# SVM regression with longitudinal data

I have about 500 variables per patient, each variable has one continous value and is measured at three different time points (after 2 month and after 1 year). With the regression I would like to predict the treatment outcome for new patients.

Is it possible to use SVM regression with such longitudinal data?

• Were you able to find any proper answer? Commented Mar 9, 2016 at 3:00

This is an interesting question and I did a quick research.

The OP asked about regression for continuous data. But the paper cited by @Vikram only works for classification.

Lu, Z., Kaye, J., & Leen, T. K. (2009). Hierarchical Fisher Kernels for Longitudinal Data. In Advances in Neural Information Processing Systems.

A related paper for regression I found is the following. Technical details can be found in Section 2.3.

Seok, K. H., Shim, J., Cho, D., Noh, G. J., & Hwang, C. (2011). Semiparametric mixed-effect least squares support vector machine for analyzing pharmacokinetic and pharmacodynamic data. Neurocomputing, 74(17), 3412-3419.

No public software is found but the authors claimed the ease of use at the end of the paper.

The main advantage of the proposed LS-SVM ... is that regression estimators can be easily computed by softwares solving a simple linear equation system. This makes it easier to apply the proposed approach to the analysis of repeated measurement data in practice.

To elaborate a bit more, there are two approaches for regression analysis using SVM (support vector machine):

• support vector regression (SVR) [Drucker, Harris; Burges, Christopher J. C.; Kaufman, Linda; Smola, Alexander J.; and Vapnik, Vladimir N. (1997); "Support Vector Regression Machines", in Advances in Neural Information Processing Systems 9, NIPS 1996, 155–161]
• least squares support vector machine (LS-SVM) [Suykens, Johan A. K.; Vandewalle, Joos P. L.; Least squares support vector machine classifiers, Neural Processing Letters, vol. 9, no. 3, Jun. 1999, pp. 293–300.]

The aforementioned Seol et al. (2011) adopted the LS-VSM approach.

Yes, this is possible. Except that in longitudinal data using Fisher Kernel works better than RBF or Linear ones. A similar setting like that of yours is given in this NIPS paper: http://research.microsoft.com/pubs/147234/NIPS08.pdf