Equivalence of Non-Iterative Algorithms for Simultaneous Low Rank Approximations of Matrices

Authors:
Kohei Inoue;Kiichi Urahama
Affiliations:
Kyushu University, Japan;Kyushu University, Japan
Venue:
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Year:
2006

Citing 0
Cited 9

Comments on "An analytical algorithm for generalized low-rank approximations of matrices"

Pattern Recognition
Simultaneous tensor subspace selection and clustering: the equivalence of high order svd and k-means clustering

Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Robust Simultaneous Low Rank Approximation of Tensors

PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
n-Mode Singular Vector Selection in Higher-Order Singular Value Decomposition

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Generalized low-rank approximations of matrices revisited

IEEE Transactions on Neural Networks
Bilinear Lanczos components for fast dimensionality reduction and feature extraction

Pattern Recognition
Matrix-variate and higher-order probabilistic projections

Data Mining and Knowledge Discovery
Are tensor decomposition solutions unique? on the Global convergence HOSVD and parafac algorithms

PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part I
A unified view of two-dimensional principal component analyses

SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition

Quantified Score

Hi-index	0.01

Visualization

Abstract

Recently four non-iterative algorithms for simultaneous low rank approximations of matrices (SLRAM) have been presented by several researchers. In this paper, we show that those algorithms are equivalent to each other because they are reduced to the eigenvalue problems of row-row and column-column covariance matrices of given matrices. Also, we show a relationship between the non-iterative algorithms and another algorithm which is claimed to be an analytical algorithm for the SLRAM. Experimental results show that the analytical algorithm does not necessarily give the optimal solution of the SLRAM.