Collaborative Representation Based Discriminant Local Preserving Projection

Linear dimensionality reduction techniques have been applied widely in data classification and recognition to extract low-dimensional features. The methods exploit a simple linear function to transform high dimensional data into a low dimensional subspace while preserving the statistical or geometrical characteristics of high dimensional datasets. The neighborhood relationship is one of the most important geometrical characteristics. The original dimensionality reduction algorithms usually set neighborhood parameters manually when defining neighborhood relationships. However, the methods based on collaborative representation select the neighbors automatically. A supervised dimensionality reduction method proposed in this paper is named Collaborative Representation based Discriminant Local Preserving Projection (CR-DLPP). First, it uses collaborative representation to select potential neighbors automatically for samples reconstruction. Then, a similarity matrix is built by calculating the Gaussian distance between the reconstructed samples. Finally, the Maximum Margin Criterion (MMC) is adopted to design an objective function, and the optimal projection matrix is obtained via eigenvalue decomposition. The results of extensive experiments on several benchmark datasets show that CR-DLPP can achieve better performance than several other typical linear dimensionality reduction methods.