Global and Local Similarity Learning in Multi-Kernel Space for Nonnegative Matrix Factorization

Area of Science:

• Machine Learning
• Data Mining
• Pattern Recognition

Background:

• Existing nonnegative matrix factorization (NMF) methods often fail to fully utilize global and local similarity information.
• Clustering algorithms benefit from enhanced intra-class similarity and inter-class separability.

Purpose of the Study:

• To propose a novel local similarity learning approach within the convex NMF framework.
• To improve clustering performance by enhancing both intra-class similarity and inter-class separability.
• To develop an integrated model for simultaneous learning of cluster structure, representation, and optimal kernel.

Main Methods:

• A novel local similarity learning approach is proposed within the convex NMF framework.
• The model learns factor matrices in an augmented kernel space using a convex combination of pre-defined kernels with auto-learned weights.
• Multiplicative updating rules are developed with theoretical convergence guarantees.

Main Results:

• The proposed model effectively enhances intra-class similarity and inter-class separability.
• Simultaneous global and local learning leads to more informative data representations.
• Experimental results validate the effectiveness of the new NMF model.

Conclusions:

• The integrated approach of local similarity learning in convex NMF offers significant advantages for clustering.
• The model's ability to mutually enhance cluster structure, representation, and kernel learning leads to superior performance.
• This method provides a powerful tool for data analysis requiring robust clustering and informative feature extraction.