Fuzzy-LFS: A Novel Localized Feature Selection with Fuzzy Region Division and Local Neighborhood Rough Set for Classification

Localized feature selection (LFS) methods divide the whole sample space to determine region-specific subsets for classification which outperform traditional feature selection with a global feature subset for the entire sample space. However, existing LFS algorithms decompose the local regions by impurity level of samples, which can misplace critical samples and impair feature selection results. To tackle this issue, this paper proposes a novel Fuzzy Localized Feature Selection (Fuzzy-LFS) algorithm, which divides local regions around each sample based on Gaussian fuzzy membership to enhance the coherence of region-specific information. Besides, to handle data fuzziness and uncertainty, Fuzzy-LFS establishes a Local Neighborhood Rough Set Model with forward greedy optimization to search the feature subsets. A novel local classifier is subsequently developed, overcoming the limitations of global classifiers unsuited for LFS while mitigating the excessive dependency on impurity level in traditional local classifiers. Specifically, for high-dimensional datasets, we introduce a Localized Feature Relevance Pre-Selection strategy, assigning sample-specific feature subsets according to local relevance to assist in dividing local regions and enhance classification performance. Through comprehensive experiments on 11 low-dimensional and 13 high-dimensional datasets, Fuzzy-LFS achieves superior classification accuracy to state-of-the-art LFS methods, demonstrating its effectiveness.