Approximate rank-detecting factorization of low-rank tensors

Author

Kiraly, Franz J. ; Ziehe, Andreas

Author_Institution

Machine Learning Group, Berlin Inst. of Technol. (TU Berlin), Berlin, Germany

fYear

2013

Firstpage

3938

Lastpage

3942

Abstract

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the gold standard PARAFAC over which it has the advantages that it can intrinsically detect the true rank, avoids spurious components, and is stable with respect to outliers and non-Gaussian noise.

Keywords

Gaussian noise; singular value decomposition; tensors; AROFAC2; CP-rank; degree 3 tensor; gold standard PARAFAC; low-rank tensors; nonGaussian noise; outliers; rank-detecting factorization; rank-one components; real world data; spurious components; synthetic data; true rank; Approximation algorithms; Clustering algorithms; Covariance matrices; Loading; Matrix decomposition; Signal processing algorithms; Tensile stress; Approximate Algebra; Simultaneous Diagonalization; Tensor Decomposition; Tensor Factorization;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on

Conference_Location

Vancouver, BC

ISSN

1520-6149

Type

conf

DOI

10.1109/ICASSP.2013.6638397

Filename

6638397