@article{(Open Science Index):https://publications.waset.org/pdf/2000,
	  title     = {Comparison between Higher-Order SVD and Third-order Orthogonal Tensor Product Expansion},
	  author    = {Chiharu Okuma and  Jun Murakami and  Naoki Yamamoto},
	  country	= {},
	  institution	= {},
	  abstract     = {In digital signal processing it is important to
approximate multi-dimensional data by the method called rank
reduction, in which we reduce the rank of multi-dimensional data from
higher to lower. For 2-dimennsional data, singular value
decomposition (SVD) is one of the most known rank reduction
techniques. Additional, outer product expansion expanded from SVD
was proposed and implemented for multi-dimensional data, which has
been widely applied to image processing and pattern recognition.
However, the multi-dimensional outer product expansion has behavior
of great computation complex and has not orthogonally between the
expansion terms. Therefore we have proposed an alterative method,
Third-order Orthogonal Tensor Product Expansion short for 3-OTPE.
3-OTPE uses the power method instead of nonlinear optimization
method for decreasing at computing time. At the same time the group
of B. D. Lathauwer proposed Higher-Order SVD (HOSVD) that is
also developed with SVD extensions for multi-dimensional data.
3-OTPE and HOSVD are similarly on the rank reduction of
multi-dimensional data. Using these two methods we can obtain
computation results respectively, some ones are the same while some
ones are slight different. In this paper, we compare 3-OTPE to
HOSVD in accuracy of calculation and computing time of resolution,
and clarify the difference between these two methods.},
	    journal   = {International Journal of Computer and Information Engineering},
	  volume    = {3},
	  number    = {3},
	  year      = {2009},
	  pages     = {533 - 539},
	  ee        = {https://publications.waset.org/pdf/2000},
	  url   	= {https://publications.waset.org/vol/27},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 27, 2009},
	}