The von Mises–Fisher Matrix Distribution in Orientation Statistics

Khatri, C. G.; Mardia, Kanti V.

doi:10.1111/j.2517-6161.1977.tb01610.x

Cited by 171 publications

(166 citation statements)

References 12 publications

(11 reference statements)

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“…x ii sinhðl i x ii Þ expðS jai l j x jj Þ dvol M ðxÞ; whose integrand is almost everywhere positive if l i 40: & It follows from Theorem 3 and Lemma 4 that the mean location of MðnÞ where n has rank k and I-form m Á c has mean location m: In particular Mðm; kÞ has mean location m: In the interesting study by Khatri et al [10] of the family MðnÞ analytic expressions for the normalizing coefficients % b n and for hðLÞ are derived. Next we want to show that empirical mean location for samples from a von Mises-Fisher distribution is almost surely well defined under the assumption in the Introduction.…”

Section: Article In Pressmentioning

confidence: 95%

The admissibility of the empirical mean location for the matrix von Mises–Fisher family

Hendriks

2005

Journal of Multivariate Analysis

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In this note we consider von Mises-Fisher families of probability densities on spheres and more generally on Stiefel manifolds, which include the orthogonal groups. It addresses the estimation of the mean direction or the mean location by empirical mean location, which for the von Mises-Fisher family coincides with the maximum likelihood estimator. It is shown that (with a few exceptions) the empirical mean location of a sample is almost surely uniquely defined and that it is unbiased in the sense that its mean location coincides with the mean location of the von Mises-Fisher distribution. The main goal, however, is to show that empirical mean location is an admissible estimator for the mean location of the von MisesFisher distribution. r

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Section: Article In Pressmentioning

confidence: 95%

The admissibility of the empirical mean location for the matrix von Mises–Fisher family

Hendriks

2005

Journal of Multivariate Analysis

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“…Furthermore, raindrops and snowflakes show strong statistics property of the direction to ground horizons. We use the von Mises distribution probability [15] density function to represent it:…”

Section: Secondary Foreground Segmentationmentioning

confidence: 99%

A primary-secondary background model with sliding window PCA algorithm

Zhu

Liu

et al. 2011

Front. Electr. Electron. Eng. China

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Rain and snow seriously degrade outdoor video quality. In this work, a primary-secondary background model for removal of rain and snow is built. First, we analyze video noise and use a sliding window sequence principal component analysis de-nosing algorithm to reduce white noise in the video. Next, we apply the Gaussian mixture model (GMM) to model the video and segment all foreground objects primarily. After that, we calculate von Mises distribution of the velocity vectors and ratio of the overlapped region with referring to the result of the primary segmentation and extract the interesting object. Finally, rain and snow streaks are inpainted using the background to improve the quality of the video data. Experiments show that the proposed method can effectively suppress noise and extract interesting targets.Keywords sliding window sequence principal component analysis, primary-secondary background model, removal of rain and snow, Gaussian mixture model (GMM)

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“…[13,16], and the references therein). The modern approach using differential forms and their exterior algebra yields the Haar measure for general compact manifolds [6,10,14,5].…”

Section: The Invariant Measure On So(p)mentioning

confidence: 99%

“…The matrix Fisher-von Mises distribution introduced by Downs [4] is an exponential family which has been studied by Khatri and Mardia [10], Jupp and Mardia [9], Prentice [16], and Mardia and Jupp [11]. A recent account of the theory for this model is given by Chikuse [2].…”

Section: Introductionmentioning

confidence: 99%

A statistical model for random rotations

León

Massé

Rivest

2006

Journal of Multivariate Analysis

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This paper studies the properties of the Cayley distributions, a new family of models for random p × p rotations. This class of distributions is related to the Cayley transform that maps a p(p − 1)/2 × 1 vector s into SO(p), the space of p × p rotation matrices. First an expression for the uniform measure on SO(p) is derived using the Cayley transform, then the Cayley density for random rotations is investigated. A closed-form expression is derived for its normalizing constant, a simple simulation algorithm is proposed, and moments are derived. The efficiencies of moment estimators of the parameters of the new model are also calculated. A Monte Carlo investigation of tests and of confidence regions for the parameters of the new density is briefly summarized. A numerical example is presented.

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The von Mises–Fisher Matrix Distribution in Orientation Statistics

Cited by 171 publications

References 12 publications

The admissibility of the empirical mean location for the matrix von Mises–Fisher family

The admissibility of the empirical mean location for the matrix von Mises–Fisher family

A primary-secondary background model with sliding window PCA algorithm

A statistical model for random rotations

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