×

A mixed effects least squares support vector machine model for classification of longitudinal data. (English) Zbl 1239.62077

Summary: A mixed effects least squares support vector machine (LS-SVM) classifier is introduced to extend the standard LS-SVM classifier for handling longitudinal data. The mixed effects LS-SVM model contains a random intercept and allows to classify highly unbalanced data, in the sense that there is an unequal number of observations for each case at non-fixed time points. The methodology consists of a regression modeling and a classification step based on the obtained regression estimates. Regression and classification of new cases are performed in a straightforward manner by solving a linear system. It is demonstrated that the methodology can be generalized to deal with multi-class problems and can be extended to incorporate multiple random effects. The technique is illustrated on simulated data sets and real-life problems concerning human growth.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
68T05 Learning and adaptive systems in artificial intelligence
65C60 Computational problems in statistics (MSC2010)

Software:

fda (R)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bachrach, L. K.; Hastie, T.; Wang, M. C.; Narasimhan, B.; Marcus, R., Bone mineral acquisition in healthy asian, hispanic, black, and caucasian youth: a longitudinal study, J. Clin. Endocrinol. Metab., 84, 12, 4702-4712 (1999)
[2] Brown, P. J.; Kenward, M. G.; Bassett, E. E., Bayesian discrimination with longitudinal data, Biostatistics, 2, 4, 417-432 (2001)
[3] De Brabanter, K.; De Brabanter, J.; Suykens, J. A.K.; De Moor, B., Optimized fixed-size kernel models for large data sets, Comput. Stat. Data Anal., 54, 6, 1484-1504 (2010) · Zbl 1284.62369
[4] De Brabanter, K.; De Brabanter, J.; Suykens, J. A.K.; De Moor, B., Approximate confidence and prediction intervals for least squares support vector regression, IEEE Trans. Neural Netw., 22, 1, 110-120 (2011)
[5] De la Cruz-Mesía, R.; Quintana, F. A.; Müller, P., Semiparametric Bayesian classification with longitudinal markers, J. R. Stat. Soc. Ser. C Appl. Stat., 56, 2, 119-137 (2007) · Zbl 1490.62363
[6] Espinoza, M.; Suykens, J. A.K.; De Moor, B., Fixed-size least squares support vector machines: a large scale application in electrical load forecasting, Comput. Manag. Sci., 3, 2, 113-129 (2006) · Zbl 1127.62121
[7] Fieuws, S.; Verbeke, G.; Maes, B.; Vanrenterghem, Y., Predicting renal graft failure using multivariate longitudinal profiles, Biostatistics, 9, 3, 419-431 (2008) · Zbl 1143.62075
[8] González-Manteiga, W.; Vieu, P., Statistics for functional data, Comput. Stat. Data Anal., 51, 10, 4788-4792 (2007) · Zbl 1162.62338
[9] James, G. M., Generalized linear models with functional predictors, J. R. Stat. Soc. Series. B Stat. Methodol., 64, 3, 411-432 (2002) · Zbl 1090.62070
[10] James, G. M.; Hastie, T. J., Functional linear discriminant analysis for irregularly sampled curves, J. R. Stat. Soc. Series. B Stat. Methodol., 63, 3, 533-550 (2001) · Zbl 0989.62036
[11] Liu, D.; Lin, X.; Ghosh, D., Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models, Biometrics, 63, 4, 1079-1088 (2007) · Zbl 1274.62825
[12] Luts, J.; Ojeda, F.; Van de Plas, R.; De Moor, B.; Van Huffel, S.; Suykens, J. A.K., A tutorial on support vector machine-based methods for classification problems in chemometrics, Anal. Chim. Acta, 665, 2, 129-145 (2010)
[13] Marshall, G.; Barón, A. E., Linear discriminant models for unbalanced longitudinal data, Stat. Med., 19, 15, 1969-1981 (2000)
[14] Müller, H. G., Functional modelling and classification of longitudinal data, Scand. J. Stat., 32, 2, 223-240 (2005) · Zbl 1089.62072
[15] Patterson, H. D.; Thompson, R., Recovery of inter-block information when block sizes are unequal, Biometrika, 58, 3, 545-554 (1971) · Zbl 0228.62046
[16] Pearce, N. D.; Wand, M. P., Explicit connections between longitudinal data analysis and kernel machines, Electron. J. Stat., 3, 797-823 (2009) · Zbl 1326.62140
[17] Ramsay, J. O.; Silverman, B. W., Functional Data Analysis (2005), Springer: Springer New York · Zbl 1079.62006
[18] Robinson, G. K., That BLUP is a good thing: the estimation of random effects, Statist. Sci., 6, 1, 15-32 (1991) · Zbl 0955.62500
[19] Schölkopf, B.; Smola, A. J., Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (2001), MIT Press: MIT Press Cambridge
[20] Suykens, J. A.K.; Alzate, C.; Pelckmans, K., Primal and dual model representations in kernel-based learning, Stat. Surv., 4, 148-183 (2010) · Zbl 06162223
[21] Suykens, J. A.K.; Vandewalle, J., Least squares support vector machine classifiers, Neural Process. Lett., 9, 3, 293-300 (1999)
[22] Suykens, J. A.K.; Van Gestel, T.; De Brabanter, J.; De Moor, B.; Vandewalle, J., Least Squares Support Vector Machines (2002), World Scientific: World Scientific Singapore · Zbl 1017.93004
[23] Vapnik, V. N., Statistical Learning Theory (1998), Wiley: Wiley New York · Zbl 0935.62007
[24] Verbeke, G.; Lesaffre, E., A linear mixed-effects model with heterogeneity in the random-effects population, J. Amer. Statist. Assoc., 91, 433, 217-221 (1996) · Zbl 0870.62057
[25] Verbeke, G.; Molenberghs, G., Linear Mixed Models for Longitudinal Data (2000), Springer: Springer New York · Zbl 0956.62055
[26] Wouters, K.; Ahnaou, A.; Cortinas Abrahantes, J.; Molenberghs, G.; Geys, H.; Bijnens, L.; Drinkenburg, W. H.I. M., Psychotropic drug classification based on sleep-wake behaviour of rats, J. R. Stat. Soc. Ser. C Appl. Stat., 56, 2, 223-234 (2007) · Zbl 1490.62386
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.