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Research on Dimensionality Reduction Algorithms Based Locally Linear Analysis

Author: LiuShengLan
Tutor: ZuoDeQin
School: Liaoning Normal University
Course: Computer Software and Theory
Keywords: High-dimensional data dimensionality reduction Manifold Learning Local linearization Local tangent space
CLC: TP301.6
Type: Master's thesis
Year: 2011
Downloads: 54
Quote: 1
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Abstract


With the rapid development of the information , multimedia and digital technology , along with the arrival of the era of high-dimensional data and has become a powerful tool in the description of the objective world , such as gene expression , video tracking , medical image processing , high -dimensional time series analysis , At the same time , the traditional classification, clustering algorithm can not be applied in the processing of high-dimensional data , there is an urgent need to find a data dimensionality reduction method , the emergence of high-dimensional data manifold learning dimensionality reduction provides a very good way . Manifold learning in more than 10 years of development , the efforts of many scholars at home and abroad , has begun to mature , and emerged much to learn . For example : isometric mapping , local linear embedded (LLE) into the local tangent space alignment (LTSA) algorithm . LLE and LTSA are based on the local approximate linearization assumptions and proposed nonlinear dimensionality reduction method can get better results in the real world of high-dimensional data . But in many cases , the local data there is often a high curvature distribution and noise , the local method is very sensitive to the above situation , this time LLE and LTSA will not be able to get the correct low- dimensional embedding manifold learning how to solve such problems become an important branch . This article is mainly for the important issues in the above manifold learning solution : ( 1 ) analysis of the geometric properties of the local tangent space , on this basis propose an adaptive neighborhood selection methods , and the LTSA algorithms be improved . ( 2 ) analysis of the impact of noise and high curvature of the low-dimensional space , and noise classification proposed an anti- noise ability angles global embedding algorithm . (3) LLE algorithm , for example , local linearization problem discussed , given an approximate linear standard , while in the source data is the case of sparsely distributed , give an analysis based on sparse embedded dimensionality reduction method . Finally, the experiments confirmed the effectiveness of the proposed method .

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CLC: > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > General issues > Theories, methods > Algorithm Theory
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