Convex Subspace Clustering by Adaptive Block Diagonal Representation.

Area of Science:

• Computer Science
• Machine Learning
• Data Mining

Background:

• Subspace clustering methods aim to discover clusters in data subspaces.
• Spectral-type approaches are a key subclass, relying on learning a coefficient matrix with block diagonal structure.
• Existing methods indirectly or directly impose structure priors, each with limitations.

Purpose of the Study:

• To propose a novel subspace clustering method, Adaptive Block Diagonal Representation (ABDR).
• To address the limitations of existing methods by explicitly enforcing block diagonality without sacrificing convexity.
• To adaptively determine the number of blocks in the coefficient matrix.

Main Methods:

• ABDR explicitly pursues block diagonality, inspired by Convex BiClustering.
• It fuses columns and rows of the coefficient matrix using a specialized convex regularizer.
• This approach ensures block diagonality even with noisy data while preserving convexity.

Main Results:

• ABDR successfully enforces block diagonal structure.
• The method adaptively determines the number of blocks.
• Experimental results show ABDR's superiority over state-of-the-art methods on synthetic and real datasets.

Conclusions:

• ABDR offers a robust and effective approach to subspace clustering.
• It combines the strengths of direct and indirect structure imposition methods.
• The proposed method demonstrates significant improvements in clustering performance.