Exponential sparsity preserving projection with applications to image recognition

Abstract Sparsity preserving projection (SPP), as a widely used linear unsupervised dimensionality reduction (DR) method, is designed to preserve the sparse reconstructive relationship of the raw data. SPP constructs an affinity weight matrix by solving a sparse representation model which does not need any parameters. Moreover, the obtained projection may contain some discriminating information even if no prior knowledge is provided. Although SPP may be more conveniently used in practice due to these advantages, it still suffers from the so-called small-sample-size problem as may other DR methods do. To solve this problem, we propose an exponential sparsity preserving projection (ESPP) by using matrix exponential, and present two efficiently numerical methods for solving the corresponding large-scale matrix exponential eigenvalue problem. ESPP avoids the singularity of the coefficient matrices, and obtains more valuable information for the SPP. Image recognition experiments are conducted on several real-world image databases and the experimental results illustrate the outperformances of ESPP.