Nonparametric Estimation of Probabilistic Membership for Subspace Clustering

Area of Science:

• Data Science
• Machine Learning
• Computer Vision

Background:

• Modern subspace clustering methods construct affinity matrices via sparse or low-rank optimization.
• Traditional affinity matrices are unsuitable for direct application of spectral clustering.
• Existing methods often use unclear affinity rearrangements before spectral clustering.

Purpose of the Study:

• To develop a nonparametric method for estimating probabilistic cluster membership directly from subspace clustering affinity matrices.
• To replace the spectral clustering step in subspace clustering with a more robust probabilistic approach.
• To improve the overall performance of subspace clustering methods.

Main Methods:

• A nonparametric likelihood is defined based on histograms and probabilistic membership.
• Probabilistic membership is modeled as a combination of probability simplices.
• A maximum a posteriori (MAP) estimation with a Bernoulli prior regularizes membership.
• Discrete cluster membership is determined by selecting maximum probability clusters.

Main Results:

• The proposed method effectively estimates probabilistic cluster membership.
• It bypasses the need for spectral clustering and affinity value rearrangement.
• State-of-the-art performance is achieved on benchmark databases for subspace clustering.

Conclusions:

• The nonparametric probabilistic membership estimation offers a superior alternative to spectral clustering in subspace clustering.
• This method provides a theoretically sound and practically effective way to derive clusters from modern affinity matrices.
• The approach demonstrates significant performance gains across various subspace clustering techniques.