MFDRRS: Modified-Fisher-Discriminant-Ratio-Based Rough-Set Heuristic Attribute Reduction for Nominal Data
Year: 2026
Type: article
Abstract: Attribute reduction is a fundamental problem in rough set theory that seeks a minimal subset of condition attributes preserving the discernibility capability of the original decision system. Traditional heuristic methods—greedy forward selection and backward elimination—suffer from two critical deficiencies: the absence of principled attribute-ranking criteria (which leads to over- or under-selection) and the omission of statistical discriminability from the search process. To address these issues, this paper presents MFDRRS, a hybrid framework that integrates three complementary strategies: (1) Fisher discriminant ratio (FDR) evaluation of attribute discriminability based on between- and within-class scatter; (2) FDR-based filtering to select statistically significant candidate attributes; and (3) greedy forward selection guided by the rough-set dependency degree, enhanced with an FDR-driven termination criterion. FDR computation quantifies the discriminative power of individual attributes, thereby facilitating the selection of an optimally discriminative candidate subset. Since the traditional FDR is defined for continuous features, we adapt the continuous-domain FDR to nominal data by proposing a modified Fisher discriminant ratio (MFDR). The MFDR first maps nominal attributes via one-hot encoding and then computes the between-class and within-class scatter matrices. The subsequent FDR-filtering and rough-set dependency analysis guarantee the optimality of the selected attribute subset. Evaluated on synthetic and real-world UCI datasets against six baselines—classical rough-set greedy forward/backward selection, exhaustive search, MI ranking, MaxRelevance, and JMI—the proposed method achieves more compact reductions with fewer attributes, maintains competitive dependency degrees, and avoids the over-selection characteristic of classical backward elimination.
Source: Entropy
DOI: 10.3390/e28111184
Authors: Xiaolin Cao, Sheng Luo, Linxiang Shi
Language: English
Topic: Rough Sets and Fuzzy Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: Shanghai Polytechnic University
OpenAlex ID: W7204107321