Research And Application Of Intrinsic Dimension Estimation

More and more high dimensional data is obtained with the development of information technologies. High dimensional data can provide more information; however, how to gain the more important information from so much data is becoming a difficult problem. After many years of research, some dimensional reduction methods were proposed, such as PCA, LLE and Laplacian Eigenmaps, etc. Through these methods, the high dimensional data can be embedded in a lower space. But a new problem has arisen. How many is the dimension of embedding space? So, intrinsic dimensional estimation is concerned. It can help to discover the intrinsic dimension of data set, and plays a guiding role in dimensional reduction.This paper focuses on the studying of the intrinsic dimensional estimation of high dimensional data. After an analysis to the problems of PDE (Packing Dimension Estimation) algorithm provided by Balázs Kégl, An IPDE (Improvement on Packing Dimension Estimation) algorithm and its implementation is presented. The experiments show that this algorithm has a higher running efficiency and stability than the PDE algorithm. Then, by combining the intrinsic dimensional estimation algorithm, dimension reduction algorithm and pattern recognition technology, the stability and validity of the IPDE algorithm is further proved in the experiment of handwriting character recognition.