TY - GEN
T1 - Uniqueness of real and complex linear independent component analysis revisited
AU - Theis, F. J.
N1 - Publisher Copyright:
© 2004 EUSIPCO.
PY - 2015/4/3
Y1 - 2015/4/3
N2 - Comon showed using the Darmois-Skitovitch theorem that under mild assumptions a real-valued random vector and its linear image are both independent if and only if the linear mapping is the product of a permutation and a scaling matrix. In this work, a much simpler, direct proof is given for this theorem and generalized to the case of random vectors with complex values. The idea is based on the fact that a random vector is independent if and only if locally the Hessian of its logarithmic density is diagonal.
AB - Comon showed using the Darmois-Skitovitch theorem that under mild assumptions a real-valued random vector and its linear image are both independent if and only if the linear mapping is the product of a permutation and a scaling matrix. In this work, a much simpler, direct proof is given for this theorem and generalized to the case of random vectors with complex values. The idea is based on the fact that a random vector is independent if and only if locally the Hessian of its logarithmic density is diagonal.
UR - http://www.scopus.com/inward/record.url?scp=84979871553&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84979871553
T3 - European Signal Processing Conference
SP - 1705
EP - 1708
BT - 2004 12th European Signal Processing Conference, EUSIPCO 2004
PB - European Signal Processing Conference, EUSIPCO
T2 - 12th European Signal Processing Conference, EUSIPCO 2004
Y2 - 6 September 2004 through 10 September 2004
ER -