MPCA: Multilinear Principal Component Analysis of Tensor Objects

TLDR

Computer vision and pattern recognition tasks often involve 2‑D/3‑D images and video sequences that are naturally represented as tensors or multilinear arrays. The paper proposes a multilinear principal component analysis (MPCA) framework for extracting features from tensor objects, including dimensionality selection methods and a discriminative tensor feature selection mechanism for gait recognition. MPCA extracts features by iteratively computing multilinear projections that capture most tensor variation, decomposing the problem into projection subproblems, and incorporating dimensionality selection and discriminative feature selection for classification. MPCA outperforms classical PCA and 2‑D PCA, proving its effectiveness as a feature extractor and delivering competitive gait recognition performance comparable to state‑of‑the‑art methods.

Abstract

This paper introduces a multilinear principal component analysis (MPCA) framework for tensor object feature extraction. Objects of interest in many computer vision and pattern recognition applications, such as 2-D/3-D images and video sequences are naturally described as tensors or multilinear arrays. The proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation. The solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems. As part of this work, methods for subspace dimensionality determination are proposed and analyzed. It is shown that the MPCA framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis (PCA) and its 2-D variant (2-D PCA). Finally, a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy, and applied to the problem of gait recognition. Results presented here indicate MPCA's utility as a feature extraction tool. It is shown that even without a fully optimized design, an MPCA-based gait recognition module achieves highly competitive performance and compares favorably to the state-of-the-art gait recognizers.