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Abstract:
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Canonical correlation analysis (CCA) is a powerful tool in multivariate statistics for finding the maximal correlation between two sets of multivariate variables. In neuroimaging studies, data often take the form of multidimensional arrays (tensors). This presents at least two challenges to CCA: estimation of huge covariance matrix and estimation of ultrahigh dimensional canonical vectors. In this paper, we propose new CCA methods that efficiently exploit the array structure of tensor data. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction and circumventing singularity of the covariance estimate. Effectiveness of the new methods is demonstrated on both synthetic and real imaging genetics data.
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