Title :
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
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;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on
Conference_Location :
Vancouver, BC
DOI :
10.1109/ICASSP.2013.6638397
