Graph-Based Multicentroid Nonnegative Matrix Factorization.

Area of Science:

• Machine Learning
• Data Mining
• Computational Geometry

Background:

• Nonnegative matrix factorization (NMF) is a standard data representation technique.
• Traditional NMF-based clustering struggles with complex data geometries due to single-centroid limitations.
• Existing methods fail to preserve local geometric structures in data points.

Purpose of the Study:

• To propose a novel multicentroid-based clustering method, graph-based multicentroid NMF (MCNMF).
• To enhance data clustering by preserving local geometric structures and improving sample membership identification.
• To overcome the limitations of single-centroid NMF in handling complex data distributions.

Main Methods:

• Constructing a neighborhood connection graph between data points and centroids.
• Representing each data point by its adjacent centroids to preserve local geometry.
• Building an undirected connected graph of centroids to form centroid clusters.
• Reconstructing the membership index matrix based on identified centroid clusters.

Main Results:

• MCNMF effectively handles data points in complex geometric structures.
• The method preserves local geometric information crucial for accurate clustering.
• Experimental results on synthetic and benchmark datasets demonstrate MCNMF's superior performance.
• MCNMF outperforms traditional single-centroid-based methods.

Conclusions:

• The proposed MCNMF method offers a significant advancement in NMF-based clustering.
• MCNMF accurately clusters data with complex geometries by utilizing multicentroid representations.
• The method provides a robust solution for sample membership identification in clustering tasks.