Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30685
A New Approach for Classifying Large Number of Mixed Variables

Authors: Hashibah Hamid

Abstract:

The issue of classifying objects into one of predefined groups when the measured variables are mixed with different types of variables has been part of interest among statisticians in many years. Some methods for dealing with such situation have been introduced that include parametric, semi-parametric and nonparametric approaches. This paper attempts to discuss on a problem in classifying a data when the number of measured mixed variables is larger than the size of the sample. A propose idea that integrates a dimensionality reduction technique via principal component analysis and a discriminant function based on the location model is discussed. The study aims in offering practitioners another potential tool in a classification problem that is possible to be considered when the observed variables are mixed and too large.

Keywords: classification, Principal Component Analysis, location model, mixed variables

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083313

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1136

References:


[1] W. R. Klecka, Discriminant Analysis. Series: Quantitative Applications in the Social Sciences. A Sage University Paper. Beverly Hills, CA: Saga, 1980.
[2] M. N├║├▒ez, A. Villarroya and J. M. Oller, "Minimum Distance Probability Discriminant Analysis for Mixed Variables," Biometrics, vol. 59, pp. 248-253, 2003.
[3] Y. H. Chan, "Biostatistics 303: Discriminant Analysis," Singapore Medical Journal, vol. 46, no. 2, pp. 54-61, 2005.
[4] M. Doumpos and C. Zopounidis, Multicriteria Decision Aid Classification Methods. Kluwer Academic Publishers, 2002.
[5] R. A. Fisher, "The Use of Multiple Measurements in Taxonomic Problems," Annals of Eugenics, vol. 7, no. 2, pp. 179-188, 1936.
[6] S. B. Bull and A. Donner, "The Efficiency of Multinominal Logistic Regression compared with Multiple Group Discriminant Analysis," Journal of the American Statistical Association, vol. 82, pp. 1118- 1122, 1987.
[7] J. A. Anderson, Logistic Discrimination. In Handbook of Statistics (Vol. 2) P. R. Krishnaiah and L. N. Kanal (Eds.). Amsterdam: North- Holland, pp. 169-191, 1992.
[8] J. J. Daudin, "Selection of Variables in Mixed-variable Discriminant Analysis," Biometrics, vol. 42, no. 3, pp. 473-481, 1986.
[9] O. Asparoukhov and W. J. Krzanowski, "Non-parametric Smoothing of the Location Model in Mixed Variable Discrimination," Statistics and Computing, vol. 10, pp. 289-297, 2000.
[10] A. Merbouha and A. Mkhadri, "Regularization of the Location Model in Discrimination with Mixed Discrete and Continuous Variables," Computational Statistics and Data Analysis, vol. 45, pp. 563-576, 2004.
[11] W. J. Krzanowski, "Discrimination and Classification using Both Binary and Continuous Variables," Journal of the American Statistical Association, vol. 70, no. 352, pp. 782-790, 1975.
[12] W. J. Krzanowski, "The Location Model for Mixtures of Categorical and Continuous Variables," Journal of Classification, vol. 10, pp. 25- 49, 1993.
[13] D. J. Hand, Construction and Assessment of Classification Rules. Chichester: John Wiley & Son, 1997.
[14] K. D. Wernecke, "A Coupling Procedure for the Discrimination of Mixed Data," Biometrics, vol. 48, no. 2, pp. 497-506, 1992.
[15] L. Xu, A. Krzyżak and C. Y. Suen, "Methods of Combining Multiple Classifiers and Their Applications to Handwriting Recognition," IEEE Transactions on Systems, Man, and Cybernetics, vol. 22, no. 3, pp. 418-435, 1992.
[16] P. C. Chang and A. A. Afifi, "Classification based on Dichotomous and Continuous Variables," Journal of the American Statistical Association, vol. 69, no. 346, pp. 336-339, 1974.
[17] W. J. Krzanowski, "Mixtures of Continuous and Categorical Variables in Discriminant Analysis," Biometrics, vol. 36, pp. 493- 499, 1980.
[18] N. I. Mahat, W. J. Krzanowski and A. Hernandez, "Strategies for Non-Parametric Smoothing of the Location Model in Mixed-Variable Discriminant Analysis," Modern Applied Science, vol. 3, no. 1, pp. 151-163, 2009.
[19] J. Aitchison and C. G. G. Aitken, "Multivariate Binary Discrimination by the Kernel Method," Biometrika, vol. 63, pp. 413-420, 1976.
[20] J. A. Anderson, "Separate Sample Logistic Discrimination," Biometrika, vol. 59, no. 1, pp. 19-35, 1972.
[21] D. J. Hand, J. J. Oliver and A. D. Lunn, "Discriminant Analysis when the Classes Arise from a Continuum," Pattern Recognition, vol. 31, no. 5, pp. 641-650, 1998.
[22] P. A. Lachenbruch, C. Sneeringer and L. T. Revo, "Robustness of the Linear and Quadratic Discriminant Function to Certain Types of Nonnormality," Communications in Statistics, vol. 1, pp. 39-56, 1973.
[23] R. A Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (3rd edition). New Jersey, Englewood Cliffs: Prentice Hall, 1992.
[24] A. Das, Discriminant Analysis and Its Applications. BDM&DM Term Paper, 2009.
[25] T. W. Anderson, An Introduction to Multivariate Statistical Analysis (2nd edition). New York: John Wiley & Sons, 1984.
[26] Guo, T. Hastie and R. Tibshirani, "Regularized Linear Discriminant Analysis and Its Application in Microarrays," Biostatistics, vol. 8, no. 1, pp. 86-100, 2007.
[27] I. G. Vlachonikolis and F. H. C. Marriott, "Discrimination with Mixed Binary and Continuous Data," Applied Statistics, vol. 31, no. 1, pp. 23-31, 1982.
[28] N. I. Mahat, W. J. Krzanowski and A. Hernandez, "Variable Selection in Discriminant Analysis Based on the Location Model for Mixed Variables," Advances in Data Analysis and Classification, vol. 1, no. 2, pp. 105-122, 2007
[29] H. Ping, "Classification Methods and Applications to Mass Spectral Data," unpublished PhD Thesis. Hong Kong: Baptist University, Department of Mathematics, 2005
[30] J. J. Dai, L. Lieu and D. Rocke, "Dimension Reduction for Classification with Gene Expression Microarray Data," Statistical Applications in Genetics and Molecular Biology, vol. 5, no. 1, article 6, 20 pages, 2006.
[31] Q. Li, "An Integrated Framework of Feature Selection and Extraction for Appearance-based Recognition," unpublished PhD Thesis. University Of Delaware: Faculty of Computer Science, 2006.
[32] J. S. Marron, M. J. Todd and J. Ahn, "Distance Weighted Discrimination," Journal of the American Statistical Association, vol. 480, pp. 1267-1271, 2007.
[33] C. Ambroise and G. J. McLachlan, "Selection Bias in Gene Extraction on the Basis of Microarray Gene-Expression Data," Proceedings of the National Academy of Sciences, 2002, vol. 99, no. 10, pp. 6562-6566.
[34] R. Simon, M. D. Radmacher, K. Dobbin and L. M. McShane, "Pitfalls in the Use of DNA Microarray Data for Diagnostic and Prognostic Classification," Journal of the National Cancer Institute, vol. 95, no. 1, pp. 14-18, 2003.
[35] Z. Qiao, L. Zhou and J. Z. Huang, "Effective Linear Discriminant Analysis for High Dimensional, Low Sample Size Data," Proceedings of the World Congress on Engineering (WCE), 2008, vol. 2, pp. 1070- 1075.
[36] G. J. McLachlan, "A Criterion for Selecting Variables for the Linear Discriminant Function," Biometrics, vol. 32, no. 3, pp. 529-534, 1976.
[37] P. Xu, G. N. Brock and R. S. Parrish, "Modified Linear Discriminant Analysis Approaches for Classification of High-Dimensional Microarray Data," Computational Statistics and Data Analysis, vol. 53, no. 5, pp. 1674-1687, 2009.
[38] Y. Lu, Q. Tian, M. Sanchez, J. Neary, F. Liu and Y. Wang, "Learning Microarray Gene Expression Data by Hybrid Discriminant Analysis," IEEE Multimedia Magazine, Special Issue on Multimedia Signal Processing and Systems in Health Care and Life Science, vol. 14, no. 4, pp. 22-31, 2007.
[39] I. G. Chong and C. H. Jun, "Performance of Some Variable Selection Methods when Multicollinearity is Present," Chemometrics and Intelligent Laboratory Systems, vol. 78, pp. 103-112, 2005.
[40] J. M. Weiner and O. J. Dunn, "Elimination of Variate in Linear Discrimination Problems," Biometrics, vol. 22, no. 2, pp. 268-275, 1966.
[41] L. Jenkins and M. Anderson, "A Multivariate Statistical Approach to Reducing the Number of Variables in Data Envelopment Analysis," European Journal of Operational Research, vol. 147, no. 1, pp. 51- 61, 2003.
[42] F. Nie, S. Xiang, Y. Song and C. Zhang, "Extracting the Optimal Dimensionality for Discriminant Analysis," International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 2, pp. 617-620, 2007.
[43] P. N. Belhumeur, J. P. Hespanha and D. J. Kriegman, "Eigenfaces vs. Fisherfaces: Recognition using Class Specific Linear Projection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, 1997.
[44] W. Zhao, R. Chellappa and N. Nandhakumar, "Empirical Performance Analysis of Linear Discriminant Classifiers," Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1998, pp. 164-169.
[45] L. F. Chen, H. Y. M. Liao, M. T. Ko, J. C. Lin and G. J. Yu, "A New LDA-based Face Recognition System which can Solve the Small Sample Size Problem," Pattern Recognition, vol. 33, no. 10, pp. 1713-1726, 2000.
[46] J. Yang and J. Y. Yang, "Optimal FLD Algorithm for Facial Feature Extraction," SPIE Proceedings of the Intelligent Robots and Computer Vision XX: Algorithms, Techniques, and Active Vision, 2001, vol. 4572, pp. 438-444.
[47] H. Yu and J. Yang, "A Direct LDA Algorithm for High-Dimensional Data with Application to Face Recognition," Pattern Recognition, vol. 34, no. 10, pp. 2067-2070, 2001.
[48] J. Yang and J. Y. Yang, "Why Can LDA be Performed in PCA Transformed Space? Rapid and Brief Communication," Pattern Recognition, vol. 36, no. 2, pp. 563-566, 2003.
[49] J. Ye and T. Xiong, "Computational and Theoretical Analysis of Null Space and Orthogonal Linear Discriminant Analysis," Journal of Machine Learning Research, vol. 7, pp. 1183-1204, 2006.
[50] S. Wold, K. Esbensen and P. Geladi, "Principal Component Analysis," Chemometrics Intelligent Laboratory Systems, vol. 2, pp. 37-52,1987.
[51] D. Ghosh, "Singular Value Decomposition Regression Modeling for Classification of Tumors from Microarray Experiments," Proceedings of the Pacific Symposium on Biocomputing, 2002, pp. 11462-11467.
[52] S. Deerwester, S. T. Dumais, G. W. Furnas, T. K. Landauer and R. Harshman, "Indexing by Latent Semantic Analysis," Journal of the American Society for Information Science, vol. 41, no. 6, pp. 391- 407, 1990.
[53] A. Kabán and M. A. Girolami, "Fast Extraction of Semantic Features from a Latent Semantic Indexed Corpus," Neural Processing Letters, vol. 15, no. 1, pp. 31-43, 2002.
[54] P. M. Garthwaite, "An Interpretation of Partial Least Squares," Journal of the American Statistical Association, vol. 89, no. 425, pp. 122-127, 1994.
[55] D. V. Nguyen and D. M. Rocke, "Tumor Classification by Partial Least Squares using Microarray Gene Expression Data," Bioinformatics, vol. 18, no. 1, pp. 39-50, 2002a.
[56] D. V. Nguyen and D. M. Rocke, "Multi-class Cancer Classification via Partial Least Squares with Gene Expression Profiles," Bioinformatics, vol. 18, pp. 1216-1226, 2002b.
[57] X. Huang and W. Pan, "Linear Regression and Two-class Classification with Gene Expression Data," Bioinformatics, vol. 19, pp. 2072-2978, 2003.
[58] A. Boulesteix, "PLS Dimension Reduction for Classification with Microarray Data," Statistical Applications in Genetics and Molecular Biology, vol. 3, pp. 1-33, 2004.
[59] R. D. Cook, Regression Graphics. New York: John Wiley & Sons, 1998.
[60] F. Chiaromonte and J. Martinelli, "Dimension Reduction Strategies for Analyzing Global Gene Expression Data with a Response," Mathematical Biosciences, vol. 176, pp. 123-144, 2002.
[61] A. Antoniadis, S. Lambert-Lacroix and F. Leblanc, "Effective Dimension Reduction Methods for Tumor Classification using Gene Expression Data," Bioinformatics, vol. 19, pp. 563-570, 2003.
[62] E. Bura and R. M. Pfeiffer, "Graphical Methods for Class Prediction using Dimension Reduction Techniques on DNA Microarray Data," Bioinformatics, vol. 19, pp. 1252-1258, 2003.
[63] W. Zhao, R. Chellappa and P. J. Philips, Subspace Linear Discriminant Analysis for Face Recognition. Technical Report CARTR- 914. University of Maryland, College Park, 1999.
[64] J. Baeka and M. Kimb, "Face Recognition using Partial Least Squares Components," Pattern Recognition," vol. 37, no. 6, pp. 1303-1306, 2004.
[65] W. Zuo, D. Zhang, J. Yang and K. Wang, "BDPCA plus LDA: A Novel Fast Feature Extraction Technique for Face Recognition," IEEE Transactions on Systems, Man, and Cybernetics: Part BCybernetics, vol. 36, no. 4, pp. 946-953, 2006.
[66] A. Caprihan, G. D. Pearlson and V. D. Calhoun, "Application of Principal Component Analysis to Distinguish Patients with Schizophrenia from Healthy Controls based on Fractional Anisotropy Measurements," Neuroimage, vol. 42, no. 2, pp. 675-682, 2008.
[67] G. P. McCabe, Principal Variables. Technical Report. West Lafayette: Purdue University, 1982.
[68] G. A. F. Seber, Multivariate Observations. New York: John Wiley & Sons, 1984.
[69] I. T. Jolliffe, Principal Component Analysis. New York: Springer- Verlag, 1986.
[70] H. B. Deng, L. W. Jin, L. X. Zhen and J. C. Huang, "A New Facial Expression Recognition Method on Local Gabor Filter Bank and PCA plus LDA," International Journal of Information Technology, vol. 11, no. 11, pp. 86-96, 2005.
[71] W. Hwang, T. K. Kim and S. C. Kee, "LDA with Subgroup PCA Method for Facial Image Retrieval," The 5th International Workshop on Image Analysis for Multimedia Interactive Services (WIAMIS), Portugal: Lisbon, April 2004, pp. 21-23.
[72] I. T. Jolliffe, Principal Component Analysis (2nd edition). New York: Springer-Verlag, 2002.
[73] B. G. Amidan and D. N. Hagedorn, Logistic Regression Applied to Seismic Discrimination. Technical Report. Pacific Northwest National Laboratory (PNNL): Washington (US), Richland, 1998.
[74] A. P. Worth and M. T. D. Cronin, "The Use of Discriminant Analysis, Logistic Regression and Classification Tree Analysis in the Development of Classification Models for Human Health Effects," Theochem, vol. 622, pp. 97-111, 2003.
[75] H. C. Kim, D. Kim and S. Y. Bang, "Extensions of LDA by PCA Mixture Model and Class-wise Features," Journal of the Pattern Recognition Society, vol. 36, pp. 1095-1105, 2003.
[76] Y. Liang, C. Li, W. Gong and Y. Pan, "Uncorrelated Linear Discriminant Analysis based on Weighted Pairwise Fisher Criterion," The Journal of the Pattern Recognition Society, vol. 40, pp. 3606- 3615, 2007.
[77] M. M. Sithole, "Variable Selection in Principal Component Analysis: Using Measures of Multivariate Association," unpublished Master Thesis. Curtin University of Technology, School of Mathematics and Statistics, 1992.
[78] C. R. Rao, "The Use and Interpretation of Principal Component Analysis in Applied Research," Sankhy─ü: The Indian Journal of Statistics, Series A, vol. 26, no. 4, pp. 329-358, 1964.
[79] W. J. Krzanowski, "Selection of Variables to Preserve Multivariate Data Structure using Principal Components," Applied Statistics, vol. 36, no. 1, pp. 22-33, 1987.
[80] D. C. Hoyle, "Automatic PCA Dimension Selection for High Dimensional Data and Small Sample Sizes," Journal of Machine Learning Research, vol. 9, pp. 2733-2759, 2008.
[81] W. K. Härdle and Z. Hlávka, Multivariate Statistics: Exercises and Solutions. New York: Springer, 2007.