基于全方位优化算法的马田分类和排序评价方法研究及应用
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摘要
数据挖掘是从数据中获取知识和信息,并进行决策的有效手段。分类是数据挖掘的重要任务,它根据样本的数据特征判定其所属类别。目前许多成熟有效且各具特点的分类方法得到了深入研究和广泛应用,但仍有各自的局限性和不足。在分类过程中,特征变量筛选通常能够起到简化问题、提高分类精度和效率的作用。
马田系统(Mahalanobis-Taguchi System, 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新型模式识别方法。MTS具有的能够筛选重要特征变量、对数据分布不需要进行假设、分类速度快等优点使得它在工业生产、企业管理和模式识别等领域得到了广泛的应用。作为一种较新的分类方法,它在理论基础和方法使用上存在一些缺陷和严谨性问题,如：特征变量筛选方法有待改进、阈值确定主观性较强、局限于二类分类等。除了用于分类和诊断之外,MTS的特点使得它还可以用于排序(综合)评价。本文针对MTS的不足,以MTS改进为主线,以优化方法为主要手段,目标是发展MTS使其成为一种实用有效的分类和排序评价方法,并应用于现实问题。本文的研究工作有以下几个方面：
(1)基于全方位优化算法的MTS二类分类方法研究
针对传统MTS在分类过程中采用正交表和信噪比筛选特征变量以及采用损失函数法确定阈值存在的缺陷,使用多目标优化和全方位优化算法替代以进行改进。综合考虑分类精度、望大特性信噪比和降维程度等目标构建了多目标优化模型并用全方位优化算法求解以筛选特征变量和确定阈值；采用数据集实验和比较的方式对方法的有效性进行了验证和讨论；将方法用于产品质量检测的现实问题。研究结果表明,该方法不仅有很高的分类精度,还能有效的筛选特征变量,对传统MTS有了较大改进。
(2)基于全方位优化算法和概率阈值模型的MTS不平衡数据分类方法研究
类别不平衡是分类问题常常面临的挑战。MTS通过马氏距离构建一个连续测量尺度而非直接对训练样本进行学习的性质有望不受类别不平衡的影响,而阈值的合理确定对该问题更加重要。提出了一种概率阈值模型用于MTS不平衡数据分类阈值的确定；综合考虑不平衡数据分类性能评估指标的g/F值、望大型信噪比和降维程度等目标构建多目标优化模型并用全方位优化算法求解以筛选特征变量；采用数据集实验和比较的方式对方法的有效性进行检验和讨论。研究结果表明,该方法对不平衡数据有良好的分类能力,同时还能筛选重要特征变量。
(3)MTS多类分类方法研究
MTS是一种二类分类方法,不能直接用于多类分类。本文研究了两种MTS多类分类方法——二叉树MTS和多马氏空间特征变量筛选MTS。二叉树MTS通过二叉树与MTS的结合,将多类分类问题进行分解。研究了二叉树MTS的实施过程和步骤,以及二叉树的构建方案等。多马氏空间特征变量筛选MTS通过为每类构建马氏空间,运用距离判别思想构建分类器,同时优化特征空间。研究了多马氏空间特征变量筛选MTS的实施过程和步骤,综合考虑分类精度、改进的望大型信噪和降维程度等目标构建多目标优化模型并用全方位优化算法求解以筛选特征变量。采用数据集实验和比较的方式对两种方法的有效性进行了检验和讨论。最后将MTS多类分类方法应用于政府投融资平台企业的信用等级评价。研究结果表明,多马氏空间特征变量筛选MTS有着更高的分类精度和特征变量筛选效果,具有更高的应用价值。
(4)MTS排序评价方法研究
MTS目前主要用于分类问题。实际上,MTS可计算出样本相对于基准空间(马氏空间)的马氏距离,得出样本偏离的程度,从而对待测样本进行排序。本文研究MTS排序评价方法,具体包括：MTS排序评价方法的过程及步骤；基于全方位优化算法的评价指标筛选模型；采用算例和比较的方式对MTS排序评价的有效性进行分析和讨论。研究结果表明,MTS排序评价方法不需要确定指标权重,能够保持评价基准的一致,且能够筛选指标,是一种有效的评价方法,但基准空间的确定机制需要进一步研究和完善。
综合以上研究工作,本文的主要贡献和创新点有：
(1)识别不同的分类或排序评价目标,在MTS特征变量筛选这一核心问题中导入优化思想,创新性的提出和研究了特征变量筛选的多目标优化模型以替代传统MTS的正交表,并采用先进的全方位优化算法求解,是一种新的特征变量筛选方法。
(2)根据不同的分类目的,采用优化或概率模型替代传统MTS的损失函数(或穷举法)来确定MTS进行分类时需要的阈值,这是MTS新的闽值确定办法。
(3)通过概率闽值模型、二叉树和多马氏空间等手段,将MTS二类分类方法成功的扩展到了不平衡数据分类和多类分类,并验证了这些方法的有效性,是新的不平衡数据分类方法和多类分类方法。
Data mining is an effective means of accessing knowledge and information from the data for further decision-making. The classification problem is one of the main issues in data mining because it aims to extract a classifier which can be used to predict the classes of objects whose class labels are unknown based on the data characteristics. Currently, many mature and effective classification methods with distinct characteristics have been thoroughly studied and widely used, but still have their own limitations and shortcomings. Feature selection, which aims to reduce the number of features (dimensions), can play a role of improving the classification accuracy, simplifying the problem and cost-saving in process of classification.
The Mahalanobis-Taguchi System (MTS) is a new classifying and diagnostic tech-nique of pattern recognition using a collection of methods of Mahalanobis distance (MD), orthogonal arrays (OAs) and signal-to-noise ratios (SNR). Advantages of MTS, such as can determine the important features, do not need to make assumptions about data distribution and high classification speed, etc., make it a wide range of applications in areas such as industrial production, business management and pattern recognition. As a relatively new classification method, it also has some shortcomings and rigorous problems about theoret-ical basis and usage, such as:lack of rigor for feature screening, subjectivity of determin-ing the threshold and confining to the two-class classification. In addition to be used for classification and diagnosis, the characteristics of MTS makes it also be used to sort evalu-ation. For shortages of the MTS, the paper aims to make the MTS an effective and practic-al classification and sort evaluation technique with the focusing on improving the theory of MTS, and apply it to real problems. These research works of the paper are the following:
(1) Research on MTS based on omni-optimizer algorithm for two-class classification
For the inadequacy of traditional MTS in feature selection by OAs and SNR as well as determining the threshold by loss function, multi-objective optimization and om-ni-optimizer algorithm are alternative for improvements. Classification accuracy and the-larger-the-better SNR as well as dimensionality reduction are considered as optimiza-tion goals to build a multi-objective optimization model, which is used for feature selection and threshold determining, is solved by omni-optimizer algorithm. For evaluating the ef-fectiveness of the proposed method, a dataset experiment for comparison is implemented. Finally, the proposed method is applied to a real case about product quality inspection. The results show that the proposed method outperforms other well-known algorithms not only on classification accuracy but also on feature selection efficiency.
(2) Research on MTS based on omni-optimizer algorithm and probabilistic thre-sholding model for imbalanced data classification
MTS establishes a classifier by constructing a continuous measurement scale rather than directly learning from the training set. Therefore, it is expected that the construction of an MTS model will not be influenced by data distribution, and this property is helpful to overcome the class imbalance problem. A probabilistic thresholding method is proposed to determine the classification threshold in MTS for imblanced data classification. Perfor-mance evaluation indicators of imbalanced data classification--g/F values and the-larger-the-better SNR as well as dimensionality reduction are considered as optimiza-tion goals to build a multi-objective optimization model, which is used for feature selection, is solved by omni-optimizer algorithm. For evaluating the effectiveness of the proposed method, a dataset experiment for comparison is implemented. The results show that the proposed method is effective not only on classification accuracy for imbalanced data but also on feature selection efficiency.
(3) Research on multi-MTS for multi-class classification
MTS is a method for two-class classification, which can not be directly used for mul-ti-class classification. Two multi-class MTS classification methods----binary tree MTS (BT-MTS) and multi-Mahalanobis-space(MS) feature-selection MTS (MF-MTS) are stu-died. BT-MTS decomposes multi-class problem by a combination of binary tree and MTS. The process and steps of implementation of BT-MTS and the construction programs for binary tree are studied. MF-MTS establishes classifier using distance criterion by estab-lishing an individual MS space for each class and can optimize the feature space at the same time. The process and steps of implementation of MF-MTS are studied. In MF-MTS, classification accuracy and the-larger-the-better SNR as well as dimensionality reduction are considered as optimization goals to build a multi-objective optimization model, which is used for feature selection, is solved by omni-optimizer algorithm. For evaluating the ef-fectiveness of the proposed two methods, a dataset experiment for comparison is imple-mented. Finally, the proposed methods are applied to a real case about credit rating of en-terprises on platform of government investment and financing. According to the results, we can conclude that the two multi-class MTS classification methods have high classification accuracy, but the MF-MTS is more valuable for application.
(4) Research on MTS based on omni-optimizer algorithm for sort evaluation
Currently, MTS is mainly used for classification problems. In fact, the MTS can sort the samples for evaluation by calculating the Mahalanobis distances of samples to refer-ence space (RS), which represents the degree of deviation from the RS. In this paper, MTS for sort evaluation is studied including:procedures of MTS for sort evaluation; variable screening model based on the omni-optimizer algorithm; validity and discussion of the MTS for sort evaluation by examples and comparative analysis. The results show that the MTS for sort evaluation method does not need to determine the index weight, can maintain consistent evaluation reference, and can screen index, which is an effective evaluation me-thod. But the mechanisms for identifying the reference space require further studies and perfect.
Based on the above research work, the main contributions and innovations of this pa-per are as follows:
(1) With identifying different goals for classification and sort evaluation, optimization ideas are imported in the core issue of MTS feature selection and multi-objective optimiza-tion model as an alternative to OAs is proposed and studied innovatively, which is solved by omni-optimizer algorithms. It is a new method for feature selection.
(2) According to the different purposes of classification. optimization or probabilistic model is used to determine threshold of MTS classification, which replaces the loss of function or exhaustive search method. It is a new threshold determining way.
(3) The MTS class classification method has been successfully extended to imba-lanced data classification and multi-class classification by means of probabilistic thresholding model, binary tree and multi-MS and the effectiveness of the methods are proved. The me-thods are new for imbalanced data classification and multi-class classification.
马田系统(Mahalanobis-Taguchi System, 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新型模式识别方法。MTS具有的能够筛选重要特征变量、对数据分布不需要进行假设、分类速度快等优点使得它在工业生产、企业管理和模式识别等领域得到了广泛的应用。作为一种较新的分类方法,它在理论基础和方法使用上存在一些缺陷和严谨性问题,如：特征变量筛选方法有待改进、阈值确定主观性较强、局限于二类分类等。除了用于分类和诊断之外,MTS的特点使得它还可以用于排序(综合)评价。本文针对MTS的不足,以MTS改进为主线,以优化方法为主要手段,目标是发展MTS使其成为一种实用有效的分类和排序评价方法,并应用于现实问题。本文的研究工作有以下几个方面：
(1)基于全方位优化算法的MTS二类分类方法研究
针对传统MTS在分类过程中采用正交表和信噪比筛选特征变量以及采用损失函数法确定阈值存在的缺陷,使用多目标优化和全方位优化算法替代以进行改进。综合考虑分类精度、望大特性信噪比和降维程度等目标构建了多目标优化模型并用全方位优化算法求解以筛选特征变量和确定阈值；采用数据集实验和比较的方式对方法的有效性进行了验证和讨论；将方法用于产品质量检测的现实问题。研究结果表明,该方法不仅有很高的分类精度,还能有效的筛选特征变量,对传统MTS有了较大改进。
(2)基于全方位优化算法和概率阈值模型的MTS不平衡数据分类方法研究
类别不平衡是分类问题常常面临的挑战。MTS通过马氏距离构建一个连续测量尺度而非直接对训练样本进行学习的性质有望不受类别不平衡的影响,而阈值的合理确定对该问题更加重要。提出了一种概率阈值模型用于MTS不平衡数据分类阈值的确定；综合考虑不平衡数据分类性能评估指标的g/F值、望大型信噪比和降维程度等目标构建多目标优化模型并用全方位优化算法求解以筛选特征变量；采用数据集实验和比较的方式对方法的有效性进行检验和讨论。研究结果表明,该方法对不平衡数据有良好的分类能力,同时还能筛选重要特征变量。
(3)MTS多类分类方法研究
MTS是一种二类分类方法,不能直接用于多类分类。本文研究了两种MTS多类分类方法——二叉树MTS和多马氏空间特征变量筛选MTS。二叉树MTS通过二叉树与MTS的结合,将多类分类问题进行分解。研究了二叉树MTS的实施过程和步骤,以及二叉树的构建方案等。多马氏空间特征变量筛选MTS通过为每类构建马氏空间,运用距离判别思想构建分类器,同时优化特征空间。研究了多马氏空间特征变量筛选MTS的实施过程和步骤,综合考虑分类精度、改进的望大型信噪和降维程度等目标构建多目标优化模型并用全方位优化算法求解以筛选特征变量。采用数据集实验和比较的方式对两种方法的有效性进行了检验和讨论。最后将MTS多类分类方法应用于政府投融资平台企业的信用等级评价。研究结果表明,多马氏空间特征变量筛选MTS有着更高的分类精度和特征变量筛选效果,具有更高的应用价值。
(4)MTS排序评价方法研究
MTS目前主要用于分类问题。实际上,MTS可计算出样本相对于基准空间(马氏空间)的马氏距离,得出样本偏离的程度,从而对待测样本进行排序。本文研究MTS排序评价方法,具体包括：MTS排序评价方法的过程及步骤；基于全方位优化算法的评价指标筛选模型；采用算例和比较的方式对MTS排序评价的有效性进行分析和讨论。研究结果表明,MTS排序评价方法不需要确定指标权重,能够保持评价基准的一致,且能够筛选指标,是一种有效的评价方法,但基准空间的确定机制需要进一步研究和完善。
综合以上研究工作,本文的主要贡献和创新点有：
(1)识别不同的分类或排序评价目标,在MTS特征变量筛选这一核心问题中导入优化思想,创新性的提出和研究了特征变量筛选的多目标优化模型以替代传统MTS的正交表,并采用先进的全方位优化算法求解,是一种新的特征变量筛选方法。
(2)根据不同的分类目的,采用优化或概率模型替代传统MTS的损失函数(或穷举法)来确定MTS进行分类时需要的阈值,这是MTS新的闽值确定办法。
(3)通过概率闽值模型、二叉树和多马氏空间等手段,将MTS二类分类方法成功的扩展到了不平衡数据分类和多类分类,并验证了这些方法的有效性,是新的不平衡数据分类方法和多类分类方法。
Data mining is an effective means of accessing knowledge and information from the data for further decision-making. The classification problem is one of the main issues in data mining because it aims to extract a classifier which can be used to predict the classes of objects whose class labels are unknown based on the data characteristics. Currently, many mature and effective classification methods with distinct characteristics have been thoroughly studied and widely used, but still have their own limitations and shortcomings. Feature selection, which aims to reduce the number of features (dimensions), can play a role of improving the classification accuracy, simplifying the problem and cost-saving in process of classification.
The Mahalanobis-Taguchi System (MTS) is a new classifying and diagnostic tech-nique of pattern recognition using a collection of methods of Mahalanobis distance (MD), orthogonal arrays (OAs) and signal-to-noise ratios (SNR). Advantages of MTS, such as can determine the important features, do not need to make assumptions about data distribution and high classification speed, etc., make it a wide range of applications in areas such as industrial production, business management and pattern recognition. As a relatively new classification method, it also has some shortcomings and rigorous problems about theoret-ical basis and usage, such as:lack of rigor for feature screening, subjectivity of determin-ing the threshold and confining to the two-class classification. In addition to be used for classification and diagnosis, the characteristics of MTS makes it also be used to sort evalu-ation. For shortages of the MTS, the paper aims to make the MTS an effective and practic-al classification and sort evaluation technique with the focusing on improving the theory of MTS, and apply it to real problems. These research works of the paper are the following:
(1) Research on MTS based on omni-optimizer algorithm for two-class classification
For the inadequacy of traditional MTS in feature selection by OAs and SNR as well as determining the threshold by loss function, multi-objective optimization and om-ni-optimizer algorithm are alternative for improvements. Classification accuracy and the-larger-the-better SNR as well as dimensionality reduction are considered as optimiza-tion goals to build a multi-objective optimization model, which is used for feature selection and threshold determining, is solved by omni-optimizer algorithm. For evaluating the ef-fectiveness of the proposed method, a dataset experiment for comparison is implemented. Finally, the proposed method is applied to a real case about product quality inspection. The results show that the proposed method outperforms other well-known algorithms not only on classification accuracy but also on feature selection efficiency.
(2) Research on MTS based on omni-optimizer algorithm and probabilistic thre-sholding model for imbalanced data classification
MTS establishes a classifier by constructing a continuous measurement scale rather than directly learning from the training set. Therefore, it is expected that the construction of an MTS model will not be influenced by data distribution, and this property is helpful to overcome the class imbalance problem. A probabilistic thresholding method is proposed to determine the classification threshold in MTS for imblanced data classification. Perfor-mance evaluation indicators of imbalanced data classification--g/F values and the-larger-the-better SNR as well as dimensionality reduction are considered as optimiza-tion goals to build a multi-objective optimization model, which is used for feature selection, is solved by omni-optimizer algorithm. For evaluating the effectiveness of the proposed method, a dataset experiment for comparison is implemented. The results show that the proposed method is effective not only on classification accuracy for imbalanced data but also on feature selection efficiency.
(3) Research on multi-MTS for multi-class classification
MTS is a method for two-class classification, which can not be directly used for mul-ti-class classification. Two multi-class MTS classification methods----binary tree MTS (BT-MTS) and multi-Mahalanobis-space(MS) feature-selection MTS (MF-MTS) are stu-died. BT-MTS decomposes multi-class problem by a combination of binary tree and MTS. The process and steps of implementation of BT-MTS and the construction programs for binary tree are studied. MF-MTS establishes classifier using distance criterion by estab-lishing an individual MS space for each class and can optimize the feature space at the same time. The process and steps of implementation of MF-MTS are studied. In MF-MTS, classification accuracy and the-larger-the-better SNR as well as dimensionality reduction are considered as optimization goals to build a multi-objective optimization model, which is used for feature selection, is solved by omni-optimizer algorithm. For evaluating the ef-fectiveness of the proposed two methods, a dataset experiment for comparison is imple-mented. Finally, the proposed methods are applied to a real case about credit rating of en-terprises on platform of government investment and financing. According to the results, we can conclude that the two multi-class MTS classification methods have high classification accuracy, but the MF-MTS is more valuable for application.
(4) Research on MTS based on omni-optimizer algorithm for sort evaluation
Currently, MTS is mainly used for classification problems. In fact, the MTS can sort the samples for evaluation by calculating the Mahalanobis distances of samples to refer-ence space (RS), which represents the degree of deviation from the RS. In this paper, MTS for sort evaluation is studied including:procedures of MTS for sort evaluation; variable screening model based on the omni-optimizer algorithm; validity and discussion of the MTS for sort evaluation by examples and comparative analysis. The results show that the MTS for sort evaluation method does not need to determine the index weight, can maintain consistent evaluation reference, and can screen index, which is an effective evaluation me-thod. But the mechanisms for identifying the reference space require further studies and perfect.
Based on the above research work, the main contributions and innovations of this pa-per are as follows:
(1) With identifying different goals for classification and sort evaluation, optimization ideas are imported in the core issue of MTS feature selection and multi-objective optimiza-tion model as an alternative to OAs is proposed and studied innovatively, which is solved by omni-optimizer algorithms. It is a new method for feature selection.
(2) According to the different purposes of classification. optimization or probabilistic model is used to determine threshold of MTS classification, which replaces the loss of function or exhaustive search method. It is a new threshold determining way.
(3) The MTS class classification method has been successfully extended to imba-lanced data classification and multi-class classification by means of probabilistic thresholding model, binary tree and multi-MS and the effectiveness of the methods are proved. The me-thods are new for imbalanced data classification and multi-class classification.
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