Tomoharu Nakashima

Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems

We examine the performance of a fuzzy genetics-based machine learning method for multidimensional pattern classification problems with continuous attributes. In our method, each fuzzy if-then rule is handled as an individual, and a fitness value is assigned to each rule. Thus, our method can be viewed as a classifier system. In this paper, we first describe fuzzy if-then rules and fuzzy reasoning for pattern classification problems. Then we explain a genetics-based machine learning method that automatically generates fuzzy if-then rules for pattern classification problems from numerical data. Because our method uses linguistic values with fixed membership functions as antecedent fuzzy sets, a linguistic interpretation of each fuzzy if-then rule is easily obtained. The fixed membership functions also lead to a simple implementation of our method as a computer program. The simplicity of implementation and the linguistic interpretation of the generated fuzzy if-then rules are the main characteristic features of our method. The performance of our method is evaluated by computer simulations on some well-known test problems. While our method involves no tuning mechanism of membership functions, it works very well in comparison with other classification methods such as nonfuzzy machine learning techniques and neural networks.

Three objective genetics-based machine learning for linguisitc rule extraction

Abstract This paper shows how a small number of linguistically interpretable fuzzy rules can be extracted from numerical data for high-dimensional pattern classification problems. One difficulty in the handling of high-dimensional problems by fuzzy rule-based systems is the exponential increase in the number of fuzzy rules with the number of input variables. Another difficulty is the deterioration in the comprehensibility of fuzzy rules when they involve many antecedent conditions. Our task is to design comprehensible fuzzy rule-based systems with high classification ability. This task is formulated as a combinatorial optimization problem with three objectives: to maximize the number of correctly classified training patterns, to minimize the number of fuzzy rules, and to minimize the total number of antecedent conditions. We show two genetic-algorithm-based approaches. One is rule selection where a small number of linguistically interpretable fuzzy rules are selected from a large number of prespecified candidate rules. The other is fuzzy genetics-based machine learning where rule sets are evolved by genetic operations. These two approaches search for non-dominated rule sets with respect to the three objectives.

Voting in Fuzzy Rule-Based Systems for Pattern Classification Problems

In this paper, we examine two kinds of voting schemes in fuzzy rule-based systems for pattern classification problems. One is the voting by multiple fuzzy if-then rules in a single fuzzy rule-based classification system. The other is the voting by multiple fuzzy rule-based classification systems. First, we discuss the voting by multiple fuzzy if-then rules, which is used as a fuzzy reasoning method for classifying input patterns in a single fuzzy rule-based classification system. The performance of the voting by multiple fuzzy if-then rules is examined by computer simulations on the iris data. Next, we discuss the voting by multiple fuzzy rule-based classification systems. Three voting methods (i.e., a perfect unison rule, a majority rule, and a weighted voting rule) are used for combining classification results by multiple fuzzy rule-based classification systems. Finally, we compare the performance of fuzzy rule-based classification systems with that of other classification methods such as neural networks and statistical techniques by computer simulations on some well-known test problems.

Hybridization of fuzzy GBML approaches for pattern classification problems

We propose a hybrid algorithm of two fuzzy genetics-based machine learning approaches (i.e., Michigan and Pittsburgh) for designing fuzzy rule-based classification systems. First, we examine the search ability of each approach to efficiently find fuzzy rule-based systems with high classification accuracy. It is clearly demonstrated that each approach has its own advantages and disadvantages. Next, we combine these two approaches into a single hybrid algorithm. Our hybrid algorithm is based on the Pittsburgh approach where a set of fuzzy rules is handled as an individual. Genetic operations for generating new fuzzy rules in the Michigan approach are utilized as a kind of heuristic mutation for partially modifying each rule set. Then, we compare our hybrid algorithm with the Michigan and Pittsburgh approaches. Experimental results show that our hybrid algorithm has higher search ability. The necessity of a heuristic specification method of antecedent fuzzy sets is also demonstrated by computational experiments on high-dimensional problems. Finally, we examine the generalization ability of fuzzy rule-based classification systems designed by our hybrid algorithm.

Incremental Update of Fuzzy Rule-Based Classifiers for Dynamic Problems

Incremental construction of fuzzy rule-based classifiers is studied in this paper. It is assumed that not all training patterns are given a priori for training classifiers, but are gradually made available over time. It is also assumed the previously available training patterns can not be used in the following time steps. Thus fuzzy rule-based classifiers should be constructed by updating already constructed classifiers using the available training patterns at each time step. Incremental methods are proposed for this type of pattern classification problems. A series of computational experiments are conducted in order to examine the performance of the proposed incremental construction methods of fuzzy rule-based classifiers using a simple artificial pattern classification problem.

Thermography based breast cancer analysis using statistical features and fuzzy classification

Medical thermography has proved to be useful in various medical applications including the detection of breast cancer where it is able to identify the local temperature increase caused by the high metabolic activity of cancer cells. It has been shown to be particularly well suited for picking up tumours in their early stages or tumours in dense tissue and outperforms other modalities such as mammography for these cases. In this paper we perform breast cancer analysis based on thermography, using a series of statistical features extracted from the thermograms quantifying the bilateral differences between left and right breast areas, coupled with a fuzzy rule-based classification system for diagnosis. Experimental results on a large dataset of nearly 150 cases confirm the efficacy of our approach that provides a classification accuracy of about 80%.

Fuzzy data mining: effect of fuzzy discretization

When we generate association rules, continuous attributes have to be discretized into intervals while our knowledge representation is not always based on such discretization. For example, we usually use some linguistic terms (e.g., young, middle age, and old) for dividing our ages into some fuzzy categories. We describe the extraction of linguistic association rules and examine the performance of extracted rules. First we modify the definitions of the two basic measures (i.e., confidence and support) of association rules for extracting linguistic association rules. The main difference between standard and linguistic association rules is the discretization of continuous attributes. We divide the domain interval of each attribute into some fuzzy regions (i.e., linguistic terms) when we extract linguistic association rules. Next, we compare fuzzy discretization with standard non-fuzzy discretization through computer simulations on a pattern classification problem with many continuous attributes. The classification performance of extracted rules on unseen test patterns is examined under various conditions. Simulation results show that linguistic association rules with rule weights have high generalization ability even when the domain of each continuous attribute is homogeneously partitioned.

Effect of rule weights in fuzzy rule-based classification systems

This paper examines the effect of rule weights in fuzzy rule-based classification systems. Each fuzzy rule in our classification system has antecedent linguistic values and a single consequent class. We use a fuzzy reasoning method based on a single winner rule in the classification phase. The winner rule for a new pattern is the fuzzy rule that has the maximum compatibility grade with the new pattern. When we use fuzzy rules with certainly grades, the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade. In this paper, the effect of rule weights is illustrated by drawing classification boundaries using fuzzy rules with/without certainty grades. It is also shown that certainly grades play an important role when a fuzzy rule-based classification system is a mixture of general rules and specific rules. Through computer simulations, we show that fuzzy rule-based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy rules with certainty grades.

Multiple regression with fuzzy data

In this paper, we propose an iterative algorithm for multiple regression with fuzzy variables. While using the standard least-squares criterion as a performance index, we pose the regression problem as a gradient-descent optimisation. The separation of the evaluation of the gradient and the update of the regression variables makes it possible to avoid undue complication of analytical formulae for multiple regression with fuzzy data. The origins of fuzzy input data are traced back to the fundamental concept of information granulation and an example FCM-based granulation method is proposed and illustrated by some numerical examples. The proposed multiple regression algorithm is applied to one-, three- and nine-dimensional synthetic data sets as well as the 13-dimensional Boston Housing dataset from the machine learning repository. The algorithms performance is illustrated by the corresponding plots of convergence of regression parameters and the values of the prediction error of the resulting regression model. General comments on the numerical complexity of the proposed algorithm are also provided.

A weighted fuzzy classifier and its application to image processing tasks

Many image processing applications involve a pattern classification stage. In this paper we propose a classifier based on fuzzy if-then rules that allows the incorporation of weighted training patterns which can be used to adjust the sensitivity of the classification with respect to certain classes. The antecedent part of fuzzy if-then rules are specified by partitioning each attributes into fuzzy sets while the consequent class and the degree of certainty are determined from the compatibility and weights of training patterns. We also introduce a learning method which adjusts the degree of certainty in order to provide improved classification performance and reduced costs. Experimental results on several image processing tasks demonstrate the efficacy of the proposed method.