论文标题
通过紧张代数的广义视觉信息分析
Generalized Visual Information Analysis via Tensorial Algebra
论文作者
论文摘要
高阶数据是使用条目是固定尺寸的数值阵列的矩阵建模的。这些称为T-scalars的阵列在卷积产物下形成了一个交换环。 T量标准中带有元素的矩阵称为t-矩阵。可以以通常的方式缩放，添加和乘以T-Matrices。有阳性矩阵，正交矩阵和赫尔米利亚对称矩阵的T矩阵概括。使用T-Matrix模型，可以概括许多众所周知的矩阵算法。特别是，T-膜用于概括SVD（单数值分解），HOSVD（高阶SVD），PCA（主要组件分析），2DPCA（二维PCA）和GCA（Grassmannian组件分析）。广义的T-Matrix算法，即TSVD，THOSVD，TPCA，T2DPCA和TGCA，应用于图像的低级别近似，重建和监督分类。实验表明，T-Matrix算法与标准矩阵算法相比有利。
Higher order data is modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are referred to as t-matrices. The t-matrices can be scaled, added and multiplied in the usual way. There are t-matrix generalizations of positive matrices, orthogonal matrices and Hermitian symmetric matrices. With the t-matrix model, it is possible to generalize many well-known matrix algorithms. In particular, the t-matrices are used to generalize the SVD (Singular Value Decomposition), HOSVD (High Order SVD), PCA (Principal Component Analysis), 2DPCA (Two Dimensional PCA) and GCA (Grassmannian Component Analysis). The generalized t-matrix algorithms, namely TSVD, THOSVD,TPCA, T2DPCA and TGCA, are applied to low-rank approximation, reconstruction,and supervised classification of images. Experiments show that the t-matrix algorithms compare favorably with standard matrix algorithms.
