A Spectral Feature Selection Approach With Kernelized Fuzzy Rough Sets

Feature evaluation is an important issue in constructing a feature selection algorithm in kernelized fuzzy rough sets, which has been proven to be an effective approach to deal with nonlinear classification tasks and uncertainty in learning problems. However, the feature evaluation function developed with kernelized fuzzy rough sets cannot better reflect the affinity relationship of samples and is time-consuming. To overcome these drawbacks, in this article, the problem of feature selection with kernelized fuzzy rough sets is studied based on the spectral graph theory. First, the within-class and between-class sample similarity matrices by using kernelized fuzzy approximation operators are constructed. Two operators, which can capture the affinity relationship of samples, are then introduced based on the sample similarity matrices. The proposed operator can be regarded as the sum of the weighted kernelized fuzzy approximation operators. Second, based on the ratio criterion, a feature evaluation function and its corresponding feature selection algorithm FRKF are presented, which can effectively evaluate the importance of features. Third, to illustrate the performance of the proposed algorithm, extensive experiments have been carried out to compare FRKF and other well-known feature selection methods, including the feature ranking methods and feature subset selection methods on various classification tasks. The experimental results on real-world datasets demonstrate that FRKF achieves the high performances in terms of the robustness, efficiency, and effectiveness.

I. Introduction

In MANY classification tasks, datasets such as gene microarray data [1] and text data [2], are usually described by hundreds or even thousands of features. Fortunately, as pointed out by many researchers [3], [4], a large amount of features is either irrelevant or redundant with respect to the target concept. How to find or rank all potentially relevant features has become a challenging task in machine learning or pattern recognition. Feature selection has been very effectively used to discover previously unknown and potentially useful features in data classification [5]–[7]. It has proven that feature selection can overcome the curse of dimensionality, speed up the computation time, improve the predictive performance, and gain a better understanding of the data.