Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics

Li, Jiao‐fen; Wen, Ya-qiong; Zhou, Xue‐lin; Wang, Kai

doi:10.1155/2020/3054764

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…Because 1 M Diag(W) is not a symmetric matrix, ( 22) cannot be solved as a kernel k-means clustering problem. Noting it is similar to the optimization problem on Stiefel manifold in [27], thus we adopt the Riemann conjugate gradient method proposed in [27] to solve (22).…”

Section: Optimization Algorithmmentioning

confidence: 99%

One-step Multiple Kernel k−means Clustering Based on Block Diagonal Property

Chen

Jian

2023

Preprint

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Multiple kernel k-means clustering (MKKC) can effiffifficiently incorporate multiple base kernels to generate an optimal kernel. However, many existing MKKC methods all need two-step operation: learning clustering indicator matrix and performing clustering on it. These results are not necessarily optimal because the optimal values of two steps are not equivalent to those of original problem. To address this issue, in this paper we propose a novel algorithm named one-step multiple kernel k-means clustering based on block diagonal property(OSMKKC-BD). By imposing a block diagonal constraint on the product of indicator matrix and its transpose and enhancing its block diagonalization, this algorithm can promote the indicator matrix to get explicit clustering indicator, so as to implement one-step clustering. Furthermore, a simple kernel weighting strategy is used to obtain an optimal kernel, and boosts the quality of optimal kernel. In addition, a three-step iterative algorithm is designed to solve the corresponding optimization problem, in which the Riemann conjugate gradient iterative method is used to solve the optimization problem about the indicator matrix. Finally, by extensive experiments on ten real data sets and comparison of clustering results with the state-of-the-art MKKC methods, it is concluded that OSMKKC-BD is effffective.

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Section: Optimization Algorithmmentioning

confidence: 99%