Principal Component Analysis With Fuzzy Elastic Net for Feature Selection

作者：Yunlong Gao, Qiang Wu, Zhenghong Xu, Chao Cao, Jinyan Pan, Guifang Shao, Feiping Nie, Qingyuan Zhu · 发表于：IEEE Transactions on Fuzzy Systems · 年份：2024 · DOI：10.1109/tfuzz.2024.3466926 · 被引用次数：11 · 研究领域：Fuzzy Logic and Control Systems、Neural Networks and Applications、Face and Expression Recognition

Feature selection serves as a fundamental technique in machine learning and data analysis, playing a crucial role in extracting valuable features from large-scale and high-dimensional datasets that may contain irrelevant features. To enhance the performance of feature selection, regularizers like${\ell _{1}}$-norm or${\ell _{2,1}}$-norm are commonly utilized to encourage sparsity. Nonetheless, these traditional regularization techniques encounter certain challenges. When correlations exist among features, the sparsity-driven regularization can unfairly diminish weights of correlated features to zero, thus ignoring the feature correlations and lacking group sparsity properties. While a straightforward combination of${\ell _{1}}$-norm and${\ell _{2}}$-norm can uncover feature correlations, it lacks adaptability and effectively balancing sparsity and correlation. To address these challenges, we introduce a novel matrix-based regularization term, called a fuzzy elastic net, in the unsupervised feature selection model. Our model is founded on principal component analysis, a well-established dimensionality reduction technique adept at finding subspaces that retain most information from raw data. The model is enhanced by a fuzzy elastic net, which promotes group or sparsity properties through adaptive parameter tuning. The new regularization term introduces a flexible fuzzy weighted scheme combining the${\ell _{2,2}}$-norm and${\ell _{2,p}}$-norm ($0< p\leq 1$). This approach all...