Robust HOSVD-Based Higher-Order Data Indexing and Retrieval

Abstract

Higher-order singular value decomposition (HOSVD), a natural multilinear extension of the matrix SVD, computes the orthonormal spaces associated with different modes of the tensor. It is widely employed for feature extraction, dimensionality reduction etc. However, due to the vast quantities of tensor entries involved in calculation, it inevitably suffers from high computational cost, especially when recalculation of HOSVD is frequently required. To address the problem, we prove theoretically that the set of HOSVD unitary matrices of a sub-tensor is equivalent to the corresponding subset of HOSVD unitary matrices of the original tensor. Therefore, if we first arrange all tensors in the database compactly as a higher-order tensor, then we only need to conduct HOSVD once on the total tensor. We subsequently propose a robust HOSVD-based multilinear approach for efficiently indexing and retrieving multifactor data, in responding to various query structures. We also apply the proposed method for indexing and retrieval of multi-camera multi-object motion trajectory. Simulation results demonstrate the superior performance of the proposed approach in terms of both robustness and efficiency.