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

Simple multiple kernel k-means (SMKKM) introduces a new minimization-maximization learning paradigm for multi-view clustering and makes remarkable achievements in some applications. As one of its variants, localized SMKKM (LSMKKM) is recently proposed to capture the variation among samples, focusing on reliable pairwise samples, which should keep together and cut off unreliable, farther pairwise ones. Though demonstrating effectiveness, we observe that LSMKKM indiscriminately utilizes the variation of each sample, resulting in unsatisfying clustering performance. To overcome this limitation, we propose a sample adaptive localized SMKKM (SAL-SMKKM) algorithm where the weight of the local alignment for each sample can be adaptively adjusted, resulting in a more challenging tri-level minimization-minimization-maximization. To deal with it, we reformulate it into a minimization problem of an optimal function characterized by minimization-maximization dynamics, prove its differentiability, and develop a reduced gradient descent method to optimize it. We then theoretically analyze the clustering performance of the proposed SAL-SMKKM by deriving its generalization error bound. In addition, we empirically evaluate the clustering performance of the proposed SAL-SMKKM on several benchmark datasets. Experiment results clearly indicate that proposed algorithms consistently outperform state-of-the-art ones. Finally, we apply the proposed SAL-SMKKM to the multi-modal parcellation of the human cerebral cortex, which is essential and helpful to understanding brain organization and function. As seen, SAL-SMKKM achieves accurate parcellation in an automatic and objective manner without any manual intervention, which once again demonstrates its validity and effectiveness in practical applications. The codes of SAL-SMKKM is publicly accessed at: https://github.com/xinwangliu/LocalizedSMKKM.