TY - JOUR
T1 - On measure transformed canonical correlation analysis
AU - Todros, Koby
AU - Hero, Alfred O.
N1 - Funding Information: Manuscript received November 27, 2011; revised April 13, 2012; accepted May 25, 2012. Date of publication June 08, 2012; date of current version August 07, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ljubisa Stankovic. This research was supported in part by ARO Grant W911NF-09-1-0310.
PY - 2012/8/27
Y1 - 2012/8/27
N2 - In this paper, linear canonical correlation analysis (LCCA) is generalized by applying a structured transform to the joint probability distribution of the considered pair of random vectors, i.e., a transformation of the joint probability measure defined on their joint observation space. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the data after transformation of the joint probability measure. We show that judicious choice of the transform leads to a modified canonical correlation analysis, which, in contrast to LCCA, is capable of detecting non-linear relationships between the considered pair of random vectors. Unlike kernel canonical correlation analysis, where the transformation is applied to the random vectors, in MTCCA the transformation is applied to their joint probability distribution. This results in performance advantages and reduced implementation complexity. The proposed approach is illustrated for graphical model selection in simulated data having non-linear dependencies, and for measuring long-term associations between companies traded in the NASDAQ and NYSE stock markets.
AB - In this paper, linear canonical correlation analysis (LCCA) is generalized by applying a structured transform to the joint probability distribution of the considered pair of random vectors, i.e., a transformation of the joint probability measure defined on their joint observation space. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the data after transformation of the joint probability measure. We show that judicious choice of the transform leads to a modified canonical correlation analysis, which, in contrast to LCCA, is capable of detecting non-linear relationships between the considered pair of random vectors. Unlike kernel canonical correlation analysis, where the transformation is applied to the random vectors, in MTCCA the transformation is applied to their joint probability distribution. This results in performance advantages and reduced implementation complexity. The proposed approach is illustrated for graphical model selection in simulated data having non-linear dependencies, and for measuring long-term associations between companies traded in the NASDAQ and NYSE stock markets.
KW - Association analysis
KW - canonical correlation analysis
KW - graphical model selection
KW - multivariate data analysis
KW - probability measure transform
UR - http://www.scopus.com/inward/record.url?scp=84865205429&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/TSP.2012.2203816
DO - https://doi.org/10.1109/TSP.2012.2203816
M3 - Article
SN - 1053-587X
VL - 60
SP - 4570
EP - 4585
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 9
M1 - 6214626
ER -