Locally linear embedding based on local correlation

The task of nonlinear dimensionality reduction is to find meaningful low-dimensional structures hidden in high dimensional data. In this paper, an unsupervised algorithm for nonlinear dimensionality reduction called locally linear embedding based on local correlation (LC-LLE) is presented. The LC-LLE algorithm is motivated by locally linear embedding (LLE) algorithm and correlation coefficient which usually gives the correlation between two random vectors. It is a major advantage of the LC-LLE to optimize the process of dimensionality reduction by giving more reasonable neighbor searching. Simulation studies demonstrate that the LC-LLE can give better results in dimension reduction than LLE. Experiments on face images data sets have shown the potential of LC-LLE in practical problem.