Rank-Constrained Spectral Clustering With Flexible Embedding.

Area of Science:

• Data Science
• Machine Learning
• Computer Vision

Background:

• Spectral clustering (SC) is effective but limited by fixed graph structures and suboptimal cluster number determination.
• Traditional SC requires post-processing (rounding) and may not identify the true number of data components.

Purpose of the Study:

• To propose a rank-constrained spectral clustering (SC) with a flexible embedding framework to overcome limitations of existing SC methods.
• To enhance cluster indicator learning and accurately determine the number of clusters.
• To effectively suppress irrelevant information and noise in high-dimensional data.

Main Methods:

• Employs adaptive probabilistic neighborhood learning to recover an ideal block-diagonal affinity matrix.
• Utilizes a flexible embedding scheme to uncover intrinsic cluster structures in a low-dimensional subspace.
• Introduces a rank constraint on the Laplacian matrix to guarantee convergence to the ground truth cluster number.

Main Results:

• The proposed method learns a block-diagonal affinity matrix simultaneously with adaptive graph construction, directly inducing cluster membership.
• The rank constraint ensures the number of clusters converges to the ground truth.
• The flexible embedding and projection learning allows for more freedom in discovering cluster structures.

Conclusions:

• The novel rank-constrained SC method offers superior performance compared to previous SC techniques.
• It effectively addresses limitations in graph structure learning and cluster number determination.
• Experimental results on synthetic and real-world data validate the algorithm's promising performance.