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Journal articles on the topic 'Linear programming-based discriminant analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Liu, Yi‐Hsin, and John Maloney. "Discriminant analysis and linear programming." International Journal of Mathematical Education in Science and Technology 28, no. 2 (March 1997): 207–10. http://dx.doi.org/10.1080/0020739970280204.

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2

Gochet, Willy, Antonie Stam, V. Srinivasan, and Shaoxiang Chen. "Multigroup Discriminant Analysis Using Linear Programming." Operations Research 45, no. 2 (April 1997): 213–25. http://dx.doi.org/10.1287/opre.45.2.213.

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3

Ubi, Jaan, Evald Ubi, Innar Liiv, and Kristina Murtazin. "Predicting Student Retention by Linear Programming Discriminant Analysis." International Journal of Technology and Educational Marketing 4, no. 2 (July 2014): 43–53. http://dx.doi.org/10.4018/ijtem.2014070104.

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The goal of the paper is to predict student retention with an ensemble method by combining linear programming (LP) discriminant analysis approaches together with bootstrapping and feature salience detection. In order to perform discriminant analysis, we linearize a fractional programming method by using Charnes-Cooper transformation (CCT) and apply linear programming, while comparing with an approach that uses deviation variables (DV) to tackle a similar multiple criteria optimization problem. We train a discriminatory hyperplane family and make the decision based on the average of the histograms created, thereby reducing variability of predictions. Feature salience detection is performed by using the peeling method, which makes the selection based on the proportion of variance explained in the correlation matrix. While the CCT method is superior in detecting true-positives, DV method excels in finding true-negatives. The authors obtain optimal results by selecting either all 14 (CCT) or the 8 (DV) most important student study related and demographic dimensions. They also create an ensemble. A quantitative course along with the age at accession are deemed to be the most important, whereas the two courses resulting in less than 2% of failures are amongst the least important, according to peeling. A five-fold Kolmogorov-Smirnov test is undertaken, in order to help university staff in devising intervention measures.

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4

Youssef, Slah Ben, and Abdelwaheb Rebai. "Discriminant analysis using fuzzy linear programming models." International Journal of Knowledge Management Studies 2, no. 4 (2008): 445. http://dx.doi.org/10.1504/ijkms.2008.019751.

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5

Glover, Fred. "Improved Linear Programming Models for Discriminant Analysis." Decision Sciences 21, no. 4 (December 1990): 771–85. http://dx.doi.org/10.1111/j.1540-5915.1990.tb01249.x.

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6

Glen, J. J. "Mathematical programming models for piecewise-linear discriminant analysis." Journal of the Operational Research Society 56, no. 3 (March 2005): 331–41. http://dx.doi.org/10.1057/palgrave.jors.2601818.

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7

SUN, MINGHE. "A MIXED INTEGER PROGRAMMING MODEL FOR MULTIPLE-CLASS DISCRIMINANT ANALYSIS." International Journal of Information Technology & Decision Making 10, no. 04 (July 2011): 589–612. http://dx.doi.org/10.1142/s0219622011004476.

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A mixed integer programming model is proposed for multiple-class discriminant and classification analysis. When multiple discriminant functions, one for each class, are constructed with the mixed integer programming model, the number of misclassified observations in the sample is minimized. This model is an extension of the linear programming models for multiple-class discriminant analysis but may be considered as a generalization of mixed integer programming formulations for two-class classification analysis. Properties of the model are studied. The model is immune from any difficulties of many mathematical programming formulations for two-class classification analysis, such as nonexistence of optimal solutions, improper solutions, and instability under linear data transformation. In addition, meaningful discriminant functions can be generated under conditions where other techniques fail. Examples are provided. Results on publically accessible datasets show that this model is very effective in generating powerful discriminant functions.

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8

Gordon, Kenneth R., Michael Palmer, and Fred Glover. "Modeling international loan portfolios through Linear Programming Discriminant Analysis." Journal of Policy Modeling 15, no. 3 (June 1993): 297–312. http://dx.doi.org/10.1016/0161-8938(93)90034-n.

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9

Retzlaff-Roberts, Donna L. "A ratio model for discriminant analysis using linear programming." European Journal of Operational Research 94, no. 1 (October 1996): 112–21. http://dx.doi.org/10.1016/0377-2217(95)00196-4.

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10

Sun, Minghe. "Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis." International Journal of Strategic Decision Sciences 1, no. 1 (January 2010): 57–80. http://dx.doi.org/10.4018/jsds.2010103004.

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New linear programming approaches are proposed as nonparametric procedures for multiple-class discriminant and classification analysis. A new MSD model minimizing the sum of the classification errors is formulated to construct discriminant functions. This model has desirable properties because it is versatile and is immune to the pathologies of some of the earlier mathematical programming models for two-class classification. It is also purely systematic and algorithmic and no user ad hoc and trial judgment is required. Furthermore, it can be used as the basis to develop other models, such as a multiple-class support vector machine and a mixed integer programming model, for discrimination and classification. A MMD model minimizing the maximum of the classification errors, although with very limited use, is also studied. These models may also be considered as generalizations of mathematical programming formulations for two-class classification. By the same approach, other mathematical programming formulations for two-class classification can be easily generalized to multiple-class formulations. Results on standard as well as randomly generated test datasets show that the MSD model is very effective in generating powerful discriminant functions.

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11

Lei, Zhen, and Stan Z. Li. "Contextual constraints based linear discriminant analysis." Pattern Recognition Letters 32, no. 4 (March 2011): 626–32. http://dx.doi.org/10.1016/j.patrec.2010.12.001.

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12

Ji, Ai-bing, Ye Ji, and Yanhua Qiao. "DEA-Based Piecewise Linear Discriminant Analysis." Computational Economics 51, no. 4 (December 7, 2016): 809–20. http://dx.doi.org/10.1007/s10614-016-9642-8.

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13

Wu, Yufei, and Guan Yu. "Weighted linear programming discriminant analysis for high‐dimensional binary classification." Statistical Analysis and Data Mining: The ASA Data Science Journal 13, no. 5 (July 4, 2020): 437–50. http://dx.doi.org/10.1002/sam.11473.

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14

Chen, Xiaobo, Jian Yang, David Zhang, and Jun Liang. "Complete large margin linear discriminant analysis using mathematical programming approach." Pattern Recognition 46, no. 6 (June 2013): 1579–94. http://dx.doi.org/10.1016/j.patcog.2012.11.019.

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15

Hardy, William E., and John L. Adrian. "A linear programming alternative to discriminant analysis in credit scoring." Agribusiness 1, no. 4 (1985): 285–92. http://dx.doi.org/10.1002/1520-6297(198524)1:4<285::aid-agr2720010406>3.0.co;2-m.

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16

Le Thi, Hoai An, and Duy Nhat Phan. "DC programming and DCA for sparse Fisher linear discriminant analysis." Neural Computing and Applications 28, no. 9 (February 11, 2016): 2809–22. http://dx.doi.org/10.1007/s00521-016-2216-9.

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17

CUI, Zi-feng, and Xiao-hua JI. "Feature selection based on linear discriminant analysis." Journal of Computer Applications 29, no. 10 (December 28, 2009): 2781–85. http://dx.doi.org/10.3724/sp.j.1087.2009.02781.

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18

Lu, Gui-Fu, Jian Zou, Yong Wang, and Zhongqun Wang. "Sparse L1-norm-based linear discriminant analysis." Multimedia Tools and Applications 77, no. 13 (September 13, 2017): 16155–75. http://dx.doi.org/10.1007/s11042-017-5193-9.

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19

Lv, Hao, Wenjie Xu, Juan You, and Shanbai Xiong. "Classification of freshwater fish species by linear discriminant analysis based on near infrared reflectance spectroscopy." Journal of Near Infrared Spectroscopy 25, no. 1 (February 2017): 54–62. http://dx.doi.org/10.1177/0967033516678801.

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Near infrared reflectance spectroscopy was used to discriminate different species of freshwater fish samples. Samples from seven freshwater fish species of the family Cyprinidae (black carp ( Mylopharyngodon piceus), grass carp ( Ctenopharyngodon idellus), silver carp ( Hypophthalmichthys molitrix), bighead carp ( Aristichthys nobilis), common carp ( Cyprinus carpio), crucian ( Carassius auratus), and bream ( Parabramis pekinensis)) were scanned by near infrared reflectance spectroscopy from 1000 nm to 1799 nm. Linear discriminant analysis models were built for the classification of species. We inspected the effect of partial least square, principal component analysis, competitive adaptive reweighted sampling, and fast Fourier transform on linear discriminant analysis. The results showed that the dimension reduction methods worked very well for this example. Linear discriminant analysis models which were combined with principal component analysis and fast Fourier transform could classify accurately all the samples under multiplicative scatter correction pre-processing. According to the loadings in principal component analysis, spectra wavelengths 1000, 1001, 1154, 1208, 1284, 1288, 1497, 1665, and 1770 nm were selected as effective wavelengths in linear discriminant analysis. The discriminant analysis was simplified by using effective wavelengths as independent variables in a linear discriminant analysis model. This study indicated that linear discriminant analysis combined with near infrared reflectance spectroscopy could be an effective strategy for the classification of freshwater fish species.

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20

Wang, Huiya, and Shanwen Zhang. "Tumor classification based on orthogonal linear discriminant analysis." Bio-Medical Materials and Engineering 24, no. 1 (2014): 1399–405. http://dx.doi.org/10.3233/bme-130944.

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21

Maria Hadria, F., and S. Jayanthy. "ARM BASED SECURITY SYSTEM USING LINEAR DISCRIMINANT ANALYSIS." ICTACT Journal on Microelectronics 3, no. 3 (October 1, 2017): 417–24. http://dx.doi.org/10.21917/ijme.2017.0074.

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22

Qi, Yudan, Huaxiang Zhang, Bin Zhang, Li Wang, and Shunxin Zheng. "Cross-media retrieval based on linear discriminant analysis." Multimedia Tools and Applications 78, no. 17 (December 14, 2018): 24249–68. http://dx.doi.org/10.1007/s11042-018-6994-1.

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23

Zhang, Genyuan. "Face Recognition based on Fuzzy Linear Discriminant Analysis." IERI Procedia 2 (2012): 873–79. http://dx.doi.org/10.1016/j.ieri.2012.06.185.

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24

Fujin Zhong and Jiashu Zhang. "Linear Discriminant Analysis Based on L1-Norm Maximization." IEEE Transactions on Image Processing 22, no. 8 (August 2013): 3018–27. http://dx.doi.org/10.1109/tip.2013.2253476.

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25

Na, Jin Hee, Myoung Soo Park, Woo-Sung Kang, and Jin Young Choi. "Linear boundary discriminant analysis based on QR decomposition." Pattern Analysis and Applications 17, no. 1 (July 26, 2012): 105–12. http://dx.doi.org/10.1007/s10044-012-0285-7.

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26

Gupta,, Yash P., Ramesh P. Rao, and Prabir K. Bagchi. "LINEAR GOAL PROGRAMMING AS AN ALTERNATIVE TO MULTIVARIATE DISCRIMINANT ANALYSIS: A NOTE." Journal of Business Finance & Accounting 17, no. 4 (September 1990): 593–98. http://dx.doi.org/10.1111/j.1468-5957.1990.tb01146.x.

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27

Nath, Ravinder, and Thomas W. Jones. "A Variable Selection Criterion in the Linear Programming Approaches to Discriminant Analysis." Decision Sciences 19, no. 3 (September 1988): 554–63. http://dx.doi.org/10.1111/j.1540-5915.1988.tb00286.x.

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28

Lee, Eva K., Richard J. Gallagher, and David A. Patterson. "A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region." INFORMS Journal on Computing 15, no. 1 (February 2003): 23–41. http://dx.doi.org/10.1287/ijoc.15.1.23.15158.

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29

Erenguc, S. Selcuk, and Gary J. Koehler. "Survey of mathematical programming models and experimental results for linear discriminant analysis." Managerial and Decision Economics 11, no. 4 (1990): 215–25. http://dx.doi.org/10.1002/mde.4090110403.

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30

Smaoui, Soulef, Habib Chabchoub, and Belaid Aouni. "Mathematical Programming Approaches to Classification Problems." Advances in Operations Research 2009 (2009): 1–34. http://dx.doi.org/10.1155/2009/252989.

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Discriminant Analysis (DA) is widely applied in many fields. Some recent researches raise the fact that standard DA assumptions, such as a normal distribution of data and equality of the variance-covariance matrices, are not always satisfied. A Mathematical Programming approach (MP) has been frequently used in DA and can be considered a valuable alternative to the classical models of DA. The MP approach provides more flexibility for the process of analysis. The aim of this paper is to address a comparative study in which we analyze the performance of three statistical and some MP methods using linear and nonlinear discriminant functions in two-group classification problems. New classification procedures will be adapted to context of nonlinear discriminant functions. Different applications are used to compare these methods including the Support Vector Machines- (SVMs-) based approach. The findings of this study will be useful in assisting decision-makers to choose the most appropriate model for their decision-making situation.

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31

Shi, Hanqin, and Liang Tao. "Visual comparison based on linear regression model and linear discriminant analysis." Journal of Visual Communication and Image Representation 57 (November 2018): 118–24. http://dx.doi.org/10.1016/j.jvcir.2018.10.026.

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32

Ricciardi, Carlo, Antonio Saverio Valente, Kyle Edmund, Valeria Cantoni, Roberta Green, Antonella Fiorillo, Ilaria Picone, Stefania Santini, and Mario Cesarelli. "Linear discriminant analysis and principal component analysis to predict coronary artery disease." Health Informatics Journal 26, no. 3 (January 23, 2020): 2181–92. http://dx.doi.org/10.1177/1460458219899210.

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Coronary artery disease is one of the most prevalent chronic pathologies in the modern world, leading to the deaths of thousands of people, both in the United States and in Europe. This article reports the use of data mining techniques to analyse a population of 10,265 people who were evaluated by the Department of Advanced Biomedical Sciences for myocardial ischaemia. Overall, 22 features are extracted, and linear discriminant analysis is implemented twice through both the Knime analytics platform and R statistical programming language to classify patients as either normal or pathological. The former of these analyses includes only classification, while the latter method includes principal component analysis before classification to create new features. The classification accuracies obtained for these methods were 84.5 and 86.0 per cent, respectively, with a specificity over 97 per cent and a sensitivity between 62 and 66 per cent. This article presents a practical implementation of traditional data mining techniques that can be used to help clinicians in decision-making; moreover, principal component analysis is used as an algorithm for feature reduction.

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33

Stam, Antonie, and Erich A. Joachimsthaler. "Solving the Classification Problem in Discriminant Analysis Via Linear and Nonlinear Programming Methods." Decision Sciences 20, no. 2 (June 1989): 285–93. http://dx.doi.org/10.1111/j.1540-5915.1989.tb01878.x.

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34

Yu, Guan, Yufeng Liu, Kim-Han Thung, and Dinggang Shen. "Multi-Task Linear Programming Discriminant Analysis for the Identification of Progressive MCI Individuals." PLoS ONE 9, no. 5 (May 12, 2014): e96458. http://dx.doi.org/10.1371/journal.pone.0096458.

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35

Ikeda, Seiichi, and Yoshiharu Sato. "Kernel Canonical Discriminant Analysis Based on Variable Selection." Journal of Advanced Computational Intelligence and Intelligent Informatics 13, no. 4 (July 20, 2009): 416–20. http://dx.doi.org/10.20965/jaciii.2009.p0416.

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We have shown that models support vector regression and classification are essentially linear in reproducing kernel Hilbert space (RKHS). To overcome the over fitting problem, a regularization term is added to the optimization process, deciding the coefficient of regularization term involves difficulties. We introduce the variable selection concept to the linear model in RKHS, where the kernel functions is treated as variable transformation when its value is given by observation. We show that kernel canonical discriminant functions for multiclass problems can be discussed under variable selection, which enables us to reduce the number of kernel functions in the discriminant function, i.e., the discriminant function is obtained as linear combinations of sufficiently small numbers of kernel functions, so, we can expect to get reasonable prediction. We discuss variable selection performance in canonical discriminant functions compared to support vector machines.

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36

Roh, Seok-Beom, Eun-Jin Hwang, and Tae-Chon Ahn. "Design of Pattern Classification Rule based on Local Linear Discriminant Analysis Classifier by using Differential Evolutionary Algorithm." Journal of Korean Institute of Intelligent Systems 22, no. 1 (February 25, 2012): 81–86. http://dx.doi.org/10.5391/jkiis.2012.22.1.81.

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37

Budiharto. "THE ACCESS CONTROL SYSTEM BASED ON LINEAR DISCRIMINANT ANALYSIS." Journal of Computer Science 10, no. 3 (March 1, 2014): 453–57. http://dx.doi.org/10.3844/jcssp.2014.453.457.

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38

Ji Wang. "Multi-spectral Palmprint Recognition Based on Linear Discriminant Analysis." International Journal of Advancements in Computing Technology 5, no. 9 (May 31, 2013): 918–24. http://dx.doi.org/10.4156/ijact.vol5.issue9.109.

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39

Wijaya, I. Gede Pasek Suta, Keiichi Uchimura, and Gou Koutaki. "Face Recognition Based on Incremental Predictive Linear Discriminant Analysis." IEEJ Transactions on Electronics, Information and Systems 133, no. 1 (2013): 74–83. http://dx.doi.org/10.1541/ieejeiss.133.74.

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40

Huitao LUO, and Weng Jie. "Research on Linear Discriminant Analysis Based on Small Samples." Journal of Convergence Information Technology 7, no. 18 (October 31, 2012): 449–55. http://dx.doi.org/10.4156/jcit.vol7.issue18.54.

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41

Gopi, E. S., and P. Palanisamy. "Formulating particle swarm optimization based membership linear discriminant analysis." Swarm and Evolutionary Computation 12 (October 2013): 65–73. http://dx.doi.org/10.1016/j.swevo.2013.03.001.

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42

Jing, Zhecheng, Guolin Wang, Shupei Zhang, and Chengqun Qiu. "Building Tianjin driving cycle based on linear discriminant analysis." Transportation Research Part D: Transport and Environment 53 (June 2017): 78–87. http://dx.doi.org/10.1016/j.trd.2017.04.005.

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43

Pnevmatikakis, Aristodemos, and Lazaros Polymenakos. "Subclass linear discriminant analysis for video-based face recognition." Journal of Visual Communication and Image Representation 20, no. 8 (November 2009): 543–51. http://dx.doi.org/10.1016/j.jvcir.2009.08.001.

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44

Buvana, M., M. Suganthi, and K. Muthumayil. "Linear discriminant analysis-based service discovery algorithm in MANET." International Journal of Internet Protocol Technology 9, no. 2/3 (2016): 90. http://dx.doi.org/10.1504/ijipt.2016.079543.

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45

Cui, Jin Rong. "Multispectral palmprint recognition using Image-Based Linear Discriminant Analysis." International Journal of Biometrics 4, no. 2 (2012): 106. http://dx.doi.org/10.1504/ijbm.2012.046244.

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46

Ramos-Guajardo, Ana B., and Przemyslaw Grzegorzewski. "Distance-based linear discriminant analysis for interval-valued data." Information Sciences 372 (December 2016): 591–607. http://dx.doi.org/10.1016/j.ins.2016.08.068.

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47

Fu, Yong-Gang, and Rui-Min Shen. "Color image watermarking scheme based on linear discriminant analysis." Computer Standards & Interfaces 30, no. 3 (March 2008): 115–20. http://dx.doi.org/10.1016/j.csi.2007.08.013.

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48

Chan. "Face Biometrics Based on Principal Component Analysis and Linear Discriminant Analysis." Journal of Computer Science 6, no. 7 (July 1, 2010): 693–99. http://dx.doi.org/10.3844/jcssp.2010.693.699.

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49

nka, Riya. "Face Recognition Based on Principal Component Analysis and Linear Discriminant Analysis." International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering 4, no. 8 (August 20, 2015): 7266–74. http://dx.doi.org/10.15662/ijareeie.2015.0408046.

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50

Liu, Xiao Ping, and Gui Yun Xu. "PSO-Based Uncorrelated Hybrid Discriminant Analysis Algorithm." Applied Mechanics and Materials 109 (October 2011): 671–75. http://dx.doi.org/10.4028/www.scientific.net/amm.109.671.

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Hybrid discriminant analysis (HDA) can overcome small sample problems and outperform PCA and LDA by unifying principal component analysis (PCA) and linear discriminant analysis (LDA) in a single framework. However, the existing HDA algorithm can’t extract more discriminant information from dataset, and model parameters are difficult to select. To deal with the above problems, a particle swarm optimal (PSO)-based uncorrelated hybrid discriminant analysis algorithm is presented. The conjugate orthogonal condition is added to optimization problem of HDA, PSO is explored to select optimal HDA parameters and the optimal solution can be achieved by solving eigenvalue problem. Simulation demonstrates merits of the proposed algorithm.

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