The Search And Application Of Subspace Dimensionality Reduction Algorithm Based On Ratio Sum Problem

In recent years,the fields of information technology such as big data,Internet of Things,cloud computing and artificial intelligence have witnessed unprecedented development.What follows is a rapid "bloat and bulge" of data.This brings us great opportunities and challenges in this information age.The opportunity is that if we make the right use of the information in the data,we can do more with less.The challenge is how to extract exactly what we need from the mass of information.Large quantity and high dimension are the common characteristics of current data.We often spend a lot of time and calculation cost in data analysis.Moreover,due to the redundancy and noise information of data itself,the results of data analysis are not ideal,which is the so-called "dimensional disaster" problem in the industry.Before practical application analysis,dimensionality reduction methods are often used to eliminate this effect.For example,for image recognition problems,the direct use of highdimensional data for training and recognition will cause errors and affect accuracy.Before training,the data is reduced in dimensionality to reduce the error caused by redundant information,so as to improve the accuracy of the recognition rate.Studies have proved that dimensionality reduction is one of the most effective methods to eliminate the "curse of dimensionality".This article will discuss the Trace ratio(TR).Most dimensionality reduction problems can be characterized by the basic TR form,and TR has achieved quite good results in practical applications.However,in the learning process of the TR target function,our research found that TR tends to find the projection direction with small variance.This trend will cause the reduced dimensionality subset to not maximize the representation of the original data.Therefore,we discussed this issue and proposed corresponding solutions.The main contents of the article are as follows:(1)This article analyzes and discusses the method of selecting the projection direction of the Trace ratio function,and points out its shortcomings through demonstration;and replaces the "global optimal" idea with the "global local" optimal,and innovatively proposes a method based on Ratio sum's subspace dimensionality reduction algorithm model,and proves the rationality of the dimensionality reduction method from a mathematical point of view.(2)For the proposed Ratio sum algorithm,three solutions are proposed respectively,Gradient Ratio sum,Greedy Ratio sum,and Alternate Ratio sum,and the detailed derivation process of the three optimization methods is given.Through comparative experiments between Ratio sum method and existing dimensionality reduction methods,the correctness of the three methods are verified respectively,combined with theoretical and numerical analysis to prove the effectiveness of the proposed model.(3)In the summary of the Ratio sum model,we use mathematical induction to prove the affiliation of Greedy Ratio sum and Alternate Ratio sum.(4)The Ratio sum dimensionality reduction method is applied to hyperspectral clustering,and the performance of the subspace dimensionality reduction algorithm based on Ratio Sum in clustering application is explored.