A learning algorithm for adaptive canonical correlation analysis of several data sets

• Published in: Neural networks Vol. 20; no. 1; pp. 139 - 152
• Main Authors: VIA, Javier, SANTAMARIA, Ignacio, PEREZ, Jesus
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 2007; Elsevier Science
• Subjects: Adaptive algorithms; Algorithms; Applied sciences; Artificial intelligence; Canonical correlation analysis (CCA); Computer science; control theory; systems; Connectionism. Neural networks; Exact sciences and technology; Hebbian learning; Humans; Learning; Learning and adaptive systems; Multivariate Analysis; Neural Networks (Computer); Principal component analysis (PCA); Recursive least squares (RLS); Hebbian learning; Recursive least squares (RLS); Adaptive algorithms; Canonical correlation analysis (CCA); Principal component analysis (PCA); Adaptive algorithm; Two layer model; Projection; Canonical correlation; Variance; Canonical analysis; Feedforward neural nets; Least squares method; Work; Learning algorithm; Tool; Data analysis; Statistical analysis; Eigenvector; Least squares problem; Neural network; Recursive algorithm; Statistical method; Correlation analysis; Recursive method; Artificial intelligence
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2006.09.011

Canonical correlation analysis (CCA) is a classical tool in statistical analysis to find the projections that maximize the correlation between two data sets. In this work we propose a generalization of CCA to several data sets, which is shown to be equivalent to the classical maximum variance (MAXVAR) generalization proposed by Kettenring. The reformulation of this generalization as a set of coupled least squares regression problems is exploited to develop a neural structure for CCA. In particular, the proposed CCA model is a two layer feedforward neural network with lateral connections in the output layer to achieve the simultaneous extraction of all the CCA eigenvectors through deflation. The CCA neural model is trained using a recursive least squares (RLS) algorithm. Finally, the convergence of the proposed learning rule is proved by means of stochastic approximation techniques and their performance is analyzed through simulations.