Isoap与LLE在降维方面的优劣分析-应用统计专业毕业论文.docx

首都经济贸易大学硕+学位论文 Isomap与LLE在降维方面的优劣分析 Abst ract With the development of society,more and more people are exposed to high dimensional data in the fields of biology,image，finance and SO on．In dealing with these high dimensionaI data we are faced with three aspects of the problem．The first iS the ”Curse of dimensionality“problem．The amount of sample data of high dimension will make the analysis of the data required to reach the US far beyond the afrordability of the US，for analysis of high-dimensional data processing has brought great challenges．The second is the。。empty space“problem．Some high dimensional data is sparse．This leads to a lot of data in the low dimensional space in which the original nature is no longer established in high dimensional space．This phenomenon leads to the decrease of correlation dimension algorithm efficiency．Finally is to increase the complexity of the calculation of the problem．With the increase of the data dimension，the complexity of the data computation will be promoted．This will lead to a decline in the pe rformance of algorithms for many processing tasks in real time，which can not meet the requirements of online payment and other real-time issues． Under this condition，descending gradually by the scholars all over the world， manifold lea rning has become a hot issue．The principle of manifold learning is to maintain a relationship between the topological invariance of high dimensionaI data and IOW dimensionaI data．Isomap and LLE published on 2000 science are two kinds of representative algorithms for manifoId learning． In this pape5 we will study and analyze the two important manifoId learning algorithms based on Isomap and LLE．The specific content includes the foIlowing three points． Firstly,the background and manifold lea rning algorithms are studied and summarized． This paper gives a brief overview of the current development trends，prospects and some problems(such as”Curse of dimensionality”)in this field．This paper introduces some bas