A Sampling-Based Method for Tensor Ring Decomposition

We propose a sampling based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the special structure of TR tensors, we can efficiently estimate the leverage scores and attain a method which has complexity sublinear in the number of input tensor entries. We provide relative error high probability guarantees for the sampled least squares problems. We compare our proposal to existing methods in experiments on both synthetic and real data. The real data comes from hyperspectral imaging, video recordings, and a subset of the COIL-100 image dataset. Our method achieves substantial speedup---sometimes two or three orders of magnitude---over competing methods, while maintaining good accuracy.