高阶张量特征提取的矩阵乘积状态
Matrix Product State for Feature Extraction of Higher-Order Tensors
摘要：
本文介绍了矩阵乘积状态（MPS）分解作为一种计算工具，用于提取由高阶张量表示的多维数据的特征。无论张量阶数如何，MPS都将其相关特征提取到所谓的最大阶数为3的核心张量中，该核心张量可用于分类。MPS主要基于连续序列的奇异值分解（SVD），实现起来非常简单，无需任何递归过程来优化局部张量。因此，与其他张量特征提取方法（诸如基于Tucker分解（TD）的高阶正交迭代（HOOI））相比，它导致大量的计算节省。基准测试结果表明，MPS可以显着减少数据的特征空间，同时实现更好的分类性能相比，HOOI。
英文摘要：
This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to the so-called core tensor of maximum order three which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement without any recursive procedure needed for optimizing local tensors. Thus, it leads to substantial computational savings compared to other tensor feature extraction methods such as higher-order orthogonal iteration (HOOI) underlying the Tucker decomposition (TD). Benchmark results show that MPS can reduce significantly the feature space of data while achieving better classification performance compared to HOOI.
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