Adaptive kernel canonical correlation analysis algorithms for maximum and minimum variance

We describe two formulations of the kernel canonical correlation analysis (KCCA) problem for multiple data sets. The kernel-based algorithms, which allow one to measure nonlinear relationships between the data sets, are obtained as nonlinear extensions of the classical maximum variance (MAX-VAR) and minimum variance (MINVAR) canonical correlation analysis (CCA) formulations. We then show how adaptive versions of these algorithms can be obtained by reformulating KCCA as a set of coupled kernel recursive least-squares algorithms. We illustrate the performance of the proposed algorithms on a nonlinear identification application and a cognitive radio detection problem.

[1]  Miguel Lázaro-Gredilla,et al.  Kernel Recursive Least-Squares Tracker for Time-Varying Regression , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Simon Haykin,et al.  Cognitive radio: brain-empowered wireless communications , 2005, IEEE Journal on Selected Areas in Communications.

[3]  Weifeng Liu,et al.  Kernel Adaptive Filtering , 2010 .

[4]  John Shawe-Taylor,et al.  Canonical Correlation Analysis: An Overview with Application to Learning Methods , 2004, Neural Computation.

[5]  Michael I. Jordan,et al.  Kernel independent component analysis , 2003 .

[6]  Ignacio Santamaría,et al.  Effective channel order estimation based on combined identification/equalization , 2006, IEEE Transactions on Signal Processing.

[7]  Sergios Theodoridis,et al.  Adaptive Learning in a World of Projections , 2011, IEEE Signal Processing Magazine.

[8]  Vince D. Calhoun,et al.  Canonical Correlation Analysis for Data Fusion and Group Inferences , 2010, IEEE Signal Processing Magazine.

[9]  Weifeng Liu,et al.  Kernel Adaptive Filtering: A Comprehensive Introduction , 2010 .

[10]  Colin Fyfe,et al.  Kernel and Nonlinear Canonical Correlation Analysis , 2000, IJCNN.

[11]  Ignacio Santamaría,et al.  A learning algorithm for adaptive canonical correlation analysis of several data sets , 2007, Neural Networks.

[12]  Ignacio Santamaría,et al.  Adaptive Kernel Canonical Correlation Analysis Algorithms for Nonparametric Identification of Wiener and Hammerstein Systems , 2008, EURASIP J. Adv. Signal Process..

[13]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[14]  Louis L. Scharf,et al.  Detection of Spatially Correlated Gaussian Time Series , 2010, IEEE Transactions on Signal Processing.

[15]  H. Knutsson,et al.  Detection of neural activity in functional MRI using canonical correlation analysis , 2001, Magnetic resonance in medicine.

[16]  Janaina Mourão Miranda,et al.  Unsupervised analysis of fMRI data using kernel canonical correlation , 2007, NeuroImage.

[17]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[18]  Vince D. Calhoun,et al.  Joint Blind Source Separation by Multiset Canonical Correlation Analysis , 2009, IEEE Transactions on Signal Processing.

[19]  Chong-sun Kim.  Canonical Analysis of Several Sets of Variables , 1973 .

[20]  Roberto López-Valcarce,et al.  Detection of Rank- $P$ Signals in Cognitive Radio Networks With Uncalibrated Multiple Antennas , 2011, IEEE Transactions on Signal Processing.