Research Of Mahalanobis-Taguchi System Theroy

Dr. Taguchi developed the Mahalanobis-Taguchi system (MTS) which is a burgeoning method of pattern recognition based on the quality engineering. MTS is the first method that used the orthogonal array to select variables. MTS regards the SN ratios along with Mahalanobis distances as the optimization target, and select the useful variables by using 2-level orthogonal array. So far, MTS is widely used, and create tremendous economic and social bennifts. In China, the research of MTS in theory and application is just commenced developing, and it needs a great deal of manpower and resource.The layout of this dissertation is shown as follows: first, the dissertation reviewed the MTS, and gived the latest progress; second, based on the analysis of MTS, by integration of distance and similarity coefficient, the dissertation create a new index for classification which can reflect both the comparability of distance value and the comparability of shapes between samples; third, through entropy value of every variable, the validity of Class I variables can be recognized, and through fuzzy cluster analysis, the validity of Class II variables can be recognized; fourth, according diffirent of classication style, by the method of 3σrule and disturbing fuzzy set, the theory and design model for MTS design in discrimination of multiclass have been studied; finally, as an example, the MTS approach has been applied to the medical diagnosis and a satisfactory result has been obtained, and provide a new teconology and method to disease diagnosis in China.The research and main conclusion of this dissertation is shown as follows:1) The research of distance in MTSIn original MTS, Mahalanobis distance is used as classification index. Selecting Mahalanobis distance is proper because it is consider the influence of relativity, relativity and etc. And in practice, Mahalanobis distance has the better discriminant ability than others.2) The research of extention of classification indexIn original MTS, distance is adopted as classification index. Distance index can reflect how close among samples in space. However, in the other hand, distance index can not reflect the similitude of samples' shape. So, this dissertation extends the classification index by integrating the distance and similarity coefficient, and thus it can reflect the similitude of samples in both sides. 3) The research of variable selectionOriginal MTS is used the method of orthogonal array and SN ratio to select variables. However, this approach would become more complex along with the increase of variable number. According to ideology of Taguchi's data analysis, this dissertation applied entropy into variable selection, and gives an example to show efficiency of entropy method.The method of experimental design and entropy could identify the harmful variables (Class I variables), but they could not identify the variables which have similar effect (Class II variables). This dissertation uses the fuzzy cluster method to identify the Class II variables.4) The research of multiple recognitionIn original MTS, because the base space is constructed only by normal data, it is more fittable to classification of two models than multiple models. According to two kinds of classification of samples, this dissertation uses the methods of 3σrule and disturbing fuzzy set to solve the problem of discrimination of multiclass.5) The research of MTS applications in medical diagnosisMTS is the method based on data analysis rather than probability distribution, and is suitable to be appled in practice. This dissertation chooses pulmonary disease as the object. Through amount of normal and abnormal data, we contruct the base space, select the useful variables; by constructing the disturbing fuzzy relationship between variables and disease types, compute the fuzzy number of samples, and so can achieve the purpose of medical diagnosis.