Blaschko, Matthew; Shelton, Jacquelyn; Bartels, Andreas; Lampert , ChristophISTA ; Gretton, Arthur
Kernel canonical correlation analysis (KCCA) is a general technique for subspace learning that incorporates principal components analysis (PCA) and Fisher linear discriminant analysis (LDA) as special cases. By finding directions that maximize correlation, KCCA learns representations that are more closely tied to the underlying process that generates the data and can ignore high-variance noise directions. However, for data where acquisition in one or more modalities is expensive or otherwise limited, KCCA may suffer from small sample effects. We propose to use semi-supervised Laplacian regularization to utilize data that are present in only one modality. This approach is able to find highly correlated directions that also lie along the data manifold, resulting in a more robust estimate of correlated subspaces. Functional magnetic resonance imaging (fMRI) acquired data are naturally amenable to subspace techniques as data are well aligned. fMRI data of the human brain are a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single and multi-variate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, the semi-supervised variants of KCCA performed better than the supervised variants, including a supervised variant with Laplacian regularization. We additionally analyze the weights learned by the regression in order to infer brain regions that are important to different types of visual processing.
Pattern Recognition Letters
The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 228180. This work was funded in part by the EC project CLASS, IST 027978, and the PASCAL2 network of excellence, IST 2002-506778.
1572 - 1583
Blaschko M, Shelton J, Bartels A, Lampert C, Gretton A. Semi supervised kernel canonical correlation analysis with application to human fMRI. Pattern Recognition Letters. 2011;32(11):1572-1583. doi:10.1016/j.patrec.2011.02.011
Blaschko, M., Shelton, J., Bartels, A., Lampert, C., & Gretton, A. (2011). Semi supervised kernel canonical correlation analysis with application to human fMRI. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2011.02.011
Blaschko, Matthew, Jacquelyn Shelton, Andreas Bartels, Christoph Lampert, and Arthur Gretton. “Semi Supervised Kernel Canonical Correlation Analysis with Application to Human FMRI.” Pattern Recognition Letters. Elsevier, 2011. https://doi.org/10.1016/j.patrec.2011.02.011.
M. Blaschko, J. Shelton, A. Bartels, C. Lampert, and A. Gretton, “Semi supervised kernel canonical correlation analysis with application to human fMRI,” Pattern Recognition Letters, vol. 32, no. 11. Elsevier, pp. 1572–1583, 2011.
Blaschko M, Shelton J, Bartels A, Lampert C, Gretton A. 2011. Semi supervised kernel canonical correlation analysis with application to human fMRI. Pattern Recognition Letters. 32(11), 1572–1583.
Blaschko, Matthew, et al. “Semi Supervised Kernel Canonical Correlation Analysis with Application to Human FMRI.” Pattern Recognition Letters, vol. 32, no. 11, Elsevier, 2011, pp. 1572–83, doi:10.1016/j.patrec.2011.02.011.