Distance-based Fisher Discriminant Analysis Model And Algorithm Research For Triangular Fuzzy Numbers And Interval-Data

The traditional discriminant analysis mainly focuses on the study of "point data",but when the big data era has coming,massive data need to deal with,the point data often has limitations.However,the symbolic data can be obtained by means of "data packaging" and other methods to acquire the general characteristics of the whole data and the relationship inner the data.In real data,there are two important sources of uncertainty:randomness and fuzziness.Randomness describes the events that will occur,and simulates the random variability of overall possible results,while fuzziness which is a tool for focusing on the boundaries of events extension.The corresponding discriminant models are constructed to processing the data contained both randomness and fuzziness,it emphasizes great importance of fuzzy statistics analysis in recent years.In this paper,the existing symbol data and fuzzy data theory are summarized,and the problem of discriminant analysis of complex data is studied with interval data and triangular fuzzy number as the object.Firstly,aiming at the classification problem of interval data,interval data fuzzy linear discriminant analysis and nonlinear fuzzy kernel discriminant analysis are proposed by this paper which is based on Hausdorff distance,and its algorithm steps are given in the next.Among them,when comes to the case of interval linear inseparable type data,the idea consists of finding a fuzzy kernel Fisher discriminant model for interval data,the kernel function is employed to each value of the interval variables of different boundary,so that the projection to the high dimensional feature space type of interval data linearly separable,the method is an extension of the generalized discriminant analysis.Then,on the classification of the fuzzy data,this paper puts forward similarity-based Fisher discriminant analysis which contains linear and nonlinear discriminant analysis.The similarity of triangular fuzzy number is employed for discrete degree within class,with a distance of triangular fuzzy number to quantify between each class of discrete degree and the idea consists of finding a projection direction vector which maximizes the radio of the dispersion degree between the class data and within the class.The model is a generalization of the classical Fisher discriminant analysis.Finally,we adopt the genetic algorithm to select the appropriate kernel function and evaluate the performance of the four classifiers and explain the applicability of the classification rules.The traditional discriminant analysis problem is generalized by the result of this paper,especially the discriminant classification of complex data such as interval number and fuzzy number.Four classifiers are constructed,including linear discriminant and nonlinear discrimination of interval data,linear discriminant and nonlinear discrimination of triangular fuzzy number.At the same time,the detailed algorithm steps are given and applied to concrete examples to show its feasibility.