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Reports (Research Report) Year : 2015

Canonical correlation analysis based on sparse penalty and 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 one matrix approximation and the orthogonal projectors onto the space spanned by the columns of 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 outperforms the state of the art sparse CCA algorithms.
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Dates and versions

hal-01202844 , version 1 (21-09-2015)

Identifiers

  • HAL Id : hal-01202844 , version 1

Cite

Abdeldjalil Aissa El Bey, Abd-Krim Seghouane. Canonical correlation analysis based on sparse penalty and through rank-1 matrix approximation. [Research Report] RR-2015-01-SC, Dépt. Signal et Communications (Institut Mines-Télécom-Télécom Bretagne-UEB); Laboratoire en sciences et technologies de l'information, de la communication et de la connaissance (UMR CNRS 6285 - Télécom Bretagne - Université de Bretagne Occidentale - Université de Bretagne Sud); Department of Electrical and Electronic Engineering (Melbourne) (University of Melbourne). 2015, pp.20. ⟨hal-01202844⟩
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