Abstract
A D-dimensional Vector, \( \vec {x} = [x_1, \ldots , x_D] \) in \( \mathbb {R}^D \) has D components, x i , where each x i is a real number, a member of \( \mathbb {R} \). Vectors are an important kind of data and everyone is familiar with points or positions in the plane or two-dimensional space \( \mathbb {R}^2 \), and in three-dimensional space \( \mathbb {R}^3 \).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L. Devroye, Non-Uniform Random Variate Generation (Springer, Berlin, 1986). http://luc.devroye.org/rnbookindex.html
R.A. Fisher, Dispersion on a sphere. Proc. R. Soc. Lond. A 217(1130), 295–305 (1953). https://doi.org/10.1098/rspa.1953.0064
P. Kasarapu, L. Allison, Minimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions. Mach. Learn. 1–46 (2015). https://doi.org/10.1007/s10994-015-5493-0
G. Marsaglia, Choosing a point from the surface of a sphere. Ann. Math. Stat. 43, 645–646 (1972). http://www.jstor.org/stable/2240001
A. Narayanan, Algorithm AS 266: maximum likelihood estimation of the parameters of the, Dirichlet distribution. J. R. Stat. Soc.: Ser. C: Appl. Stat. 40(2), 365–374 (1991). https://doi.org/10.2307/2347605. http://www.jstor.org/stable/2347605
S. Sra, A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of I s (x). Comput. Stat. 27(1), 177–190 (2012). https://doi.org/10.1007/s00180-011-0232-x
C.S. Wallace, D.L. Dowe, Estimation of the von Mises concentration parameter using minimum message length, in Proceedings of the 12th. Australian Statistical Society Conference (1993)
A.T.A. Wood, Simulation of the von Mises Fisher distribution. Commun. Stat. Simul. Comput. 23(1), 157–164 (1994). https://doi.org/10.1080/03610919408813161
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Allison, L. (2018). Vectors. In: Coding Ockham's Razor. Springer, Cham. https://doi.org/10.1007/978-3-319-76433-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-76433-7_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76432-0
Online ISBN: 978-3-319-76433-7
eBook Packages: Computer ScienceComputer Science (R0)