Orthogonal sparsity preserving projections for feature extraction

Sparse representation has been extensively studied in the signal processing community, which surprisingly pointed out that one target signal can be accurately represented as a linear combination of very few measurement signals, often called atoms, in a given dictionary. This discovery has soon been employed to the field of pattern recognition and more recently, given rise to a newly developed unsupervised feature extraction method named sparsity preserving projections (SPP), which aims at seeking a linear embedded space where the sparse reconstructive relations among the data in the dictionary can be preserved. However, SPP is non-orthogonal and still has some space for improvement. Specially, by taking into consideration the preservation of some neat property of a dictionary, this paper presents an orthogonal sparsity preserving projections (OSPP). OSPP iteratively calculate a projective vector which can preserve the sparse reconstructive relations as SPP dose, and at the same enforcing it to be orthogonal to all previously obtained vectors. Empirical study shows that OSPP has more powerful sparsity preserving ability than SPP and hence is expected to have better classification performance, since sparsity is potentially related to discrimination. Experiments on the public Yale face databases validate the effectiveness of OSPP, as compared with several representative unsupervised feature extraction methods.