Discriminant Support Vector Machine For Dimensionality Reduction Based On Ordinal Regression

With the development of modern science and technology,the research of artificial intelligence technology has attracted extensive attention.Data-based machine learning is an important part of its research,that is,learning regularities from collected data samples and using these regularities to predict future observed data or things that cannot be observed,however,the presence of large amounts of the complex phenomenon in the realistic environment with things,with the collected data of observation of things is increasing,"dimension curse" emerged,it refers to,in the absence of simple hypothesis,estimates that a has the function of multiple variables reaches a certain accuracy required for exponential growth in the number of sample size in a variable.Although high-dimensional data can provide us with more characteristic information of samples,higher data dimensions also bring problems in machine learning calculation.Therefore,research on the dimensionality reduction algorithm for high-dimensional data is now a hot topic in the field of machine learning.Ordinal regression learning,which frequently occurs in social science and information retrieval,is a supervised learning method based on ranking information prediction variables.Its training samples are marked by a group of Ordinal Numbers,which are used to represent the ranking among different categories.Unlike linear regression problems,ordinal regression is a machine learning method that considers both linear regression and classification problems.The types used to mark Ordinal Numbers are limited,and the measured distances between ordinal Numbers are not defined.In this paper,the support vector dimensionality reduction algorithm based on ordinal regression is studied,we proposed the ordinal regression support vector dimensionality reduction machine(ORDR-U)and the ordinal regression sort support vector dimension reduction machine(ORDR-M).The ORDR-U,first,the SVORIM model is used to obtain the dimensionality reduction matrix through recursive iteration calculation,the dimensionality reduction matrix is calculated by multiple recursive iterations of mapping vector,this method obtains the optimal projection vector in the sense of ordered regression of support vectors in each solution,and overcomes the limitation of dimension in traditional dimensionality reduction algorithms by using recursive iteration scheme;The ORDR-M is improved on the basis of the above algorithm,the algorithm optimizes the selection of mapping vectors,it makes full use of advantages of iterative calculation for multiple mapping vector,the mapping vectors corresponding to the more effective features are sorted and combined into a dimensionality reduction matrix according to the classification accuracy of the SVORIM model,in other words,the dimensionality reduction matrix in the sense of optimal classification accuracy of SVORIM model is obtained,it makes the better classification effect.Due to the existence of sorting information in the data set of sequential regression learning,compared with the traditional dimensionality reduction algorithm,the two algorithms can not only retain the order information between labels better,but also solve the problem of dimensionality limitation of the mapping matrix by recursive iterative optimization.Finally,the effectiveness of the algorithm in this paper is verified by numerical experiments...