Canonical correlation analysis (CCA) has proven an effective tool fortwo-view dimension reduction due to its profound theoretical foundation andsuccess in practical applications. In respect of multi-view learning, however,it is limited by its capability of only handling data represented by two-viewfeatures, while in many real-world applications, the number of views isfrequently many more. Although the ad hoc way of simultaneously exploring allpossible pairs of features can numerically deal with multi-view data, itignores the high order statistics (correlation information) which can only bediscovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardlyyet naturally generalizes CCA to handle the data of an arbitrary number ofviews by analyzing the covariance tensor of the different views. TCCA aims todirectly maximize the canonical correlation of multiple (more than two) views.Crucially, we prove that the multi-view canonical correlation maximizationproblem is equivalent to finding the best rank-1 approximation of the datacovariance tensor, which can be solved efficiently using the well-knownalternating least squares (ALS) algorithm. As a consequence, the high ordercorrelation information contained in the different views is explored and thus amore reliable common subspace shared by all features can be obtained. Inaddition, a non-linear extension of TCCA is presented. Experiments on variouschallenge tasks, including large scale biometric structure prediction, internetadvertisement classification and web image annotation, demonstrate theeffectiveness of the proposed method.
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