Adaptive Neighborhood For Nonlinear Dimensionality Reduction Algorithms

Dimensionality Reduction is an important branch of computer science and applied mathematics.From the 21 stcentury,as a company of the development of the computer & Internet technology,the databases we can obtain have so high dimension and large amount.When we face old problems on high-dimensional big data,some algorithms which we knew before won't work or be able to run directly because of the tremendous cost of calculation.In order to reach the most significant information from high-dimensional data,scientists design some of dimensionality reduction algorithms,such as the Principal Component Analysis,Multidimensional Scaling,Locally Linear Embedding and so on.PCA and MDS are two linear dimensionality reduction algorithms,and the linearity assumption of them make it limited to use them in some circumstances.Nonlinear dimensionality reduction algorithms,taken LLE as an example,are discovered and used from the 21 st century.The development of nonlinear dimensionality reduction algorithms is on behalf of the boom of DR.Many algorithms,such as LLE,are involved in the choice of neighbor points,i.e.how to define neighborhood area.The most popular methods,k-neighbor method & epsilon-neighbor method are both too positive to choose a fine parameter.If we have little knowledge of the structure of database,blindly choosing the parameter may lead to bad results.In this paper,we will try to find a way of defining neighbors without positively giving a parameter to the algorithm,which comes from the h-index,an important index in journal ranking.This thesis will also introduce an improvement of LLE & MDS,namely Locally Distance-kept Amendment,after the explanation of those algorithms,and try to give an amelioration of the result of dimensionality reduction of traditional algorithms.