Yoshifumi Kusunoki

Variable-precision dominance-based rough set approach and attribute reduction

In this paper, a variable-precision dominance-based rough set approach (VP-DRSA) is proposed together with several VP-DRSA-based approaches to attribute reduction. The properties of VP-DRSA are shown in comparison to previous dominance-based rough set approaches. An advantage of VP-DRSA over variable-consistency dominance-based rough set approach in decision rule induction is emphasized. Some relations among the VP-DRSA-based attribute reduction approaches are investigated.

A unified approach to reducts in dominance-based rough set approach

The Dominance-based Rough Set Approach (DRSA), which is an extension of the Rough Set Approach (RSA), analyzes a sorting problem for a given data set. Attribute reduction is one of major topics in RSA as well as DRSA. By attribute reduction, we can find an important attribute set, which is called a reduct. In this paper, we propose a new approach to reducts in DRSA. A few kinds of reducts have been already proposed in DRSA, therefore, we clarify relations among the proposed and previous ones. We prove that they are consolidated into four kinds. Moreover, we show that all kinds of reducts can be enumerated based on two discernibility matrices.

A Comprehensive Study on Reducts in Dominance-Based Rough Set Approach

In this paper, we propose new reducts in the dominance-based rough set approach. The relations with previous ones are clarified. Moreover, a comprehensive enumeration method of all kinds of reducts is proposed. We show that all kinds of reducts are enumerated based on two discernibility matrices associated with generalized decisions.

Empirical Risk Minimization for Variable Precision Dominance-Based Rough Set Approach

In this paper, we characterize Variable Precision Dominance-based Rough Set Approach VP-DRSA from the viewpoint of empirical risk minimization. VP-DRSA is an extension of the Dominance-based Rough Set Approach DRSA that admits some degree of misclassification error. From a definable set, we derive a classification function, which indicates assignment of an object to a decision class. Then, we define an empirical risk associated with the classification function. It is defined as mean hinge loss function. We prove that the classification function minimizing the empirical risk function corresponds to the lower approximation in VP-DRSA.

Rule induction via clustering decision classes

In this paper, we examine the effects of the application of LEM2 to a hierarchical structure of decision classes. We consider classification problems with multiple decision classes by nominal condition attributes. To such a problem, we first apply an agglomerative hierarchical clustering method to obtain a dendrogram of decision classes, i.e., a hierarchical structure of decision classes. At each branch of the dendrogram, we then apply LEM2 to induce rules inferring a cluster to which an object belongs. A classification system suitable for the proposed rule induction method is designed. By a numerical experiment, we compare the proposed methods with different similarity measure calculations, the standard application of LEM2 and a method with randomly generated dendrogram. As the result, we generally demonstrate the advantages of the proposed method.

Structure-Based Attribute Reduction: A Rough Set Approach

We provide an introduction to a rough set approach to attribute reduction. Analyzed data sets consist of objects which are described by attributes and partitioned into decision classes. Rough set theory deals with uncertainty decision classes with respect to attributes by approximating them to precise sets. The aim of attribute reduction is to remove redundant attributes as well as find important ones for classification. Several types of attribute reduction have been proposed especially according to preserving structures of approximated decision classes. We introduce definitions and theoretical results about structures-based attribute reduction.

Rule Induction for Decision Tables with Ordered Classes

In this paper, we study rule induction based on the rough set theory. In the rough set theory, we induce minimal rules from a decision table, which is a data set composed of objects. Each object is described by condition attributes and classified by a decision attribute. When the decision attribute of a given decision table is ordinal, we may induce rules w.r.t. upward/downward unions of decision classes. This approach would be better in simplicity of obtained rules than inducing rules w.r.t. decision classes directly. However, because of independent applications of rule induction methods, inclusion relations among upward/downward unions in the conclusions of obtained rules are not inherited to the premises of those. This non-inheritance may debase the quality of obtained rules. In this paper, we propose two approaches to inherit the implication relations among the conclusions of obtained rules to the premises of those. Moreover, we propose an approach to classification unseen objects using rules w.r.t. upward/downward unions of decision classes. The performances of the proposed approaches are examined by numerical experiments.

Boolean kernels and clustering with pairwise constraints.

Clustering is a method to group given data into clusters. In this research, we focus on data sets with nominal attributes. For such nominal data sets, it is important to pursue clusters having simple logical representations (patterns) as well as gathering similar objects and separate dissimilar ones. However, conventional clustering methods do not explicitly deal with patterns of clusters. In this paper, we propose a class of kernel functions to approach that problem. For each data point, we associate a Boolean function which expresses the set of patterns covering the point. Hence, the feature space of the proposed kernel is the space of Boolean functions. Using background knowledge, which is also given by a Boolean function, some of patterns are ruled out to obtain appropriate clusters. We call the kernel function restricted by the Boolean function as Boolean kernel or RDF (restricted downward function) kernel. We apply RDF kernel functions to clustering with pairwise constraints. By a numerical experiment, we demonstrate usefulness of RDF kernel functions.

LEM2-based rule induction from data tables with imprecise evaluations

We propose a rough set approach to data tables with imprecise evaluations. Treatments of imprecise evaluations are described and four rule induction schemas are proposed. For each rule induction schema, we apply LEM2-based rule induction algorithm by defining the positive object set appropriately. The performances of the proposed rule induction algorithms are examined by numerical experiments.

A Multi-class Support Vector Machine Based on Geometric Margin Maximization

Support vector machines (SVMs) are popular supervised learning methods. The original SVM was developed for binary classification. It selects a linear classifier by maximizing the geometric margin between the boundary hyperplane and sample examples. There are several extensions of the SVM for multi-class classification problems. However, they do not maximize geometric margins exactly. Recently, Tatsumi and Tanino have proposed multi-objective multi-class SVM, which simultaneously maximizes the margins for all class pairs. In this paper, we propose another multi-class SVM based on the geometric margin maximization. The SVM is formulated as minimization of the sum of inverse-squared margins for all class pairs. Since this is a nonconvex optimization problem, we propose an approximate solution. By numerical experiments, we show that the propose SVM has better performance in generalization capability than one of the conventional multi-class SVMs.