Application of Or-based Rule Antecedent Fuzzy Neural Networks to Iris Data Classification Problem

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1 Vol.1 (DTA 016, pp Application of Or-based Rule Antecedent Fuzzy eural etworks to Iris Data Classification roblem Chang-Wook Han Department of Electrical Engineering, Dong-Eui University, 176 Eomgwangno, Busanjin-gu, Busan 730, Korea Abstract. Fuzzy neural networks have been successfully applied to many classification problems. This paper applies Or-based rule antecedent fuzzy neural networks to Iris data classification problem. Or-based rule antecedent fuzzy neural networks can guarantee a parsimonious knowledge base with reduced number of rules by allowing union in the rule antecedent. Genetic algorithms optimize the binary connections of the Or-based rule antecedent fuzzy neural networks, and followed by gradient-based learning refinement of the optimized binary connections. To verify the performance of the Or-based rule antecedent fuzzy neural networks, Iris database available on the Machine Learning Repository site at the University of California at Irvine is used. Keywords: Fuzzy neural networks, Genetic algorithms, Iris data classification 1 Introduction owadays artificial intelligence-based classification of real world problems becomes more popular because the classification problems require more accurate classification results and the artificial intelligence can meet the requirement. Variety of researches related to artificial intelligence-based, especially fuzzy neural network-based classification has been considered [1]-[3]. This paper applies Or-based rule antecedent fuzzy neural networks [] to Iris data classification problem. Or-based rule antecedent fuzzy neural networks can guarantee a parsimonious knowledge base with reduced number of rules by allowing union in the rule antecedent. Genetic algorithms [5] optimize the binary connections of the Orbased rule antecedent fuzzy neural networks, and followed by gradient-based learning refinement of the optimized binary connections. To verify the performance of the Orbased rule antecedent fuzzy neural networks, Iris database available on the Machine Learning Repository site at the University of California at Irvine is used. Or-based Rule Antecedent Fuzzy eural etworks [] This paper is a new application version of the Or-based rule antecedent fuzzy neural networks, proposed by the author in [], to Iris data classification problem. Therefore, ISS: ASTL Copyright 016 SERSC

2 Vol.1 (DTA 016 the same version of Or-based rule antecedent fuzzy neural networks and its optimization method in [] are used in this paper. For this reason, all of this section directly refers to []. For more details about the Or-based rule antecedent fuzzy neural networks, please refer to []. AD neuron is a nonlinear logic processing element with n-inputs x [0,1] n producing an output y governed by the expression n Ti 1 y = AD(x; w ( w s x. where w denotes an n-dimensional vector of adjustable connections (weights. s denoting some s-norm and t standing for a t-norm. Individual inputs (coordinates of x are combined or-wise with the corresponding weights and these results produced at the level of the individual aggregation are aggregated and-wise with the aid of the t- norm. By reverting the order of the t- and s-norms in the aggregation of the inputs, we end up with a category of neurons, y= (x; w n S ( wi t xi i1 To construct the networks, we first elaborate on the union-based logic processor (UL which consists of and AD fuzzy neurons, as shown in Fig. 1, where, i, i and i are the membership grades of the fuzzy sets (negative, (zero and (positive for the input variable x i, i=1,,3,, respectively. i i. (1 ( 1 F1 1 1 F 3 F3 3 3 F Fig. 1. Structure of an UL UL (k h k AD An important characteristic of UL is that union operation of input fuzzy sets is allowed to appear in their antecedents, i.e., incomplete structure. For fuzzy system of complex processes with high input dimension, the UL is preferable because it achieves bigger coverage of input domain compared to the complete structure. For example, consider a system with x 1, x as its inputs and y as its output characterized by three linguistic terms,, and, respectively. The incomplete structure rule If x 1= then y= covers the following three complete structure rules: 18 Copyright 016 SERSC

3 Vol.1 (DTA 016 (i If (x 1= and (x = then y= (ii If (x 1= and (x = then y= (iii If (x 1= and (x = then y= Similarly, the rule If (x 1= or and (x = or then y= covers the following four complete structure rules: (i If (x 1= and (x = then y= (ii If (x 1= and (x = then y= (iii If (x 1= and (x = then y= (iv If (x 1= and (x = then y= x 1 F 1 UL (1 x x 3 F F 3 Fuzzification UL (... y Defuzzification x F W UL (0 u Fig.. Structure of Or-based rule antecedent fuzzy neural networks with input and 1 output variables characterized by 3 fuzzy sets (U=0 Fig. describes the Or-based rule antecedent fuzzy neural networks constructed with the aid of ULs. The neurons in the output layer are placed to aggregate the outputs of ULs for each corresponding consequences. In Fig., the connections to the ULs are described as bold lines which contain a set of connection lines as shown in Fig. 1. The only parameter that has to be controlled in this network is the number of UL (U, which will be set large enough in the experiment. 3 Experimental Results In this section we consider Iris data classification problem. Iris data is available on the Machine Learning Repository site at the University of California at Irvine. The Iris database has 150 instances (50 in each of three classes. It has input attributes (sepal length, sepal width, petal length, petal width and 1 output attribute (Iris Setosa, Iris Versicolour, Iris Virginica as shown in Table 1. For the Or-based rule antecedent fuzzy neural networks, we use 3-uniformly distributed Gaussian membership function overlapped in 0.5, and set U=0. We select 70% of the data from the three classes evenly as random for the training and the rest 30% is used for testing. Genetic algorithms optimize binary connection weights. After that gradient-based learning further refines these optimized binary connection weights in the unit interval. Table describes the parameters used in this experiment. Copyright 016 SERSC 19

4 Vol.1 (DTA 016 Table 1. Attribute information of Iris database Attribute umber Attribute Domain 1 Sepal length (cm Sepal width.0. (cm 3 etal length (cm etal width (cm 5 Class Iris Setosa, Iris Versicolour, Iris Virginica Table. arameter setup for the optimization Algorithm arameter Value Genetic algorithms opulation size 00 Generation no. 500 Crossover rate 0.8 Mutation rate 0.0 Gradient-based learning Learning rate 0.01 Iteration no time independent simulations have been performed with different training and testing data set selected from the three classes evenly. The average classification rates over 30 time independent simulations are described in Table 3. Table shows the maximum, minimum, and average number of rules after 30 time independent simulations. As can be seen, the optimized Or-based rule antecedent fuzzy neural networks have 7 to 11 rules covering most of the essential input space with reasonable classification rate. Table 3. Average classification rates over 30 time independent simulations Algorithm Average classification rate (% Training data set Testing data set Genetic algorithms Gradient-based learning Table. Resulting number of rules after 30 time independent simulations Min rule no. Max rule no. Average rule no Copyright 016 SERSC

5 Vol.1 (DTA 016 Conclusions This paper applied Or-based rule antecedent fuzzy neural networks to Iris data classification problem available on the Machine Learning Repository site at the University of California at Irvine. Or-based rule antecedent fuzzy neural networks can guarantee a parsimonious knowledge base with reduced number of rules by allowing union in the rule antecedent. Genetic algorithms optimized the binary connections of the Orbased rule antecedent fuzzy neural networks and the gradient-based learning further refined the optimized binary connections in the unit interval. As is shown in the experimental results, Or-based rule antecedent fuzzy neural networks can be successfully applied to Iris data classification problem with a reduced number of rules. References 1. Subramanian, K., Suresh, S., Sundararajan,.: A Metacognitive euro-fuzzy Inference System (McFIS for Sequential Classification roblems. IEEE Transactions on Fuzzy Systems, Vol. 1, o. 6 ( Rafi, D.M., Bharathi, C.R.: Optimal Fuzzy Min-Max eural etwork (FMM for Medical Data Classification using Modified Group Search Optimizer Algorithm. International Journal of Intelligent Engineering & Systems, Vol. 9, o. 3 ( Chen, Y.-C., Wang, L.-H., Chen, S.-M.: Generating Weighted Fuzzy Rules from Training Data for Dealing with the Iris Data Classification roblem. International Journal of Applied Science and Engineering, ( Han, C.W.: Evolutionary Optimization of Union-based Rule-Antecedent Fuzzy eural etworks and Its Applications. Lecture otes in Computer Science, Vol. 536 ( Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA (1989 Copyright 016 SERSC 1