TY - JOUR
T1 - Analysis of cost function based on Kullback-Leibler divergence in independent component analysis for two uniformly distributed source signals
AU - Tanzawa, Kota
AU - Koshita, Shunsuke
AU - Abe, Masahide
AU - Kawamata, Masayuki
PY - 2018/1/1
Y1 - 2018/1/1
N2 - Independent component analysis plays a central role in blind source separation, leading to many applications of signal processing such as telecommunications, speech processing, and biomedical signal processing. Although the independent component analysis requires cost functions for evaluation of mutual independence of observed signals, little has been reported on theoretical investigation of the characteristics of such cost functions. In this paper, we mathematically analyze the cost function based on Kullback-Leibler divergence in independent component analysis. Our analysis proves that the cost function becomes unimodal when the number of source signals is two and both of the source signals have uniform distributions. In order to derive this result, we make use of whitening of observed signals and we describe the cost function in closed-form.
AB - Independent component analysis plays a central role in blind source separation, leading to many applications of signal processing such as telecommunications, speech processing, and biomedical signal processing. Although the independent component analysis requires cost functions for evaluation of mutual independence of observed signals, little has been reported on theoretical investigation of the characteristics of such cost functions. In this paper, we mathematically analyze the cost function based on Kullback-Leibler divergence in independent component analysis. Our analysis proves that the cost function becomes unimodal when the number of source signals is two and both of the source signals have uniform distributions. In order to derive this result, we make use of whitening of observed signals and we describe the cost function in closed-form.
KW - Cost function
KW - Independent component analysis
KW - Kullback-Leibler divergence
KW - Uniform distribution
KW - Unimodality
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U2 - 10.1541/ieejeiss.138.282
DO - 10.1541/ieejeiss.138.282
M3 - Article
AN - SCOPUS:85044789357
VL - 138
SP - 282
EP - 286
JO - IEEJ Transactions on Electronics, Information and Systems
JF - IEEJ Transactions on Electronics, Information and Systems
SN - 0385-4221
IS - 4
ER -