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.