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

Inner product dependence, as an important feature evaluation function in fuzzy rough set theory, has the advantage of maintaining the maximum membership degree of samples to decisions while effectively characterizing classification errors. However, it is noteworthy that this method has limitations in describing classification errors: it can only estimate errors through partial samples and cannot achieve a more accurate error description for the overall sample set. To address this issue, this study constructs an inner product dependence function that can comprehensively represent the characteristics of the overall sample from the perspective of the domain and analyzes its relevant properties in depth. By leveraging matrix operations, this study design a feature selection algorithm based on the minimum classification error criterion (MCEFS). Furthermore, to cope with the dynamic changes in data environments, this study proposes an incremental feature selection algorithm based on block matrices (BM-MCEFS) by exploring the theory and methodological analysis of fuzzy rough sets in conjunction with incremental techniques. Finally, through a series of comparative experiments conducted on 10 public datasets, this paper fully verifies the feasibility of the proposed static algorithm and the effectiveness of the incremental algorithm.