Completion of High Order Tensor Data with Missing Entries via Tensor-train Decomposition

TL;DR

This paper introduces TT-WOPT, an efficient tensor-train based algorithm for completing high-order tensor data with missing entries, outperforming existing methods especially at very high missing rates.

Contribution

The paper proposes a novel tensor-train decomposition based algorithm, TT-WOPT, that effectively handles high-order tensor completion with missing data, overcoming the curse of dimensionality.

Findings

Outperforms existing methods on synthetic and natural image data.

Maintains high accuracy even with missing rates of 85% to 99%.

Demonstrates linear scalability to tensor order.

Abstract

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this problem, we propose an efficient algorithm called TT-WOPT (Tensor-train Weighted OPTimization) to find the latent core tensors of tensor data and recover the missing entries. Tensor-train decomposition, which has the powerful representation ability with linear scalability to tensor order, is employed in our algorithm. The experimental results on synthetic data and natural image completion demonstrate that our method significantly outperforms the other related methods. Especially when the missing rate of data is very high, e.g., 85% to 99%, our algorithm can achieve much better performance than other state-of-the-art algorithms.