Improving Sparse Representation-Based Classification Using Local Principal Component Analysis

TL;DR

This paper enhances sparse representation-based classification by incorporating local principal component analysis to adapt dictionaries for better accuracy on nonlinear and sparsely sampled data.

Contribution

It introduces a novel local PCA-based method to enlarge the training set and improve SRC performance on complex data manifolds.

Findings

Achieves higher accuracy than traditional SRC on synthetic and face datasets.

Effective in cases of sparse sampling and nonlinear class manifolds.

Improves robustness under dimension reduction.

Abstract

Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes test samples can be written as linear combinations of their same-class training samples, the success of SRC depends on the size and representativeness of the training set. Our proposed classification algorithm enlarges the training set by using local principal component analysis to approximate the basis vectors of the tangent hyperplane of the class manifold at each training sample. The dictionary in SRC is replaced by a local dictionary that adapts to the test sample and includes training samples and their corresponding tangent basis vectors. We use a synthetic data set and three face databases to demonstrate that this method can achieve higher classification accuracy than SRC in cases of sparse sampling, nonlinear class manifolds, and stringent dimension reduction.