Methods for factorization and approximation of Tensors by partial Fiber Sampling

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.