Local Tensor Completion Based on Locality Sensitive Hashing

Abstract

Tensor completion can be applied to fill in the missing data, which is import for many data applications where the data are incomplete. To infer the missing data, existing tensorcompletion algorithms generally assume that the tensor data have global low-rank structure and apply a single model to fit the overall observed data through the global optimization. However, there are different correlation levels among application data, thus the ranks of some sub-tensors can be even lower relative to that of the large tensor. Fitting a single model to all data will compromise the performance of data recovery. To increase the accuracy in missing data recovery, we propose to apply local tensor completion (Local-TC) to recover data from sub-tensors, with each containing data of higher correlations. Although promising, as the tensor data are only organized logically, it is difficult to determine the relationship among data. We propose to exploit locality-sensitive hash (LSH) to quickly find the data correlation and reorganize tensor data, based on which data entries with high correlations are put into the same sub-tensor. The experiment results demonstrate that Local-TC is very effective in increasing the recovery accuracy.