Department of Statistics, University of California, Irvine, California.
Shanghai University of Finance and Economics, Shanghai, China.
Biometrics. 2021 Sep;77(3):890-902. doi: 10.1111/biom.13354. Epub 2020 Aug 24.
We propose a novel regularized mixture model for clustering matrix-valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (eg, low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix-normal distributions with regularization terms, and then develop an expectation maximization type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution.
我们提出了一种新的正则化混合模型，用于聚类矩阵数据。该方法假设每个聚类的协方差结构可分，并对每个聚类的均值信号施加稀疏结构（例如，低秩性，空间稀疏性）。我们将该问题表述为矩阵正态分布的有限混合模型，并带有正则化项，然后开发了一种期望最大化类型的算法，以进行有效的计算。从理论上讲，我们证明了对于各种惩罚函数的选择，所提出的估计量都是强一致的。模拟和对脑信号研究的两个应用证实了该方法的出色性能，包括比竞争对手更高的预测准确性以及解决方案的科学可解释性。
