Mahalanobis distance measurement based locally linear embedding algorithm

Euclidean distance is normally used to measure the similarity between samples in locally linear embedding algorithm(LLE). But for some high dimensional data, such as images, Euclidean distance can not accurately reflect the similarity between samples. A Mahalanobis distance metric based locally linear embedding algorithm (MLLE) is proposed. Firstly, MLLE ascertains a Mahalanobis metric from the existing samples. Then, the Mahalanobis metric is used to choose neighborhoods and to reduce the dimensionality of the existing samples and the new samples. The comparison result of MLLE algorithm and some classical manifold based algorithms on ORL and USPS databases proves that MLLE algorithm is effective in recognizing images.