Fuzzy–Rough Sets for Information Measures and Selection of Relevant Genes From Microarray Data

Several information measures such as entropy, mutual information, and f-information have been shown to be successful for selecting a set of relevant and nonredundant genes from a high-dimensional microarray data set. However, for continuous gene expression values, it is very difficult to find the true density functions and to perform the integrations required to compute different information measures. In this regard, the concept of the fuzzy equivalence partition matrix is presented to approximate the true marginal and joint distributions of continuous gene expression values. The fuzzy equivalence partition matrix is based on the theory of fuzzy-rough sets, where each row of the matrix represents a fuzzy equivalence partition that can automatically be derived from the given expression values. The performance of the proposed approach is compared with that of existing approaches using the class separability index and the predictive accuracy of the support vector machine. An important finding, however, is that the proposed approach is shown to be effective for selecting relevant and nonredundant continuous-valued genes from microarray data.