Application Of Dimensionality Reduction Via Local Smoothness Assumption

With the development of society,high dimensional data process is playing a more and more important role in people's life.But in many practical problems,high dimensional data process is very difficult.In this context,dimensionality reduction becomes more and more popular in the field of high dimensional data process as the times require.This paper first reviews the basic concepts and the development history of semi-supervised learning,introducing the basic concepts of graph-based semi-supervised learning and mapping method,and then put forward the innovation of the generalized Laplace matrix.Using the generalized Laplace matrix we build a new graph-based semi-supervised learning regularization model.Moreover,this paper put forward a linear dimensionality reduction algorithm via local smoothness assumption.The main contribution can be summarized into the following two parts:1.Put forward the innovation of the generalized Laplace matrix and build a new graph-based semi-supervised learning regularization model.Because the model is a convex optimization problem,it can guarantee the solution of the model is a closed form solution.Also,this article use mathematical reasoning and experiments to show the new algorithm's local smoothness can satisfy the smoothness assumptions of graph-based semi-supervised learning,also it can obtain higher classification accuracy rate.2.Put forward a linear dimensionality reduction algorithm via local smoothness assumption.By detecting the geometric distribution of the examples in a local region,local smoothness term transfers the neighborhood structural information carried by the original data to the lowdimensional space.The strength of the proposed method is validated by applying it to face recognition problem on typical databases,including FERET,Yale,ORL and AVIRIS repositories.