PMID- 15006101
OWN - NLM
STAT- MEDLINE
DCOM- 20040401
LR  - 20191210
IS  - 0899-7667 (Print)
IS  - 0899-7667 (Linking)
VI  - 16
IP  - 2
DP  - 2004 Feb
TI  - One-bit-matching conjecture for independent component analysis.
PG  - 383-99
AB  - The one-bit-matching conjecture for independent component analysis (ICA) could be 
      understood from different perspectives but is basically stated as "all the 
      sources can be separated as long as there is a one-to-one 
      same-sign-correspondence between the kurtosis signs of all source probability 
      density functions (pdf's) and the kurtosis signs of all model pdf's" (Xu, Cheung, 
      & Amari, 1998a). This conjecture has been widely believed in the ICA community 
      and implicitly supported by many ICA studies, such as the Extended Infomax (Lee, 
      Girolami, & Sejnowski, 1999) and the soft switching algorithm (Welling & Weber, 
      2001). However, there is no mathematical proof to confirm the conjecture 
      theoretically. In this article, only skewness and kurtosis are considered, and 
      such a mathematical proof is given under the assumption that the skewness of the 
      model densities vanishes. Moreover, empirical experiments are demonstrated on the 
      robustness of the conjecture as the vanishing skewness assumption breaks. As a 
      by-product, we also show that the kurtosis maximization criterion (Moreau & 
      Macchi, 1996) is actually a special case of the minimum mutual information 
      criterion for ICA.
FAU - Liu, Zhi-Yong
AU  - Liu ZY
AD  - Department of Computer Science and Engineering, Chinese University of Hong Kong, 
      Shatin, New Territories. zyliu@cse.cuhk.edu.hk
FAU - Chiu, Kai-Chun
AU  - Chiu KC
FAU - Xu, Lei
AU  - Xu L
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
PL  - United States
TA  - Neural Comput
JT  - Neural computation
JID - 9426182
SB  - IM
MH  - *Algorithms
MH  - Mathematics
MH  - *Neural Networks, Computer
MH  - Nonlinear Dynamics
MH  - Normal Distribution
MH  - *Signal Processing, Computer-Assisted
EDAT- 2004/03/10 05:00
MHDA- 2004/04/02 05:00
CRDT- 2004/03/10 05:00
PHST- 2004/03/10 05:00 [pubmed]
PHST- 2004/04/02 05:00 [medline]
PHST- 2004/03/10 05:00 [entrez]
AID - 10.1162/089976604322742074 [doi]
PST - ppublish
SO  - Neural Comput. 2004 Feb;16(2):383-99. doi: 10.1162/089976604322742074.