Pattern recognition in multilinear space and its applications: mathematics, computational algorithms and numerical validations

详细信息    查看全文

• 作者：Hayato Itoh ; Atsushi Imiya ; Tomoya Sakai
• 关键词：Dimension reduction ; Principal component analysis ; Tensor principal component analysis ; Singular value decomposition ; Discrete cosine transform
• 刊名：Machine Vision and Applications
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：27
• 期：8
• 页码：1259-1273
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Pattern Recognition; Image Processing and Computer Vision; Communications Engineering, Networks;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1769
• 卷排序：27

文摘

We clarify the mathematical equivalence between low-dimensional singular value decomposition and low-order tensor principal component analysis for two- and three-dimensional images. Furthermore, we show that the two- and three-dimensional discrete cosine transforms are, respectively, acceptable approximations to two- and three-dimensional singular value decomposition and classical principal component analysis. Moreover, for the practical computation in two-dimensional singular value decomposition, we introduce the marginal eigenvector method, which was proposed for image compression. For three-dimensional singular value decomposition, we also show an iterative algorithm. To evaluate the performances of the marginal eigenvector method and two-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for six datasets of two-dimensional image patterns. To evaluate the performances of the iterative algorithm and three-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for datasets of gait patterns and human organs. For two- and three-dimensional images, the two- and three-dimensional discrete cosine transforms give almost the same recognition rates as the marginal eigenvector method and iterative algorithm, respectively.