TY - JOUR
T1 - A new algorithm of non-Gaussian component analysis with radial kernel functions
AU - Kawanabe, Motoaki
AU - Sugiyama, Masashi
AU - Blanchard, Gilles
AU - Müller, Klaus Robert
N1 - Funding Information:
Acknowledgments MK acknowledges Shinto Eguchi and Vladimir Spokoiny for valuable comments. This work was supported in part by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778, MEXT, Grant-in-Aid for Young Scientists 17700142, Grand-in-Aid for Scientific Research (B) 1830057 and BMBF, CCNB grant 01GQ0415. This publication only reflects the authors’ views.
PY - 2007/3
Y1 - 2007/3
N2 - We consider high-dimensional data which contains a linear low-dimensional non-Gaussian structure contaminated with Gaussian noise, and discuss a method to identify this non-Gaussian subspace. For this problem, we provided in our previous work a very general semi-parametric framework called non-Gaussian component analysis (NGCA). NGCA has a uniform probabilistic bound on the error of finding the non-Gaussian components and within this framework, we presented an efficient NGCA algorithm called Multi-index Projection Pursuit. The algorithm is justified as an extension of the ordinary projection pursuit (PP) methods and is shown to outperform PP particularly when the data has complicated non-Gaussian structure. However, it turns out that multi-index PP is not optimal in the context of NGCA. In this article, we therefore develop an alternative algorithm called iterative metric adaptation for radial kernel functions (IMAK), which is theoretically better justifiable within the NGCA framework. We demonstrate that the new algorithm tends to outperform existing methods through numerical examples.
AB - We consider high-dimensional data which contains a linear low-dimensional non-Gaussian structure contaminated with Gaussian noise, and discuss a method to identify this non-Gaussian subspace. For this problem, we provided in our previous work a very general semi-parametric framework called non-Gaussian component analysis (NGCA). NGCA has a uniform probabilistic bound on the error of finding the non-Gaussian components and within this framework, we presented an efficient NGCA algorithm called Multi-index Projection Pursuit. The algorithm is justified as an extension of the ordinary projection pursuit (PP) methods and is shown to outperform PP particularly when the data has complicated non-Gaussian structure. However, it turns out that multi-index PP is not optimal in the context of NGCA. In this article, we therefore develop an alternative algorithm called iterative metric adaptation for radial kernel functions (IMAK), which is theoretically better justifiable within the NGCA framework. We demonstrate that the new algorithm tends to outperform existing methods through numerical examples.
KW - Linear dimension reduction
KW - Non-Gaussian subspace
KW - Projection pursuit
KW - Semiparametric model
KW - Stein's identity
UR - http://www.scopus.com/inward/record.url?scp=33847203655&partnerID=8YFLogxK
U2 - 10.1007/s10463-006-0098-9
DO - 10.1007/s10463-006-0098-9
M3 - Article
AN - SCOPUS:33847203655
SN - 0020-3157
VL - 59
SP - 57
EP - 75
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
IS - 1
ER -