Name
Abstract | ||
|---|---|---|
When analyzing high-dimensional data, it is often appropriate to pay attention only to the direction of each datum, disregarding its norm. The von Mises---Fisher (vMF) distribution is a natural probability distribution for such data. When we estimate the parameters of vMF distributions, parameter 驴 which corresponds to the degree of concentration is difficult to obtain, and some approximations are necessary. In this article, we propose an iterative algorithm using fixed points to obtain the maximum likelihood estimate (m.l.e.) for 驴. We prove that there is a unique local maximum for 驴. Besides, using a specific function to calculate the m.l.e., we obtain the upper and lower bounds of the interval in which the exact m.l.e. exists. In addition, based on these bounds, a new and good approximation is derived. The results of numerical experiments demonstrate the new approximation exhibits higher precision than traditional ones. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s00180-007-0030-7 | Computational Statistics |
Keywords | DocType | Volume |
fixed point,von mises-fisher distribution · concentration parameter · modified bessel function of the first kind · maximum likelihood estimate · successive substitution method,high-dimensional data,parameter estimation,higher precision,new approximation,maximum likelihood estimate,vMF distribution,natural probability distribution,exact m,unique local maximum,von Mises-Fisher distribution,good approximation | Journal | 22 |
Issue | ISSN | Citations |
1 | 1613-9658 | 13 |
PageRank | References | Authors |
1.75 | 3 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Akihiro Tanabe | 1 | 13 | 2.09 |
| kenji fukumizu | 2 | 1683 | 158.91 |
| Shigeyuki Oba | 3 | 290 | 27.68 |
| Takashi Takenouchi | 4 | 182 | 19.44 |
| Shin Ishii | 5 | 212 | 24.55 |