Half-Quadratic Minimization for Unsupervised Feature Selection on Incomplete Data.

Area of Science:

• Data Science
• Machine Learning
• Computer Science

Background:

• Unsupervised feature selection (UFS) is crucial for dimensionality reduction in high-dimensional data.
• Existing UFS methods struggle with incomplete datasets and are sensitive to outliers.
• Real-world applications, particularly in industry, frequently encounter incomplete data.

Purpose of the Study:

• To develop a new UFS method addressing limitations of existing approaches.
• To effectively perform feature selection on incomplete datasets.
• To mitigate the impact of outliers in UFS models.

Main Methods:

• The proposed method utilizes an indicator matrix to manage unobserved information during feature selection.
• Half-quadratic minimization is employed to assign weights, downplaying outliers and emphasizing important samples.
• An alternative optimization strategy is designed and its convergence is theoretically and experimentally validated.

Main Results:

• Experimental results on synthetic and real-world incomplete datasets demonstrate the method's effectiveness.
• The proposed UFS method shows superior performance compared to previous techniques.
• Improved clustering performance was observed in the low-dimensional space derived from high-dimensional data.

Conclusions:

• The novel UFS method successfully handles incomplete data and reduces outlier sensitivity.
• The technique offers a robust solution for feature selection in challenging real-world scenarios.
• This advancement has significant implications for data analysis in fields relying on high-dimensional data.