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.

中文翻译：

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正则化矩阵数据聚类及其在图像分析中的应用

我们提出了一种新的正则化混合模型，用于对矩阵值数据进行聚类。所提出的方法为每个簇假定一个可分离的协方差结构，并为每个簇的平均信号强加一个稀疏结构（例如，低秩、空间稀疏）。我们将问题表述为具有正则化项的矩阵正态分布的有限混合模型，然后开发一种用于高效计算的期望最大化类型的算法。理论上，我们证明了所提出的估计量对于惩罚函数的各种选择是高度一致的。模拟和脑信号研究的两个应用证实了所提出方法的出色性能，包括比竞争对手更好的预测精度和解决方案的科学解释性。