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Graph Regularized Tensor Train Decomposition

机译：图规则化张量火车分解

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With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high, dimensionality reduction is an important problem. Most of the current tensor dimensionality reduction methods rely on finding low-rank linear representations using different generative models. However, it is well-known that high-dimensional data often reside in a low-dimensional manifold. Therefore, it is important to find a compact representation, which uncovers the low-dimensional tensor structure while respecting the intrinsic geometry. In this paper, we propose a graph regularized tensor train (GRTT) decomposition that learns a low-rank tensor train model that preserves the local relationships between tensor samples. The proposed method is formulated as a non-convex optimization problem on the Stiefel manifold and an efficient algorithm is proposed to solve it. The proposed method is compared to existing tensor based dimensionality reduction methods as well as tensor manifold embedding methods for unsupervised learning applications.
机译：随着数据采集技术的进步，张量对象被收集在包括多媒体，医疗和高光谱成像的各种应用中。随着张量物体的维度通常非常高，减少维度是一个重要问题。大多数电流张量减少方法依赖于使用不同的生成模型找到低级线性表示。然而，众所周知，高维数据通常驻留在低维歧管中。因此，重要的是找到一个紧凑的表示，其在尊重内在几何形状的同时揭示低维张量结构。在本文中，我们提出了一个图形规则化的张力列车（GRTT）分解，用于学习低级张力列车模型，这些模型保留了张量样本之间的局部关系。将所提出的方法配制成Stiefel歧管上的非凸优化问题，提出了一种有效的算法来解决它。将所提出的方法与现有的基于卷的维数减少方法以及无监督学习应用的张量歧管嵌入方法进行比较。

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