Sparse and smooth canonical correlation analysis through rank-1 matrix approximation

Abstract

Canonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA and smooth or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far, the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper, two new algorithms for sparse CCA and smooth CCA are proposed. These algorithms differ from the existing ones in their derivation which is based on penalized rank-1 matrix approximation and the orthogonal projectors onto the space spanned by the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithms are tested on simulated experiments. On these results, it can be observed that they outperform the state of the art sparse CCA algorithms.

Efficient Blind Source Separation Method for fMRI Using Autoencoder and Spatiotemporal Sparsity Constraints

“…3) scBSS: Computation of the error matrix using full data matrix to estimate dictionary and sparse code through alternating minimization. State-of-the-art swBSS methods that have been quite successful for neuroimaging data include sparse PCA (sPCA) [45], sparse CCA (sCCA) [46], [47], sparse PLS (sPLS) [48], [49], multi-task sparse model (MTS) [50], and sparse two dimensional CCA (s2DCCA) [51]. On the other hand, improved fast ICA (ifICA) utilizes a fast ICA algorithm and l 0 -norm [52] and sparse spatial ICA employs an entropy bound minimization algorithm (ssICA) and l 1 -norm [33].…”

“…A regularized and a sparse CCA employed penalized rank-1 matrix approximation on the product of the orthogonal projectors of two sets of data to improve interpretability and performance of the canonical variates [47]. To simultaneously handle the sparse decomposition of mixed signals, the BSS problem was reformulated as a multi-task sparse problem that exploited the connection between tasks to achieve higher retrieval accuracy [50].…”

“…Consider on the other hand deflation based sparse methods [46], [47], [48], [49], [55] that exploit a different fidelity term given by ||Y −…”

A Projection CCA Method for Effective fMRI Data Analysis

“…In [20], [21], the specificity and sensitivity of dictionary learning methods were improved by including autocorrelation constraints in fMRI data. In [22], a sparse CCA method, derived via penalized rank one matrix approximation, was applied to restingstate fMRI data analysis. However, the presence of spatial structure and connectedness of the local neighbourhood voxels in fMRI data has not been exploited in sparsity based CCA methods.…”