One-Stage Shifted Laplacian Refining for Multiple Kernel Clustering.

Area of Science:

• Machine Learning
• Data Mining
• Clustering Algorithms

Background:

• Multiple kernel clustering (MKC) leverages graph learning for similarity structure analysis.
• Existing MKC methods use a "three-stage" scheme, leading to information distortion and compromised clustering accuracy.
• Simultaneous preservation of Laplacian reconstruction energy and cluster information is challenging in traditional approaches.

Purpose of the Study:

• To propose a novel one-stage shifted Laplacian refining (OSLR) method for multiple kernel clustering (MKC).
• To overcome the limitations of traditional multi-stage MKC methods, specifically information distortion and simultaneous energy preservation.
• To enhance the efficiency and effectiveness of nonlinear clustering tasks.

Main Methods:

• OSLR employs a "one-stage" scheme focusing on Laplacian learning, treating kernel matrices as affinity graphs.
• Each Laplacian is transformed into an approximately shifted Laplacian (ASL) to refine a consensus Laplacian.
• The consensus Laplacian is projected onto a Fantope space to concentrate information on larger eigenvalues.

Main Results:

• Theoretically reduces memory complexity to O(n) and computation complexity to O(n^2).
• Experimental results demonstrate superior performance compared to state-of-the-art MKC methods on benchmark datasets.
• The method effectively preserves reconstruction information and clustering information.

Conclusions:

• The proposed OSLR method offers an efficient and effective solution for multiple kernel clustering.
• This one-stage approach mitigates information distortion inherent in traditional multi-stage methods.
• OSLR advances the field of nonlinear clustering by improving accuracy and computational efficiency.