复共线性数据环境下的马田分类理论研究及应用

项目名称： 复共线性数据环境下的马田分类理论研究及应用

项目编号： No.71271114

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 管理科学

项目作者： 程龙生

作者单位： 南京理工大学

项目金额： 56万元

中文摘要： 马田系统（MTS）是一种结合马氏距离、正交表和信噪比进行分类和诊断的方法。现实问题高维的变量特性导致复共线性数据环境，而这会使得马氏距离失真，进而降低MTS分类正确率。本项目研究复共线性数据环境下MTS分类理论，具体有：构建结合马氏距离、核函数、伪逆矩阵或岭参数的新测量尺度以克服复共线性影响并提高区分度，研究新测量尺度有效性；研究MTS的基准空间生成、更新机制及判稳准则；在正交表、信噪比基础上研究采用优化模型处理特征筛选问题；研究阈值确定办法，建立MTS平衡数据/不平衡数据二类分类和多类分类规则；研究多MTS分类器集成技术；开展MTS分类方法应用研究。项目面向复共线性数据环境，以MTS改进为主线，旨在发展MTS使之成为在复共线性数据环境下先进实用的分类技术。预期在测量尺度改进、基准空间构建与优化方面会取得创新性成果，丰富分类理论及方法，更好地指导分类实践。

中文关键词： 复共线性；马田系统；基准空间；分类；多属性决策

英文摘要： The Mahalanobis-Taguchi System (MTS) is a classifying and diagnostic technique using a collection of methods of Mahalanobis distance (MD), orthogonal table and signal-to-noise ratio. The characteristics of high-dimensional variable in some real problems lead to the data environment of multicollinearity, which will make the MD distortion and thereby affect the correct classification rate of MTS. This project will research on the classisfication theory of MTS in the data environment of multicollinearity. The main contents are as follows: build new measurement scale which is combined with MD, kernel function and pseudo-inverse matrix(or ridge parameter) to overcome the influence of multicollinearity and improve the discrimination, and validate the new measurement scale; study the generation mechanism and update mechanism of MTS reference space and its steady criteria; research the feature screening problem using optimization model based on orthogonal table and signal-to-noise ratio; study the model for computing threshold and build the classification rules for balanced/imbalanced binary class and multi-class of MTS; study the integrated technology of multi-MTS classification; implement application research using classification method of MTS. Facing the data environment of multicollinearity, the project aims to deve

英文关键词： multi-collinearity；Mahalanobis-Taguchi system；reference space；classification；multi-attribute decision making