Two Principal Points of Symmetric Distributions

Mizuta, Masahiro

doi:10.1007/978-3-642-72253-0_23

Cited by 2 publications

(3 citation statements)

References 6 publications

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“…where F is the distribution function and y 1 , …, y K are a set of points (Mizuta, 1998). Thus, ξ 1 , …,ξ K are the K principal points of random variable X minimizing the expected distance of X to the nearest ξ k .…”

Section: Theoretical Results Concerning K‐meansmentioning

confidence: 99%

“…Thus, ξ 1 , …,ξ K are the K principal points of random variable X minimizing the expected distance of X to the nearest ξ k . According to Mizuta (1998), the K ‐means algorithm can be used to estimate the principal points of a given theoretic distribution, but this conjecture has yet to be investigated. In fact, Tarpey, Li, and Flury (1995) indicated that principal points are special cases of self‐consistent points – the set of points to which the K ‐means algorithm converges (not necessarily the global minimum).…”

Section: Theoretical Results Concerning K‐meansmentioning

confidence: 99%

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K‐means clustering: A half‐century synthesis

Steinley

2006

Brit J Math & Statis

854

550

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This paper synthesizes the results, methodology, and research conducted concerning the K-means clustering method over the last fifty years. The K-means method is first introduced, various formulations of the minimum variance loss function and alternative loss functions within the same class are outlined, and different methods of choosing the number of clusters and initialization, variable preprocessing, and data reduction schemes are discussed. Theoretic statistical results are provided and various extensions of K-means using different metrics or modifications of the original algorithm are given, leading to a unifying treatment of K-means and some of its extensions. Finally, several future studies are outlined that could enhance the understanding of numerous subtleties affecting the performance of the K-means method.

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Section: Theoretical Results Concerning K‐meansmentioning

confidence: 99%

Section: Theoretical Results Concerning K‐meansmentioning

confidence: 99%

K‐means clustering: A half‐century synthesis

Steinley

2006

Brit J Math & Statis

854

550

View full text Add to dashboard Cite

show abstract

“…Analitical solutions for problem (4.2), called principal points, were first given in [Flury, 1990] for Y following an elliptical distribution, with k = 2 and for general dimension p. In [Tarpey et al, 1995] it was shown that principal points are a special case of what is called self-consistent points. Results on principal points for general k for univariate distributions can be found in [Zoppè, 1995, Mizuta, 1998].…”

Section: Introductionmentioning

confidence: 99%

Statistical distances for model validation and clustering. Applications to flow cytometry and fair learning.

Valdés¹

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Precisely the most detailed presentation and practical implementation of this methodology, as well as experiments in real data and comparisons with other state of the art methods is what we propose as the second chapter of this work. In particular, we present the main functionalities of optimalFlow , an R package that we have developed to facilitate the use of our methods. We have also made a package, optimalFlowData, with the data used for our experiments. Both are available as free software in gitHub and have been submitted to BioConductor.

show abstract

Two Principal Points of Symmetric Distributions

Cited by 2 publications

References 6 publications

K‐means clustering: A half‐century synthesis

K‐means clustering: A half‐century synthesis

Statistical distances for model validation and clustering. Applications to flow cytometry and fair learning.

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