Learning Robust and Sparse Principal Components With the α-Divergence

Area of Science:

• Data Science
• Machine Learning
• Statistical Analysis

Background:

• Principal Component Analysis (PCA) is a widely used dimensionality reduction technique.
• Robust Principal Component Analysis (RPCA) methods are needed to handle datasets with outliers.
• Existing RPCA methods may not fully exploit the local structure of datasets.

Purpose of the Study:

• To propose novel robust principal component analysis (RPCA) methods.
• To leverage the local structure of datasets for improved robustness.
• To introduce a generalized framework for RPCA using α-divergence.

Main Methods:

• Methods derived by minimizing the α-divergence between sample distribution and Gaussian density model.
• Development of orthogonal, non-orthogonal, and sparse RPCA variants.
• Demonstration that classical PCA is a special case (Kullback-Leibler divergence).

Main Results:

• Proposed methods effectively recover principal components (PCs) by down-weighting outliers.
• Simulations show successful application in fMRI signal recovery.
• Demonstrated effectiveness in foreground-background (FB) separation for video analysis.

Conclusions:

• The novel α-divergence-based RPCA methods offer enhanced robustness against outliers.
• These methods provide a flexible framework applicable to various data structures.
• Successful application in real-world problems like FB separation and image reconstruction validates the approach.