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Abstract

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, CCA learns representations tied more closely to underlying process generating the
the data and can ignore high-variance noise directions. However, for data where acquisition in a given modality is
expensive or otherwise limited, CCA may suffer from small sample effects. We propose to use semisupervised
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 CCA on human fMRI data, with regression to single and multivariate
labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition,
the semi-supervised variants of CCA 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.