Research On Intrinsic Dimensionality Estimation Of High-Dimensional Data Set

In this paper we are concerned with the intrinsic dimensionality estimation of high-di -mensional data.The researching on intrinsic dimension estimating techniques has become an important research direction in the realm of high-dimensional data processing. Exactly questing the intrinsic dimension is helpful for people to discover the intrinsic configuration of the data,and plays a guiding role in dimension reduction and other subsequent processes.The main contents of this paper are listed as the following two:1. Analyze the existing techniques in the realm of the intrinsic dimensionality estimation.Propose a criterion for classifying the existing techniques with my earnestly studying and well understanding of a series of typical estimating techniques in different periods.The two classifications are eigenvalue's methods and geometric methods.For each classification,I analyze the typical methods of it and summarize the common characteristics of them. Particularlly,I make a deep research for saveral newest estimating techniques,such as the maximum likelihood estimation, the packing number estimation and the k-nearest neighbor graph estimation.2. Propose a new intrinsic dimension estimator.With my well understanding on LLE(locally linear embedding) and Laplacian Eigenmap,a analysis on the similarity of two methods'dimension reducing results for the same data set. Under the heuristic experience of how LLE is applied to estimating the intrinsic dimension,I disconer the feasibility of applying Laplacian Eigenmap to estimating the intrinsic dimension,and by finding a suitable loss function I make the feasibility come true----I propose a new intrinsic dimension estimating technique based on Laplacian Eigenmap. Comparisons during the new technique and global PCA as well as LLE have been done by processing real-life data,which are considered as evidences for the usability and validity of the new technique.In these experiments,the important effect on the new technique's application of weight parameter is discovered,and I give a primary suggestion on how to choose this parameter.