Bi-Sparse Unsupervised Feature Selection.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• High-dimensional unlabeled datasets pose challenges for feature selection.
• Principal Component Analysis (PCA) is a common technique for unsupervised feature selection (UFS).
• Existing PCA-based methods often use single sparse regularization, limiting their effectiveness.

Purpose of the Study:

• To introduce a novel bi-sparse method, BSUFS, for improved unsupervised feature selection.
• To enhance PCA by incorporating dual sparsity norms ($\ell _{2,p}$ and $\ell _{q}$) for discriminative feature extraction.
• To provide a unified framework for bi-sparse optimization in UFS.

Main Methods:

• Incorporation of $\ell _{2,p}$-norm and $\ell _{q}$-norm into classical PCA.
• Development of a proximal alternating minimization (PAM) algorithm for solving the non-convex model.
• Utilizing Stiefel manifold optimization and sparse optimization techniques.

Main Results:

• BSUFS effectively selects relevant features and filters out irrelevant noise.
• Demonstrated effectiveness on synthetic and real-world datasets through extensive numerical experiments.
• The bi-sparse optimization approach shows significant advantages in feature selection.

Conclusions:

• BSUFS offers superior performance in unsupervised feature selection compared to existing methods.
• The proposed bi-sparse optimization framework is effective and versatile.
• BSUFS shows potential for applications beyond feature selection, including image processing.