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.
Highlights
Canonical correlation analysis (CCA) [1] is a multivariate analysis method, the aim of which is to identify and quantify the association between two sets of variables
We adopt an alternative formulation of the CCA problem which is based on rank-1 matrix approximation of the orthogonal projectors of data sets [13]. Based on this new formulation of the CCA problem, we developed a new sparse CCA based on penalized rank-1 matrix approximation which aims to overcome the drawback of CCA in the context of high-dimensional data and improved interpretability
The average angles are estimated over Nk Monte-Carlo run such that: 5 Experiments we present several computer simulations in the context of blind channel estimation in single-input multiple-output (SIMO) systems and blind source separation to demonstrate the effectiveness of the proposed algorithm
Summary
Canonical correlation analysis (CCA) [1] is a multivariate analysis method, the aim of which is to identify and quantify the association between two sets of variables. We adopt an alternative formulation of the CCA problem which is based on rank-1 matrix approximation of the orthogonal projectors of data sets [13]. Aïssa-El-Bey and Seghouane EURASIP Journal on Advances in Signal Processing (2017) 2017:25 avoid abrupt or sudden variations These proposed 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 [7, 10,11,12].
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