We consider the problem of extracting a common structure from multiple tensor data sets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs a common basis represented by linear combinations of the original variables that lose little information of the multiple tensor data sets. We also develop an estimation algorithm for MCCA that guarantees mode-wise global convergence. Numerical studies are conducted to show the effectiveness of MCCA.

中文翻译：

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通过 Kronecker 乘积表示进行多线性公共分量分析

我们考虑从多个张量数据集中提取公共结构的问题。为此，我们提出了基于模式协方差矩阵的 Kronecker 乘积的多线性公共分量分析 (MCCA)。MCCA 构建了一个公共基，由原始变量的线性组合表示，这些变量丢失了多张量数据集的很少信息。我们还为 MCCA 开发了一种估计算法，以保证模式方式的全局收敛。进行了数值研究以显示 MCCA 的有效性。