the use of natural language mapping numeric data into linguistic terms. This integration promises to provide, to a great etent, more intelligent systems to handle real life ambiguous recognition 7

8 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. model Etension Numeric attributes are modeled in terms of fuzzy sets Neural Net with Fuzzy Sets Fuzzy-SIAC Similarity Function using Fuzzy Sets 8

9 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. Numeric Attributes as Linguistic Variables Let CB denotes a case base (or training set) Let A={a 1, a 2,.., a m } the set of m attributes that describes an eample e of CB. For a numeric attribute p, the values that appear for it in CB constitute the universe of the variable. After modeling, the set of linguistic terms Rp= {P 1 P 2,, P /Rp/ } is considered the set of representative values of attribute p, where P i represents the ith fuzzy set. Eample: attribute age of the person Rp={ young, middle-age, old } 9

10 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. The Neural Net with Fuzzy Sets 40 Adding a preprocessor layer, where a preprocessor neuron is inserted for each representative value f A1 f A f A3 Activation in the original model Activation in the Fuzzy-SIAC All model f P ( pq ) = P ( pq ) µ i i 10

11 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. The Neural Net with Fuzzy Sets Let a, b be attributes of A. The value labeled by w Ai,Bj represents the weight associated to the arc between processing neurons N Ai and N Bj. A measure based on Relative frequency is used and then nonsymmetric weight matri is obtained. w A, B i j n f k= 1 Ai = n ( a k= 1 f ik A i ) f B ( a j ik ( b ) jk ) It is a systematic way of generating inclusion measures for ordinary sets in the form of a rational epression solely based on cardinalities of the sets involved. 11

12 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. The Similarity Function using Fuzzy Sets An Interpretative CBR is defined considering the value inferred for the target attribute in the object (t ). Definition 1. The strength of the value a with respect to T is a measure of the influence of this predictive value in the activation of the target neuron representing the value T of the target attribute t. S( a, T) = A R i w a A R i A, T i a f A i f A i ( a ( a ) f ) T f T ( t ( t ) ) 12

13 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. The Similarity Function using Fuzzy Sets Definition 2. The (degree of) equivalence between two values a and a y for predictive attribute a in the contet of target attribute t is defined as: δ t ( a, a ) y = 1 T R t S( a, T ) R t S( a y, T ) Definition 3. The importance of predictive attribute a for object in the contet of target attribute t is defined as its relative strength among all predictive attributes I t (, a ) = S( a, t ) S( p, t p P ) 13

14 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. The Similarity Function using Fuzzy Sets Definition 4. The similarity between objects and y, is the weighted sum of equivalences, using importance as weights: p P ( p p ) β (, y) = I (, p ) δ, t t y The most similar cases recovered allow the user to understand the solution given by the ANN. This is in fact the justification 14

15 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. A simple measure of the performance for the ANN and CBR were applied by using the following epressions: PerformanceANN ( CS ) = 1 q CS (, t = t ) q CS q PerformanceCBR ( CS ) = 1, q q CS e kq ( t = t ) CS e 15

16 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. Nine international datasets from UCIMLR are used, only having numerical attributes, without missing values and one target attribute. A discretization method Equal Width and trapezoidal membership functions developed from these same intervals were used to select a set of representative values for each attribute. A 10-fold cross validation was applied, and the performance mean (m) and the performance variance (s 2 ) with the ANN and CBR module considering all cases in the control data for each data set were calculated. 16

17 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. Two variants of the etended model were considered: Fuzzy-SIAC All model, when all linguistic term are considered Fuzzy-SIAC Ma model, when the Principle of Maimum Membership Degree is applied. A comparison of the paired samples was carried out, using both non-parametric tests: the Friedman two-way Analysis of Variance and the Wilcoon signed-rank test. The analysis of the results shows that the performance mean and variance of the ANN in the three variants considered do not have a significant difference (significance of the test: and respectively). 17

18 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. A system developed by using the proposed model and the former one will not have significant differences of performance. The advantages of the hybridization used in the original model are preserved, guaranteeing robustness and interpretability. 18

19 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. A natural framework to include epert knowledge by using linguistic terms when numeric attributes is used. Although fuzzy modeling usually carries out two contradictory requirements, which are the interpretability and the accuracy, the proposed model follows the new trend of increasing the good balance between them. 19

20 Etending a Hybrid CBR-ANN by ing Predictive Attributes using Fuzzy Sets. End Thanks for your attention! Questions? Comments? 20