A new mathematical programming approach to multi-group classification problems

Bal, Hasan; Örkçü, H. Hasan

doi:10.1016/j.cor.2010.04.003

Cited by 17 publications

(10 citation statements)

References 24 publications

(33 reference statements)

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“…We have implemented a number of literature classifiers to compare the classification rates with our proposed SRW_HB and DR_SRW_HB. The group of classifiers include Naïve Bayes, SMO (support vector machine), Logistic regression, Bagging, Adaboost, NN and three mathematical programming-based multiclass classifiers: HB, Gehrlein (1986) and Bal and Orkcu (2011).…”

Section: Computational Resultsmentioning

confidence: 99%

“…All the mathematical programming-based classification methods, including SRW_HB, HB, and approaches proposed by Gehrlein (1986) and Bal and Orkcu (2011), are implemented in General Algebraic Modeling System (GAMS) 24.1 (GAMS Development Corporation, 2013) and solved using CPLEX 12.3 solver on a 2.40 GHz speed, 2393 MHz cpu computer system. Optimality gap is set as 0 when solving MILP problems.…”

Section: Computational Resultsmentioning

confidence: 99%

“…Sueyoshi (1999Sueyoshi ( , 2001Sueyoshi ( , 2004Sueyoshi ( , 2006, Sueyoshi and Goto (2009), Orkcu (2011) andGehrlein (1986) have all proposed hyper planes-based classifiers using either linear programming or mixed integer programming techniques. Ryoo (2006) and Bagirov, Ugon, and Webb (2011) propose models on piece-wise linear classifiers.…”

Section: Mathematical Programmingmentioning

confidence: 99%

“…A binary classifier is solely applicable to classification problems with two classes while a multi-class classifier can deal with problems with more than 2 classes. Compared with the large number of binary classifiers, there are relatively fewer multi-class classifiers in literature (Bal & Orkcu, 2011). Common strategies of tackling a multi-class classification problem include either solving the problem once using a multi-class classification algorithm or decomposing the whole problem into a series of binary problems and solving iteratively the sub-problems using binary classifiers (Ou & Murphey, 2007;Wang, Chen, & Qin, 2010).…”

Section: Introductionmentioning

confidence: 98%

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Sample re-weighting hyper box classifier for multi-class data classification

Yang

Liu

Tsoka

et al. 2015

Computers & Industrial Engineering

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a b s t r a c tIn this work, we propose two novel classifiers for multi-class classification problems using mathematical programming optimisation techniques. A hyper box-based classifier (Xu & Papageorgiou, 2009) that iteratively constructs hyper boxes to enclose samples of different classes has been adopted. We firstly propose a new solution procedure that updates the sample weights during each iteration, which tweaks the model to favour those difficult samples in the next iteration and therefore achieves a better final solution. Through a number of real world data classification problems, we demonstrate that the proposed refined classifier results in consistently good classification performance, outperforming the original hyper box classifier and a number of other state-of-the-art classifiers.Furthermore, we introduce a simple data space partition method to reduce the computational cost of the proposed sample re-weighting hyper box classifier. The partition method partitions the original dataset into two disjoint regions, followed by training sample re-weighting hyper box classifier for each region respectively. Through some real world datasets, we demonstrate the data space partition method considerably reduces the computational cost while maintaining the level of prediction accuracies.

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Section: Computational Resultsmentioning

confidence: 99%

Section: Computational Resultsmentioning

confidence: 99%

Section: Mathematical Programmingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Sample re-weighting hyper box classifier for multi-class data classification

Yang

Liu

Tsoka

et al. 2015

Computers & Industrial Engineering

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“…This problem exists in many situations and plays a key role in decision making. 1 ,..., k G G Most researches on DA have focused on the following problem, proposing new mathematical programming models and evaluating the classificatory performance of proposed models against that of the standard parametric classification procedures (Bal and Örkcü, 2010). Sueyoshi (2006) summarized previous research on DA and classified them into four groups as follows.…”

Section: Introductionmentioning

confidence: 99%

A Modified Super-Efficiency DEA Approach for Solving Multi-Groups Classification Problems

Wu¹,

An²,

Liang

2011

IJCIS

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Among the various discriminant analysis (DA) methods, researchers have investigated several directions in this area: statistics, econometrics, computer data mining technologies and mathematical programming. Recently, as a nonparametric mathematical programming approach, Data envelopment analysis has been applied in DA area and received great attention. In this paper, we propose a new discriminant approach based upon the relative distance measured by super-efficiency data envelopment analysis (DEA). This approach may generally avoid the drawbacks that usually occur in statistics discriminations of constructing function to determine a DMU's category. On the other hand, this approach may maintain discriminant capabilities by incorporating the non-parametric feature of DEA into DA. At the same time, it can also inherit the advantages of avoiding the process of dealing with different dimensional data in DEA. Our approach can be used to classify a sample's category by the discrimination results, even in the multiple-groups situation. Therefore, it can be applied to the discriminant analysis in various real-life cases.

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Predictive Analytics: Classification in Medicine and Biology

Lee

2016

Healthcare Analytics: From Data to Knowledge to Healthcare Improvement

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A new mathematical programming approach to multi-group classification problems

Cited by 17 publications

References 24 publications

Sample re-weighting hyper box classifier for multi-class data classification

Sample re-weighting hyper box classifier for multi-class data classification

A Modified Super-Efficiency DEA Approach for Solving Multi-Groups Classification Problems

Predictive Analytics: Classification in Medicine and Biology

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