基于度量学习理论的马田系统改进及其应用研究  

Improvement and application of Mahalanobis-Taguchi system based on metric learning

作　　者：常志朋 顾玉萍[3] 陈闻鹤 CHANG Zhipeng;GU Yuping;CHEN Wenhe(School of Business,Anhui University of Technology,Maanshan 243002,China;Key Laboratory of Multidisciplinary Management and Control of Complex Systems of Anhui Higher Education Institutes,Anhui University of Technology,Maanshan 243002,China;School of Management Science and Engineering,Anhui University of Finance&Economics,Bengbu 233030,China;School of Economics&Management,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]安徽工业大学商学院,安徽马鞍山243002 [2]安徽工业大学复杂系统多学科管理与控制安徽普通高校重点实验室,安徽马鞍山243002 [3]安徽财经大学管理科学与工程学院,安徽蚌埠233030 [4]南京理工大学经济管理学院,江苏南京210094

出　　处：《管理工程学报》2025年第2期221-233,共13页Journal of Industrial Engineering and Engineering Management

基　　金：国家自然科学基金项目(71673001);安徽省高校人文社会科学基金重大项目(SK2021ZD0034);安徽省普通高校重点实验室开放基金重点项目(CS2020-ZD02)。

摘　　要：为提升马田系统的识别性能,本文利用度量学习理论对其进行改进。一是将传统协方差马氏距离改进为以度量矩阵为参变量的马氏距离函数,然后利用简单直接的KISSME度量学习算法估计一个最能反映数据间内在关系的度量矩阵,该度量矩阵可以使同类样本更紧凑、非同类样本更分离,这有助于提升马田系统的识别性能。二是基于拉近同类样本、推远非同类样本的思想,定义一个新的特征子集评估函数代替田口方法中的信噪比,这有助于筛选出可以提高马田系统识别性能的特征。改进后的马田系统仍然保持了原理简单、易于操作的优势。本文选取6个UCI数据集进行验证,得出改进后的马田系统在Accuracy、Specificity、G-means和降维率等方面均明显优于传统马田系统的结论。最后,本文通过返贫识别验证了改进后马田系统的可行性和有效性。The Mahalanobis-Taguchi system(MTS) is a simple principle-based pattern recognition method proposed in the early 1990s by Dr.Taguchi,a famous Japanese quality engineer,which is easy to operate in practice.The MTS was introduced into China in 2000,and it is widely used in product quality inspection and improvement,mechanical fault,and medical diagnoses and multi-attribute decision-making.The method is integrated by Mahalanobis distance and Taguchi method.As a pattern recognition method,the unique advantage of MTS is that it uses Mahalanobis distance to construct a measurement scale with a reference base for recognition and does not need complicated statistical theory.However,with the expansion of the application field of MTS,its limitations are gradually manifested;therefore,some scholars have suggested improvements to the MTS,which mainly focus on two aspects:One is the improvement of Mahalanobis distance.When a variable has multicollinearity,the covariance matrix in the Mahalanobis distance is invertible.Taguchi proposes to calculate the Mahalanobis distance using Schmidt orthogonalization,which does not depend on the covariance matrix and is,therefore,not affected by the multicollinearity.Some other scholars propose other methods,such as pseudo-inverse,ridge estimation,and regularization,to calculate Mahalanobis distance to solve the multicollinearity problem.With the rapid development of the Internet and big data technology,the types of data to be processed are increasingly complex,such that the MTS often needs to process data with dynamic,high-dimensional,high-noise,and nonlinear characteristics.To solve this problem,some scholars attempted to construct the interval Mahalanobis distance,steady Mahalanobis distance,sparse principal component Mahalanobis distance,kernel principal component Mahalanobis distance,kernel interval Mahalanobis distance,and other variations,all of which have achieved good results.The other aspect is the improvement of the Taguchi method.To improve the robustness of the Mahalanobis dis

关 键 词：马田系统 度量学习 KISSME 返贫识别 

分 类 号：O235[理学—运筹学与控制论] C93[理学—数学]