Research And Applicat Ion Of Manifold Learning

Manifold is an important concept in differential geometry. In the field of engineering recent years, manifold learning is a research focus of the machine learning, which is based on local linear and global nonlinear assumptions. As manifold learning can effectively detect the intrinsic nonlinear structure in high dimensional data space, reconstruct the intrinsic manifold in low dimensional space, and keep the nonlinear structural characteristics, so it is an effective dimension reduction algorithm and data visualization algorithm.Due to the excellent nonlinear dimension reduction characteristics of manifold learning, it has been applied to several filed of engineering, such as the dimension reduction of hyperspectral remote sensing data. Though, when applying manifold learning to classification of hyperspectral remote sensing image as a nonlinear dimension reduction, we encounter several problems:the intrinsic dimension estimation, noise interference, adjacent points selection, sample points outside the learning problems, etc. So when applying manifold learning to dimensionality reduction of hyperspectral data, the study is mainly focusing on the problems above, and so is the algorithm improvement and innovation. Based on research of manifold learning algorithm in hyperspectral remote sensing data processing and air handwriting recognition, we propose three innovation:(1) The actual hyperspectral remote sensing images are large scale images, and current manifold dimensionality reduction algorithm of hyperspectral data has no consider about large scale image problem. To make up the shortfall, this paper presents an improved dimensionality reduction algorithm of large-scale hyperspectral scenes using manifold called IISOMAP-LLE(Incremental Isometric Map and Locally Linear Embedding).(2) In the IISOMAP-LLE algorithm there also has adjacent points selection problem. There are two kind of parameter K selection methods, the local dynamic and global static, which in second one can improve the computing speed. In this paper we propose a manifold dimensionality reduction algorithm of large-scale hyperspectral scenes based on ISODATA(Iterative Self Organizing Data Analysis Techniques Algorithm) and GA(Genetic Algorithm).(3) For sample points outside the learning problems, incremental ISOMAP(Isometric Map) algorithm is proposed, which can decent the computing using incremental learning method and also can be applied to the streaming data. This paper designs and realizes an air handwriting recognition system based on MEMS(Micro Electro Mechanical System), in which incremental ISOMAP algorithm is used to transform3D handwritten trajectory to the2D, and at last recognized the characters using the trained artificial neural network.