@article{(Open Science Index):https://publications.waset.org/pdf/14985,
	  title     = {An Improved Algorithm for Calculation of the Third-order Orthogonal Tensor Product Expansion by Using Singular Value Decomposition},
	  author    = {Chiharu Okuma and  Naoki Yamamoto and  Jun Murakami},
	  country	= {},
	  institution	= {},
	  abstract     = {As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.
},
	    journal   = {International Journal of Computer and Information Engineering},
	  volume    = {4},
	  number    = {2},
	  year      = {2010},
	  pages     = {193 - 202},
	  ee        = {https://publications.waset.org/pdf/14985},
	  url   	= {https://publications.waset.org/vol/38},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 38, 2010},
	}