Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Self-Organizing Network for Normal Mixtures

자기조직화 신경망을 이용한 정규혼합분포의 추정

  • Received : 20110700
  • Accepted : 20111000
  • Published : 2011.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

A self-organizing network is designed to estimate parameters of normal mixtures. SOMN achieves fast convergence and low possibility of divergence even when sample sizes are small, while PMLE eliminate unnecessary components. The proposed network effectively combines the good properties of SOMN and PMLE. Simulation verifies that the proposed network eliminates unnecessary components in normal mixtures when sample sizes are relatively small.

본 연구에서는 자기조직화 신경망이 필요한 노드만을 가지고 최적화하여 정규혼합분포를 추정하는 모형을 제안한다. 제안한 모형은 SOMN모형과 벌점가능도를 사용한 모형을 결합한 것이다. SOMN의 장점은 수렴속도가 빠르고 표본의 크기가 작아도 발산하는 가능성이 낮다는 것이며, 벌점가능도를 사용한 모형은 필요없는 성분의 수를 줄일 수 있다는 것이다. 모의실험을 통하여 제안한 모형이 기대한 결과를 얻음을 확인하였다.

Keywords

References

  1. Ahn, S. and Baik, S. W. (2011). Estimating parameters in multivariate normal mixtures, The Korean Communications in Statistics, 18, 357-366. https://doi.org/10.5351/CKSS.2011.18.3.357
  2. Ciuperca, G., Ridolfi, A. and Idier, J. (2003). Penalized maximum likelihood estimator for normal mixtures, Scandinavian Journal of Statistics, 30, 45-59. https://doi.org/10.1111/1467-9469.00317
  3. Dempster, A., Laird, N. and Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B, 39, 1-38.
  4. Hathaway, R. J. (1985). A constrained formulation of maximum likelihood estimation for normal mixture distributions, Annals of Statistics, 13, 795-800. https://doi.org/10.1214/aos/1176349557
  5. Kullback, S. and Leibler, R. A. (1951). On information and sufficiency, The Annals of Mathematical Statistics, 22, 79-86. https://doi.org/10.1214/aoms/1177729694
  6. Redner, R. A. and Walker, H. F. (1984). Mixture densities, maximum Likelihood and the EM algorithm, SIAM Review, 26, 195-239. https://doi.org/10.1137/1026034
  7. Robbins, H. and Monro, S. (1951). A stochastic approximation method, The Annals of Mathematical Statistics, 22, 400-407. https://doi.org/10.1214/aoms/1177729586
  8. Titterington, D. M. (1984). Recursive parameter estimation using incomplete data, Journal of the Royal Statistical Society: Series B, 46, 257-267.
  9. Yin, H. and Allinson, N. (2001a). Self-organizing mixture networks for probability density estimation, IEEE Transactions on Neural Networks, 12, 405-411. https://doi.org/10.1109/72.914534
  10. Yin, H. and Allinson, N. (2001b). Bayesian self-organizing map for Gaussian mixtures, IEE Proceedings - Vision, Image, and Signal Processing, 234-240.
  11. Xu, L. and Jordan, M. I. (1996). On convergence properties of the EM algorithm for Gaussian mixtures, Neural Computation, 8, 129-151. https://doi.org/10.1162/neco.1996.8.1.129

Cited by

  1. Parallel Implementations of the Self-Organizing Network for Normal Mixtures vol.19, pp.3, 2012, https://doi.org/10.5351/CKSS.2012.19.3.459