TY - GEN
T1 - Measure transformed canonical correlation analysis with application to financial data
AU - Todros, Koby
AU - Hero, Alfred O.
PY - 2012/10/12
Y1 - 2012/10/12
N2 - In this paper, a new nonlinear generalization of linear canonical correlation analysis (LCCA) is derived. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the considered pair of random vectors after transformation of their joint probability distribution. The proposed transform is structured by a pair of nonnegative functions called the MT-functions. It preserves statistical independence and maps the joint probability distribution into a set of joint probability measures on the joint observation space. Specification of MT-functions in the exponential family, leads to MTCCA, which, in contrast to LCCA, is capable of detecting nonlinear dependencies. In the paper, MTCCA is illustrated for recovery of a nonlinear system with known structure, and for construction of networks that analyze long-term associations between companies traded in the NASDAQ and NYSE stock markets.
AB - In this paper, a new nonlinear generalization of linear canonical correlation analysis (LCCA) is derived. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the considered pair of random vectors after transformation of their joint probability distribution. The proposed transform is structured by a pair of nonnegative functions called the MT-functions. It preserves statistical independence and maps the joint probability distribution into a set of joint probability measures on the joint observation space. Specification of MT-functions in the exponential family, leads to MTCCA, which, in contrast to LCCA, is capable of detecting nonlinear dependencies. In the paper, MTCCA is illustrated for recovery of a nonlinear system with known structure, and for construction of networks that analyze long-term associations between companies traded in the NASDAQ and NYSE stock markets.
KW - Association analysis
KW - multivariate data analysis
KW - probability measure transform
UR - http://www.scopus.com/inward/record.url?scp=84867224598&partnerID=8YFLogxK
U2 - 10.1109/SAM.2012.6250511
DO - 10.1109/SAM.2012.6250511
M3 - Conference contribution
AN - SCOPUS:84867224598
SN - 9781467310710
T3 - Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
SP - 361
EP - 364
BT - 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012
T2 - 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012
Y2 - 17 June 2012 through 20 June 2012
ER -