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Area of Science:

Machine Learning
Data Mining
Computer Vision

Background:

Subspace clustering aims to group data points belonging to underlying subspaces.
Existing methods like sparse subspace clustering and low-rank representation have limitations.
Many methods implicitly rely on a block diagonal property for correct clustering.

Purpose of the Study:

To provide a unified theoretical guarantee for the block diagonal property in subspace clustering.
To develop a novel method that directly enforces the block diagonal structure.
To improve the accuracy and robustness of subspace clustering algorithms.

Main Methods:

A general formulation for subspace clustering is proposed, unifying existing approaches.
A novel block diagonal matrix induced regularizer is introduced.
Block Diagonal Representation (BDR) model is developed using the regularizer.
An alternating minimization solver is proposed for the nonconvex BDR model.

Main Results:

A unified theoretical guarantee for the block diagonal property is established.
The proposed BDR method directly pursues the block diagonal structure.
The alternating minimization solver for BDR is proven to converge.
Experiments demonstrate the effectiveness of BDR on real-world datasets.

Conclusions:

The BDR method offers a principled and effective approach to subspace clustering.
The unified theoretical framework advances the understanding of existing subspace clustering techniques.
BDR shows superior performance compared to existing methods in practice.