LAPLACIAN PRINCIPAL COMPONENTS ANALYSIS (LPCA)

Systems and methods perform Laplacian Principal Components Analysis (LPCA). In one implementation, an exemplary system receives multidimensional data and reduces dimensionality of the data by locally optimizing a scatter of each local sample of the data. The optimization includes summing weighted distances between low dimensional representations of the data and a mean. The weights of the distances can be determined by a coding length of each local data sample. The system can globally align the locally optimized weighted scatters of the local samples and provide a global projection matrix. The LPCA improves performance of such applications as face recognition and manifold learning.