The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Comparison of several criteria for ordering independent components

독립성분의 순서화 방법 비교

  • Choi, Eunbin (Department of Statistics, Korea University) ;
  • Cho, Sulim (Department of Statistics, Korea University) ;
  • Park, Mira (Department of Preventive Medicine, Eulji University)
  • Received : 2017.09.05
  • Accepted : 2017.11.20
  • Published : 2017.12.31
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Abstract

Independent component analysis is a multivariate approach to separate mixed signals into original signals. It is the most widely used method of blind source separation technique. ICA uses linear transformations such as principal component analysis and factor analysis, but differs in that ICA requires statistical independence and non-Gaussian assumptions of original signals. PCA have a natural ordering based on cumulative proportion of explained variance; howerver, ICA algorithms cannot identify the unique optimal ordering of the components. It is meaningful to set order because major components can be used for further analysis such as clustering and low-dimensional graphs. In this paper, we compare the performance of several criteria to determine the order of the components. Kurtosis, absolute value of kurtosis, negentropy, Kolmogorov-Smirnov statistic and sum of squared coefficients are considered. The criteria are evaluated by their ability to classify known groups. Two types of data are analyzed for illustration.

독립성분분석은 혼합된 신호에서 원신호들을 분리하기 위해서 사용되는 다변량 분석방법으로서, 블라인드 음원 분리 중 가장 널리 사용되는 방법이다. 독립성분분석은 주성분분석이나 요인분석과 같이 선형변환을 사용하지만, 원신호들의 통계적 독립과 비정규성 가정을 필요로 한다는 점에서 다르다. 설명되는 분산의 누적비율이 클수록 더 중요한 성분을 의미하게 되는 주성분분석과 달리, 독립성분분석에서는 독립성분들의 중요순서를 결정하는데 적절한 유일한 기준이 정해지지 않는다. 군집분석이나 차원축소된 그래프 작성 등과 같은 후속 연구를 진행하기 위해서는 일부의 주요 독립성분을 사용하게 되므로, 성분의 순서를 정하는 것은 의미가 있다. 본 연구에서는 성분의 순서를 결정하기 위한 몇 가지 기준의 성능을 비교하였다. 첨도와 첨도의 절댓값, 음의 엔트로피, 콜모고로프-스미르노프 통계량, 계수제곱합을 이용한 방법이 고려되었다. 이들은 알려진 그룹을 분류하는 능력을 기준으로 평가되었다. 두 가지 형태의 자료를 이용한 분석결과를 제시하였다.

Keywords

References

  1. Anderson, E. (1935). The irises of the gaspe peninsula, Bulletin of American Iris Society, 59, 2-5.
  2. Cichocki, A. and Amari, S. (2002). Adaptive Blind Signal and Image Processing: Learning Al- gorithms and Applications, Number V. 1 in Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. Wiley.
  3. Cristescu, R., Ristaniemi, T., Joutsensalo, J., and Karhunen, J. (2000). Delay estimation in cdma communications using a fast ica algorithm. In Proceedings of the International Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000). In press.
  4. De Martino, F., Gentile, F., Esposito, F., Balsi, M., Di Salle, F., Goebel, R., and Formisano, E. (2007). Classification of fmri independent components using ic-fingerprints and support vector machine classifiers, Neuroimage, 34, 177-194. https://doi.org/10.1016/j.neuroimage.2006.08.041
  5. Enderle, J. D. and Bronzino, J. D. (2012). Introduction to Biomedical Engineering, Academic Press, Seoul.
  6. Hendrikse, A., Veldhuis, R., and Spreeuwers, L. (2007). Component ordering in independent component analysis based on data power, 28th Symposium on Information Theory in the Benelux, 211-218.
  7. Hyvarinen, A. (2013). Independent component analysis: recent advances, Philosophical Transactions of the Royal Society A, 371, 20110534.
  8. Hyvarinen, A. and Oja, E. (2000). Independent component analysis: algorithms and applications. Neural Networks, 13, 411-430. https://doi.org/10.1016/S0893-6080(00)00026-5
  9. Intarapanich, A., Shaw, P. J., Assawamakin, A., Wangkumhang, P., Ngamphiw, C., Chaichoompu, K., Piriyapongsa, J., and Tongsima, S. (2009). Iterative pruning pca improves resolution of highly structured populations, BMC Bioinformatics, 10, 382. https://doi.org/10.1186/1471-2105-10-382
  10. Koch, I. (2014). Analysis of Multivariate and High-Dimensional Data, Cambridge University Press, Cambridge.
  11. Kumagai, T. and Utsugi, A. (2004). Removal of artifacts and fluctuations from MEG data by clustering methods, Neurocomputing, 62, 153-160. https://doi.org/10.1016/j.neucom.2002.08.002
  12. Liang, L., Zollner, S., and Abecasis, G. R. (2007). Genome: a rapid coalescent-based whole genome simulator, Bioinformatics, 23, 1565-1567. https://doi.org/10.1093/bioinformatics/btm138
  13. Lu, W. and Rajapakse, J. C. (2003). Eliminating indeterminacy in ICA, Neurocomputing, 50, 271-290. https://doi.org/10.1016/S0925-2312(01)00710-X
  14. Naik, G. R. and Kumar, D. K. (2011). An overview of independent component analysis and its applications, Informatica, 35, 63-81.
  15. Shannon, C. E. (2001). A mathematical theory of communication, ACM SIGMOBILE Mobile Computing and Communications Review, 5, 3-55.
  16. Stone, J. V. (2004). Independent Component Analysis: A Tutorial Introduction, A Bradford Book.
  17. Zhang, Q., Sun, J., Liu, J., and Sun, X. (2007). A novel ica-based image/video processing method, Independent Component Analysis and Signal Separation, 836-842.
  18. Zhu, Y., Chen, T. L., Zhang, W., Jung, T.-P., Duann, J.-R., Makeig, S., and Cheng, C.-K. (2006). Noninvasive study of the human heart using independent component analysis. In BioInformatics and BioEngineering, 2006. BIBE 2006. Sixth IEEE Symposium on, 340-347.