Sample Adaptive Localized Simple Multiple Kernel K-Means and its Application in Parcellation of Human Cerebral Cortex

Area of Science:

• Machine Learning
• Computer Vision
• Computational Neuroscience

Background:

• Simple multiple kernel k-means (SMKKM) and its variant localized SMKKM (LSMKKM) are effective for multi-view clustering.
• LSMKKM's limitation is its indiscriminate use of sample variation, leading to suboptimal clustering.
• Existing methods struggle to adaptively handle sample-specific variations in multi-view clustering.

Purpose of the Study:

• To propose a novel algorithm, SAL-SMKKM, that adaptively adjusts local alignment weights for each sample.
• To address the limitations of LSMKKM by introducing a sample-adaptive approach.
• To improve the performance and robustness of multi-view clustering algorithms.

Main Methods:

• Developed a sample adaptive localized SMKKM (SAL-SMKKM) algorithm with a tri-level minimization-minimization-maximization objective.
• Reformulated the problem into a differentiable minimization problem solvable with a reduced gradient descent method.
• Provided theoretical analysis of SAL-SMKKM's generalization error bound.

Main Results:

• SAL-SMKKM consistently outperforms state-of-the-art algorithms on benchmark datasets.
• Empirical evaluations demonstrate significant improvements in clustering performance.
• The algorithm achieves accurate, automatic, and objective multi-modal parcellation of the human cerebral cortex.

Conclusions:

• SAL-SMKKM effectively addresses the limitations of previous methods by adaptively weighting sample variations.
• The proposed algorithm offers superior clustering performance and demonstrates practical utility in neuroscience.
• SAL-SMKKM provides a valid and effective approach for complex multi-view clustering tasks.