Convex Sparse Spectral Clustering: Single-View to Multi-View.

Area of Science:

• Machine Learning
• Data Mining
• Computer Vision

Background:

• Spectral clustering (SC) is a prevalent technique for data clustering.
• SC involves embedding data into a lower dimension using eigenvectors of the Laplacian matrix, followed by k-means clustering.

Purpose of the Study:

• To introduce a sparse spectral clustering (SSC) method by incorporating sparse regularization on the data embedding.
• To develop a convex relaxation for the non-convex SSC model to enable efficient computation.
• To extend SSC to pairwise SSC for enhanced clustering using multi-view data.

Main Methods:

• Proposed sparse regularization on UU^T, where U is the data embedding.
• Introduced a convex relaxation of the non-convex SSC model using convex hull of fixed rank projection matrices.
• Employed the alternating direction method of multipliers (ADMM) for efficient optimization of the convex SSC model.
• Developed pairwise SSC to leverage multi-view information for improved clustering.

Main Results:

• The proposed sparse regularization on UU^T aims for a block-diagonal structure, indicating sparsity.
• The convex relaxation allows for efficient solving of the SSC model.
• Pairwise SSC demonstrates improved clustering performance by utilizing multi-view data.
• Experimental results on real-world datasets validate the effectiveness of the proposed SSC and pairwise SSC methods compared to baselines.

Conclusions:

• The developed sparse spectral clustering (SSC) methods offer effective solutions for data clustering.
• The convex relaxation and ADMM provide an efficient computational framework for SSC.
• Pairwise SSC effectively enhances clustering by integrating multi-view information, demonstrating the versatility of the proposed approach.