Hermite Polynomials and Measures of Non-gaussianity
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- 作者：Jouni Puuronen (12) jouni.puuronen@helsinki.fi
Aapo Hyv盲rinen (12) aapo.hyvarinen@helsinki.fi - 关键词：ICA – ; Hermite polynomials – ; non ; Gaussianity
- 刊名：Lecture Notes in Computer Science
- 出版时间：2011
- 出版年：2011
- 期刊代码：99_0302-9743
- 类别：cp
- 卷：6792
- 期：1
- 页码：205-212
- 数据来源：sp
摘要
We first review some rigorous properties of the Hermite polynomials, and demonstrate their usefulness in estimating probability distributions as series from data samples. We then proceed to explain how these series can be used to obtain precise and robust measures of non-Gaussianity. Our measures of non-Gaussianity detect all kinds of deviations from Gaussianity, and thus provide reliable objective functions for ICA. With a linear computational complexity with respect to the sample size, our method is also suitable for large data sets.