Discriminant Analysis with High Dimensional von Mises - Fisher Distributions
نویسندگان
چکیده
منابع مشابه
Discriminant Analysis with High Dimensional von Mises - Fisher Distributions
This paper extends previous work in discriminant analysis with von Mises-Fisher distributions (e. g., Morris and Laycock, Biometrika, 1974) to general dimension, allowing computation of misclassification probabilities. The main result is the probability distribution of the cosine transformation of a von Mises-Fisher distribution, that is, the random variable , where , satisfying , is a random d...
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This paper concerns the issue of the maximum-likelihood estimation (MLE) for the concentration parameters of the von Mises-Fisher (vMF) distributions, which are crucial to directional data analysis. In particular, we study the numerical approximation approach for solving the implicit nonlinear equation arising from building the MLE of the concentration parameter κ of vMF distributions. In addit...
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Several large scale data mining applications, such as text categorization and gene expression analysis, involve high-dimensional data that is also inherently directional in nature. Often such data is L2 normalized so that it lies on the surface of a unit hypersphere. Popular models such as (mixtures of) multi-variate Gaussians are inadequate for characterizing such data. This paper proposes a g...
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The von Mises and Fisher distributions are spherical analogues to the Normal distribution on the unit circle and unit sphere, respectively. The computation of their moments, and in particular the second moment, usually involves solving tedious trigonometric integrals. Here we present a new method to compute the moments of spherical distributions, based on the divergence theorem. This method all...
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ژورنال
عنوان ژورنال: ATHENS JOURNAL OF SCIENCES
سال: 2014
ISSN: 2241-8466
DOI: 10.30958/ajs.1-4-1