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Two dimensional canonical correlation analysis (2DCCA) is a data driven method that has been used in image analysis to preserve the spatial structure of images. 2DCCA finds pairs of left and right linear transforms by directly operating on two dimensional data (i.e., image data) such that the correlation between their projections is maximized without neglecting the local spatial structure of the data. However, in context to high dimensional data, the performance of 2DCCA suffers from interpretability of learned projection variables. In this

Objective: Canonical correlation analysis (CCA) is a data driven method that has been successfully used in functional magnetic resonance imaging (fMRI) data analysis. Standard CCA extracts meaningful information from a pair of data sets by seeking pairs of linear combinations from two sets of variables with maximum pairwise correlation. So far, however, this method has been used without incorporating prior information available for fMRI data. In this paper, we address this issue by proposing a new CCA method named pCCA (for projection CCA). Methods: The proposed method is obtained by projection onto a set of basis vectors that better characterize temporal information in the fMRI data set. A methodology is presented to describe the basis selection process using discrete cosine transform (DCT) basis functions. Employing DCT guides the estimated canonical variates, yielding a more computationally efficient CCA procedure. Results: The performance gain of the proposed pCCA algorithm over standard and regularized CCA is illustrated on both simulated and real fMRI datasets from resting state, block paradigm task-related and event-related experiments. The results show that pCCA can successfully extract the task as well restingstate latent components with increased specificity. Conclusion: In addition to offering a new CCA approach, when applied on fMRI data, the proposed algorithm adapts to variations of brain activity patterns and reveals the functionally connected brain regions. Significance: The proposed method can be seen as a regularized CCA method where regularization is introduced via basis expansion, which has the advantage of enforcing smoothness on canonical components.

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