Local Regularized Least-Square Dimensionality Reduction

In this paper, we propose a new nonlinear dimensionality reduction algorithm by adopting regularized least-square criterion on local areas of the data distribution. We first propose a local linear model to describe the characteristic of the low-dimensional coordinates of the neighborhood centered in each data point, and use regularized least-square criterion to evaluate the fitness of the low-dimensional embedding. Next, we form an optimization task similar to the graph Laplacian and efficiently retrieve the solution via eigenvalue decomposition. The relationship between our method and the Laplacian Eigenmaps are discussed, and experimental results are presented.