On The Data Reduction Method Of Manifold Learning

With the development of information and technology,the data that people are facing is increasing exponentially and entering the era of big data.So it is necessary to explore and excavate the rules in massive data through data dimensionality reduction.As a kind of data reduction method developed in the past ten years,manifold learning has become a hot topic in the field of machine learning research,integrating the fields of computational science,mathematics and intelligent science.The diffusion mapping(Diffusion Maps)algorithm is a global feature retention method based on manifold learning.In this paper,we mainly explore the diffusion maps algorithm.And we improve the algorithm aiming at the shortcomings of diffusion maps algorithm,so as to improve the dimensionality reduction effect of the algorithm and expand the application area of the algorithm.The full text is divided into three chapters.The first chapter mainly introduces the research background,the basic definition and the research status at home and abroad,and finally gives the research content of this thesis.The second chapter classifies and summarizes the existing data reduction methods,such as PCA,MDS,LE,LTSA,LLE and so on,and analyzes the computational complexity and advantages and disadvantages of data dimensionality reduction algorithm.In the third chapter,first of all,we can construct different adjacency graph according to the difference between the number of adjacent points in diffusion maps algorithm,so as to produce different dimensionality reduction effects.We improve the distance function to make the distance between data points more uniform and improve the dimensionality reduction effect of the algorithm.Then,when the density of data set changes greatly,it is difficult to get a good dimensionality reduction result for diffusion maps algorithm.We propose a diffusion maps algorithm based on density.Finally,the validity of the new algorithm is proved by the comparison and analysis of the data experiment.