Abstract
Regularized Generalized Canonical Correlation Analysis (RGCCA) extends regularized canonical correlation analysis to more than two sets of variables. Sparse GCCA (SGCCA) was recently proposed to address the issue of variable selection. However, the variable selection scheme offered by SGCCA is limited to the covariance (τ = 1) link between blocks. In this paper we go beyond the covariance link by proposing an extension of SGCCA for the full RGCCA model (τ ∈ [0, 1]). In addition, we also propose an extension of SGCCA that exploits pre-given structural relationships between variables within blocks. Specifically, we propose an algorithm that allows structured and sparsity-inducing penalties to be included in the RGCCA optimization problem.
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References
Chen, X., Liu, H.: An efficient optimization algorithm for structured sparse CCA, with applications to eQTL mapping. Stat. Biosci. 4, 3–26 (2011)
Combettes, P.L., Pesquet, J.C.: Proximal splitting methods in signal processing. In: Bauschke, H.H., Burachik, R.S., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H. (eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp. 185–212. Springer, New York (2011)
De Leeuw, J.: Block relaxation algorithms in statistics. In: Bock, H.-H., Lenski, W., Richter, M.M. (eds.) Information Systems and Data Analysis, pp. 308–325. Springer, Berlin (1994)
Fleiss, J.L.: Measuring nominal scale agreement among many raters. Psychol. Bull. 76, 378–382 (1971)
Hadj-Selem, F., Löfstedt, T., Duchesnay, E., Frouin, V., Guillemot, V.: Iterative Smoothing Algorithm for Regression with Structured Sparsity (2016, Submitted paper)
Michel, V., Gramfort, A., Varoquaux, G., Eger, E., Thirion, B.: Total variation regularization for f MRI-based prediction of behavior. IEEE Trans. Med. Imaging 30, 1328–1340 (2011)
Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. 103, 127–152 (2004)
Parikh, N., Boyd, S.: Proximal Algorithms. Now Publishers Inc., New York (2013)
Philippe, C., Puget, S., Bax, D.A., Job, B., Varlet, P., Junier, M.P., Andreiuolo, F., Carvalho, D., Reis, R., Guerrini-Rousseau, L., Roujeau, T., Dessen, P., Richon, C., Lazar, V., Le Teuff, G., Sainte-Rose, C., Geoerger, B., Vassal, G., Jones, C., Grill, J.: Mesenchymal transition and PDGFRA amplification/mutation are key distinct oncogenic events in pediatric diffuse intrinsic pontine gliomas. PloS one 7, 1–14 (2012)
Qin, Z., Scheinberg, K., Goldfarb, D.: Efficient block-coordinate descent algorithms for the Group Lasso. Math. Program. Comput. 5, 143–169 (2013)
Schäfer, J., Strimmer, K.: A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat. Appl. Genet. Mol. Biol. 4, 1–30 (2005)
Schmidt, M., Le Roux, N., Bach, F.: Convergence rates of inexact proximal-gradient methods for convex optimization (2011). ArXiv:1109.2415
Tenenhaus, A., Tenenhaus, M.: Regularized generalized canonical correlation analysis. Psychometrika 76, 257–284 (2011)
Tenenhaus, A., Philippe, C., Guillemot, V., Lê Cao, K.A., Grill, J., Frouin, V.: Variable selection for generalized canonical correlation analysis. Biostatistics 15, 569–583 (2014)
van den Berg, E., Schmidt, M., Friedlander, M.P., Murphy, K.: Group sparsity via linear-time projection. Technical report TR-2008-09, Department of Computer Science, University of British Columbia, Vancouver (2008)
Vinod, H.: Canonical ridge and econometrics of joint production. J. Econom. 4, 147–166 (1976)
Witten, D.M., Tibshirani, R., Hastie, T.: A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10, 515–534 (2009)
Acknowledgements
This work was supported by grants from the French National Research Agency: ANR IA BRAINOMICS (ANR-10-BINF-04), and a European Commission grant: MESCOG (FP6 ERA-NET NEURON 01 EW1207).
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Löfstedt, T. et al. (2016). Structured Variable Selection for Regularized Generalized Canonical Correlation Analysis. In: Abdi, H., Esposito Vinzi, V., Russolillo, G., Saporta, G., Trinchera, L. (eds) The Multiple Facets of Partial Least Squares and Related Methods. PLS 2014. Springer Proceedings in Mathematics & Statistics, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-40643-5_10
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DOI: https://doi.org/10.1007/978-3-319-40643-5_10
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