Discrimination of Volumetric Shapes Using Orthogonal Tensor Decomposition
Discrimination of Volumetric Shapes Using Orthogonal Tensor Decomposition
复制标题
使用正交张量分解辨别体积形状
DOI：
10.1007/978-3-030-04747-4_26
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Atsushi Imiya
中科院分区：
文献类型：
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作者：
Hayato Itoh;Atsushi Imiya
医学图像分析中处理的器官、细胞和细胞中的微结构都是体积数据。体积数据的采样值表示为三向阵列数据。从基于主成分分析（PCA）的模式识别的角度出发，为了对多路数据进行定量判别，需要对多路数据阵列的子空间进行距离度量。本文旨在将基于PCA的向量空间模式识别方法扩展到多线性数据的模式识别中。首先，我们将基于向量的模式识别的线性子空间之间的正则角推广到基于张量的模式识别的多线性子空间之间的正则角。此外，利用Stiefel流形之间的传递，我们引入了线性子空间集合的新度量。然后，我们将向量空间中Stiefel流形之间的传输推广到多线性空间中Stiefel流形的传输，用于多路阵列数据的判别分析。
Organs, cells and microstructures in cells dealt with in medical image analysis are volumetric data. Sampled values of volumetric data are expressed as three-way array data. For the quantitative discrimination of multiway forms from the viewpoint of principal component analysis (PCA)-based pattern recognition, distance metrics for subspaces of multiway data arrays are desired. The paper aims to extend pattern recognition methodologies based on PCA for vector spaces to those for multilinear data. First, we extend the canonical angle between linear subspaces for vector-based pattern recognition to the canonical angle between multilinear subspaces for tensor-based pattern recognition. Furthermore, using transportation between the Stiefel manifolds, we introduce a new metric for a collection of linear subspaces. Then, we extend the transportation of between Stiefel manifolds in vector space to the transportation of the Stiefel manifolds in multilinear spaces for the discrimination analysis of multiway array data.