Discernibility matrix-based feature selection approaches with fuzzy dominance-based neighborhood rough sets

Abstract

Monotonic classification tasks (MCTs) are a critical type of classification tasks, characterized by the monotonic constraints between features and decision. As an essential dimensionality reduction technique, feature selection using discernibility matrices (DMs) has gained considerable attention. Relevant studies in MCTs have effectively addressed the construction of DMs, followed by the reduct computation via the discernibility function method. However, they remain restricted within crisp dominance rough sets (DRSs) and overlook other potential usages of DMs in feature selection. To address these issues, this paper constructs a DM based on a fuzzy DRS model and combines it with feature grouping to propose a composite feature selection algorithm for MCTs, termed DMCD. Firstly, fuzzy dominance-based neighborhood rough sets are established as the theoretical foundation, and a DM corresponding to fuzzy rank dependency is constructed. The discernibility function method can thus be employed to calculate all the reducts. Next, we use the DM to quantify the discriminative power of features and design a fuzzy-rank-entropy-based distance measure, which is then employed to group features with similar classification information. At each iteration of DMCD, the most discriminative features carrying distinct classification information are selected from these groups and sequenced. After this procedure, a wrapper technique is applied to derive the optimal feature subset. Finally, experiments on twenty real datasets demonstrate the robustness of the FDNRS model and the effectiveness of the DMCD algorithm.