Comparing Some Methods of Kernel Discriminant Analysis Under Fuzzy Environment

Abstract

One of the most widely used statistical methods in the field of data analysis is the method of discriminant analysis, and the use of discriminant analysis requires the availability of a number of assumptions, the most important of which is that the data of explanatory variables have a multivariate normal distribution. The discriminant analysis often suffers from the problem of small sample size, especially when it is applied to classify several dimensions; we deal with this problem through the use of the Kernel Discriminant Analysis method (KDAM). But in many situations in real world suffuref from inaccuracy in measurements that is leads to inaccuracy in conducting the required statistical analyzes, so it is necessary to get out of the traditional pattern of data to that fuzzy pattern by finding a fuzzy information system based on the principle of cutting in the fuzzy group to find measurements of data that represent the phenomenon with certainty and which represent the group of important elements that represent those phenomenon. In this paper, we form the estimation function of the kernel density with an application in discriminant analysis to be a comparison in estimation density function depends on the choice of bandwidth, which controls the smoothing of the estimate and on the choice of the kernel function., some methods were used to estimate the bandwidth parameter, which is least square Cross validation, Biased cross validation and Bayes discriminant rule Method under fuzzy measurements. The estimation of Kernel density is important in multivariate data analysis, and it depends heavily on the appropriate selection of the bandwidth matrix (H) that reduces the mean integration square error (MISE) and the error rate (