Methods for Factorization and Approximation of Tensors by Partial Fiber Sampling

CESAR F. CAIAFA; ANDRZEJ CICHOCKI

Aruba, DUTCH ANTILLES

Workshop; CAMSAP 2009 (3rd International Workshop on Computational Advances in Multi-Sensor Adaptive Processing); 2009

IEEE

In this paper we present, discuss and compare new methods for the reconstruction of tensors by partial sampling, i.e. based on the information contained only in a subset of their entries. As a generalization of the CUR matrix decomposition, which approximates a matrix from a subset of its rows and columns, we present two methods called Tree-CUR and FSTD (Fiber Sampling Tensor Decomposition) for estimating a tensor by using a subset of its n-mode fibres, i.e. some row, column and tube fibers for a 3-dimensional tensor case. As our experimental results show, these new methods are potentially useful tools for signal processing with huge datasets since they provide fast algorithms for calculating low-rank approximations without needing to sample the whole dataset.