Locally linear low-rank tensor approximation

Recently, collecting and storing higher order data has become more feasible with the use of methods from multilinear algebra. High order data usually lies in a low dimensional subspace or manifold along each mode and its intrinsic structure can be revealed by linear methods such as higher order SVD. However, these linear approaches may not capture the local nonlinearities in the data that may occur due to moving sensors or other nonlinearities in the measurements. In this paper, we propose to use a piecewise linear model to better identify the non-linearities in higher order data. The proposed approach decomposes the higher-order data into subtensors and fits a low rank model to each subtensor. The proposed approach is applied to simulated datasets and a video sequence captured across different angles to show its robustness to non-linear structures.