Information Theoretic Subspace Clustering.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Subspace clustering aims to group data points from multiple subspaces.
• Outliers and noise significantly degrade the performance of traditional subspace clustering algorithms.
• Existing methods often struggle with robustly identifying underlying data structures in the presence of anomalies.

Purpose of the Study:

• To develop novel information theoretic objective functions for robust subspace clustering.
• To unify existing group sparsity methods within a common half-quadratic (HQ) optimization framework.
• To enhance the resilience of low-rank representation (LRR) based clustering against outliers.

Main Methods:

• Proposed information theoretic objective functions combining structured low-rank representations (LRRs) and outlier-handling measures.
• Justification of group sparsity-induced measures (l2,1-norm, lα-norm, correntropy) via half-quadratic (HQ) optimization.
• Development of information theoretic subspace clustering algorithms using correntropy and Parzen window estimation for outlier detection.

Main Results:

• A unified framework for HQ-based group sparsity methods was established.
• Correntropy-based methods demonstrated effectiveness in handling outliers under various distributions.
• Pairwise link constraints were successfully integrated as prior structure for LRRs.
• Iterative algorithms were developed to solve non-convex information theoretic loss functions.

Conclusions:

• The proposed methods significantly improve the robustness of LRR subspace clustering.
• Experimental results on benchmark datasets show superior performance compared to state-of-the-art methods.
• The approach offers a promising direction for handling complex, noisy data in subspace clustering.