In this paper, a new supervised classification method dedicated to binary predictors is proposed. Its originality is to combine a model-based classification rule with similarity measures thanks to the introduction of new family of exponential kernels. Some links are established between existing similarity measures when applied to binary predictors. A new family of measures is also introduced to unify some of the existing literature. The performance of the new classification method is illustrated on two real datasets (verbal autopsy data and handwritten digit data) using 76 similarity measures.
@article{bwmeta1.element.doi-10_1515_demo-2015-0017, author = {Seydou N. Sylla and St\'ephane Girard and Abdou Ka Diongue and Aldiouma Diallo and Cheikh Sokhna}, title = {A classification method for binary predictors combining similarity measures and mixture models}, journal = {Dependence Modeling}, volume = {3}, year = {2015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_demo-2015-0017} }
Seydou N. Sylla; Stéphane Girard; Abdou Ka Diongue; Aldiouma Diallo; Cheikh Sokhna. A classification method for binary predictors combining similarity measures and mixture models. Dependence Modeling, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_demo-2015-0017/
[1] Andrews, J.L. and P.D. McNicholas (2012). Model-based clustering, classification, and discriminant analysis via mixtures of multivariate t-distributions. Stat. Comp. 22(5), 1021–1029. [Crossref] | Zbl 1252.62062
[2] Batagelj, V. and M. Bren (1995). Comparing resemblance measures. J. Classif. 12, 73–90. [Crossref] | Zbl 0833.62054
[3] Baulieu, F.B. (1989). A classification of presence/absence based dissimilarity coefficients. J. Classif. 6, 233–246. [Crossref] | Zbl 0691.62056
[4] Bergé, L., C. Bouveyron, and S. Girard. (2012). HDclassif: an R package for model-based clustering and discriminant analysis of high-dimensional data. J. Stat. Softw. 46(6), 1–29.
[5] Bouguila, N., D. Ziou, and J. Vaillancourt (2003). Novel mixtures based on the Dirichlet distribution: application to data and image classification. In Machine Learning and Data Mining in Pattern Recognition, Perner P. ed., 172–181, Springer-Verlag, Berlin Heidelberg. | Zbl 1029.68562
[6] Bouveyron, C. and C. Brunet (2012). Simultaneous model-based clustering and visualization in the Fisher discriminative subspace. Stat. Comp. 22, 301–324. [Crossref] | Zbl 1322.62162
[7] Bouveyron, C., M. Fauvel and S. Girard (2015). Kernel discriminant analysis and clustering with parsimonious Gaussian process models. Stat. Comp., 25, 1143–1162. [Crossref] | Zbl 1331.62302
[8] Bouveyron, C., S. Girard and C. Schmid (2007). High-dimensional discriminant analysis. Commun. Stat. A-Theor. 36, 2607– 2623. [Crossref] | Zbl 1128.62072
[9] Bouveyron, C., S. Girard and C. Schmid (2007). High-dimensional data clustering. Comput. Stat. Data An. 52, 502–519. | Zbl 05560174
[10] Byass, P., D.L. Huong and H.V. Minh (2003). A probabilistic approach to interpreting verbal autopsies: methodology and preliminary validation in Vietnam. Scand. J. Public Health 31(62), 32–37. [Crossref]
[11] Cattell, R. (1966). The scree test for the number of factors. Multivar. Behav. Res. 1(2), 245–276. [Crossref]
[12] Celeux, G. and G. Govaert (1991). Clustering criteria for discrete data and latent class models. J. Classif. 8, 157–176. [Crossref] | Zbl 0775.62150
[13] Dundar, M.M. and D.A. Landgrebe (2004). Toward an optimal supervised classifier for the analysis of hyperspectral data. IEEE Trans. Geosci. Remote Sens. 42(1), 271–277. [Crossref]
[14] Fauvel, M., C. Bouveyron and S. Girard (2015). Parsimonious Gaussian process models for the classification of hyperspectral remote sensing images. IEEE Geosci. Remote Sens. Lett., to appear. | Zbl 1331.62302
[15] Forbes, F. and D. Wraith (2014). A new family of multivariate heavy-tailed distributions with variable marginal amounts of tail-weight: application to robust clustering. Stat. Comp. 24(6), 971–984. [Crossref] | Zbl 1332.62204
[16] Franczak, B.C., R.P. Browne and P.D. McNicholas (2014). Mixtures of shifted asymmetric Laplace distributions. IEEE Trans. Pattern Anal. Mach. Intell. 36(6), 1149–1157. [Crossref]
[17] Goodman, L.A and W.H. Kruskal (1954). Measures of association for cross classifications. J. Amer. Statist. Assoc. 49, 732– 764. | Zbl 0056.12801
[18] Goodman, L.A and W.H. Kruskal (1959). Measures of association for cross classifications II. Further discussion and references. J. Amer. Statist. Assoc. 54, 35–75. [Crossref]
[19] Gönen, M. and E. Alpaydin (2011). Multiple kernel learning algorithms. J. Mach. Learn. Res. 12, 2211–2268. | Zbl 1280.68167
[20] Guermeur, Y. (2002). Combining discriminant models with new multi-class SVMs. Pattern Anal. Appl. 5(2), 168–179. | Zbl 1021.68080
[21] Guermeur, Y. (2007). VC theory of large margin multi-category classifiers. J. Mach. Learn. Res. 8, 2551–2594. | Zbl 1222.62070
[22] Hastie, T., R. Tibshirani and J. Friedman (2009). The Elements of Statistical Learning. Second edition. Springer, Berlin. | Zbl 1273.62005
[23] Hofmann, T., B. Schölkopf and A. Smola (2008). Kernel methods in machine learning. Annals Stat. 36(3), 1171–1220. [Crossref][WoS] | Zbl 1151.30007
[24] Huong, D.L., H.V. Minh and P. Byass (2003). Applying verbal autopsy to determine cause of death in rural Vietnam. Scand. J. Public Health 31(62), 19–25. [Crossref]
[25] LeCun, Y., L. Bottou, Y. Bengio and P. Haffner (1998). Gradient-based learning applied to document recognition. Proceedings of IEEE 86(11), 2278–2324. [Crossref]
[26] Jaccard, P. (1901). Etude comparative de la distribution florale dans une portion des Alpes et du Jura. Bull. Soc. Vaudoise Sci. Nat. 37, 547–579.
[27] Lee, S. and G. McLachlan (2013). Finite mixtures of multivariate skew t-distributions: some recent and new results. Stat. Comp. 24(2), 181–202. [Crossref] | Zbl 1325.62107
[28] Lin, T.I. (2010). Robust mixture modeling using multivariate skew t-distribution. Stat. Comp. 20, 343–356. [Crossref]
[29] McLachlan, G. (1992). Discriminant Analysis and Statistical Pattern Recognition. Wiley, New York. | Zbl 1108.62317
[30] McLachlan, G., D. Peel and R. Bean (2003). Modelling high-dimensional data by mixtures of factor analyzers. Comput. Stat. Data An. 41, 379–388. | Zbl 1256.62036
[31] McNicholas, P. and B. Murphy (2008). Parsimonious Gaussian mixture models. Stat. Comp. 18, 285–296. [Crossref]
[32] Mika, S., G. Ratsch, J. Weston, B. Schölkopf and K.R. Müller (1999). Fisher discriminant analysis with kernels. In Neural Networks for Signal Processing IX, Y.-H. Hu, J. Larsen, E. Wilson and S. Douglas eds., 41–48. The Institute of Electrical and Electronics Engineers, Inc. New York.
[33] Montanari, A. and C. Viroli (2010). Heteroscedastic factor mixture analysis. Stat. Modeling 10, 441–460.
[34] Murphy, T.B., N. Dean and A.E. Raftery (2010). Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications. Annals Appl. Stat. 4, 219–223. [WoS][Crossref] | Zbl 1189.62105
[35] Pekalska, E. and B. Haasdonk (2009). Kernel discriminant analysis for positive definite and indefinite kernels. IEEE Trans. Pattern Anal. Mach. Intell. 31(6), 1017–1032. [WoS][Crossref]
[36] Scholkopf, B. and A.J. Smola (1990). Learning with Kernels. The MIT Press, Cambridge MA. | Zbl 1019.68094
[37] Seung-Seok, C., C. Sung-Hyuk and C. Tappert (2010). A survey of binary similarity and distance measures. J. Syst. Cybern. Informatics 8, 43–48.
[38] Shawe-Taylor, J. and N. Cristianini (2004). Kernel Methods for Pattern Analysis, Cambridge University Press. | Zbl 0994.68074
[39] Reeves, B.C. and M.A. Quigley (1997). A review of data-derived methods for assigning causes of death from verbal autopsy data. Int. J. Epidemiol. 26, 1080–1089. [Crossref]
[40] Sneath, P.H.A. and R.R. Sokal (1973). Numerical Taxonomy: the Principles and Practice of Numerical Classification, W.H. Freeman and Company, San Francisco. | Zbl 0285.92001
[41] Sylla, S., S. Girard, A. Diongue, A. Diallo and C. Sokhna (2014). Classification supervisée par modèle de mélange: Application aux diagnostics par autopsie verbale. 46èmes Journées de Statistique organisées par la Société Française de Statistique, Rennes.
[42] Tversky, A. (1977). Feature of similarity, Psychol. Rev. 84, 327–352.
[43] Vilca, F., N. Balakrishnan and C. Zeller (2014). Multivariate skew-normal generalized hyperbolic distribution and its properties. J. Multivar. Anal. 128, 73–85. [WoS][Crossref] | Zbl 06300394
[44] Wang, J., J. Lee and C. Zhang (2003). Kernel trick embedded Gaussian mixture model. In Algorithmic Learning Theory, Gavalda, R., Jantke, K. P., Takimoto, E. eds., 159–174. Springer-Verlag, Berlin Heidelberg. | Zbl 1263.68147
[45] Wraith, D. and F. Forbes (2015). Location and scale mixtures of Gaussians with flexible tail behaviour: properties, inference and application to multivariate clustering. Comput. Stat. Data An. 90, 61–73. [WoS]
[46] Xu, Z., K. Huang, J. Zhu, I. King and M.R. Lyu (2009). A novel kernel-based maximum a posteriori classification method. Neural Networks 22, 977–987, 2009. [WoS][Crossref] | Zbl 1335.68214