Based Locally Linear Embedding Of High Dimensional Data Dimensionality Reduction

With the development of Science and technology, the dimension of data get more and more high. So, It is very difficult for people to get any useful message from these complex data. Therefore, it is imperative for us to map these high-dimensional data onto a relatively low-dimensional space, and then find those messages that hide in these data. For this purpose, the paper mainly refers to the following parts:Firstly, we summarize the current developments of dimension-reduction and some popular methods for dimension-reduction.Secondly, we introduce a method of non-linear dimensionality reduction---Locally Linear Embedding. And we analyze several parameters selection methods of this algorithm and make some improvements, especially for the choice of neighborhood---k. And then we find an effective way to solve this problem. At the last of this part, we apply the LLE to medical data and data from other fields, and show its superiority.Thirdly, we analyze and compare two non-linear dimensionality reduction methods:Locally Linear Embedding and Isometric Feature Mapping. We mainly make a comparison between them in operating efficiency.Finally, since the LLE is sensitive for outliers and disjoint manifolds, we have made some improvements for the LLE algorithm and presents Robust Locally Linear Embedding (RLLE). Comparing to normal LLE, experiments show that the RLLE have significantly improved the normal LLE when there are outliers and disjoint manifolds in the data.