A block matrix incremental feature selection method based on fuzzy rough minimum classification error

In fuzzy rough set models, inner-product correlation serves as an effective evaluation function for feature selection, with its key advantage lying in its ability to characterize the minimum classification error inherent in the model. However, existing inner-product-based methods typically rely only on a subset of samples to approximate this error, making it difficult to fully and accurately capture the discriminative structure across the entire sample space. To address this limitation, this paper proposes a global-sample-oriented inner-product correlation criterion. By constructing a continuous and non-vanishing fuzzy membership structure over the entire universe of discourse, the proposed criterion significantly enhances the theoretical soundness and practical consistency of inner-product-based feature evaluation. Building upon this foundation and leveraging efficient matrix computation techniques, we design a static feature selection algorithm based on the Minimum Classification Error-based Feature Selection (MCEFS) criterion. Furthermore, to meet the demand for efficient updates in dynamic data environments, we develop a block-wise updating mechanism for the fuzzy decision and fuzzy relation matrices. We rigorously derive and prove a block-based incremental update strategy for the fuzzy lower approximation matrix, which effectively eliminates redundant recomputation of fuzzy lower approximations and substantially improves computational efficiency. Based on this strategy, we propose an incremental feature selection algorithm-Block Matrix-based MCEFS (BM-MCEFS). Finally, comprehensive comparative experiments on 12 public benchmark datasets validate the effectiveness and feasibility of the static MCEFS algorithm and clearly demonstrate the superior performance of BM-MCEFS in terms of computational efficiency and numerical stability.