Non Orthogonal Tensor Diagonalization, a Tool for Block Tensor Decompositions
This paper presents algorithms for non orthogonal tensor diagonalization, which can be used for block tensor decomposition. The diagonalization can be performed along two or more tensor dimensions simultaneously. The method seeks for one diagonalizing matrix of determinant 1 for each mode that together convert a given tensor into a tensor that meets a block revealing condition. Perturbation analysis of the algorithm showing how small changes in the tensor translate in small changes of the diagonalization outcome is provided. The algorithm has a low computational complexity, comparable to complexity of the fastest available canonical polyadic decomposition algorithms. For example, the diagonalization of order 3 tensor of the size NxNxN has the complexity of the order O(N^4) per iteration. If the tensor has a different shape, a Tucker compression should be applied prior to the diagonalization. The algorithm can be applied in cumulant based independent subspace decomposition or for tensor deconvolution and feature extraction using the convolutive model.