Supervised locally linear embedding algorithm based on orthogonal matching pursuit

Supervised locally linear embedding (SLLE) has been proposed for classification tasks. SLLE can take full use of the label information and select neighbours only in the same class. However, SLLE uses the least squares (LSs) method for solving a set of linear equations to obtain linear representation coefficients, which relates to the inverse of a matrix. If the matrix is singular, the solution to the set of linear equations does not exist. Additionally, if the size of neighbourhood is not appropriate, some further neighbours along the manifold would be selected. To remedy those, this study deals with SLLE based on orthogonal matching pursuit (SLLE-OMP) by introducing OMP into SLLE. In SLLE-OMP, LS is replaced by OMP and OMP can reselect new neighbours from old ones. Experimental results on some real-world datasets show that SLLE-OMP can achieve better classification performance compared with SLLE.