Multiscale tensor decomposition

Large datasets usually contain redundant information and summarizing these datasets is important for better data interpretation. Higher-order data reduction is usually achieved through low-rank tensor approximation which assumes that the data lies near a linear subspace across each mode. However, non-linearities in the data cannot be captured well by linear methods. In this paper, we propose a multiscale tensor decomposition to better approximate local nonlinearities in tensors. The proposed multiscale approach constructs hierarchical low-rank structure by dividing the tensor into subtensors sequentially and fitting a low-rank model to each subtensor.