Limit theorems for the number of maxima in random samples from planar regions.
Bai, Zhi-Dong, Hwang, Hsien-Kuei, Liang, Wen-Qi, Tsai, Tsung-Hsi (2001)
Electronic Journal of Probability [electronic only]
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Bai, Zhi-Dong, Hwang, Hsien-Kuei, Liang, Wen-Qi, Tsai, Tsung-Hsi (2001)
Electronic Journal of Probability [electronic only]
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We present a test for identifying clusters in high dimensional data based on the k-means algorithm when the null hypothesis is spherical normal. We show that projection techniques used for evaluating validity of clusters may be misleading for such data. In particular, we demonstrate that increasingly well-separated clusters are identified as the dimensionality increases, when no such clusters exist. Furthermore, in a case of true bimodality, increasing the dimensionality makes identifying...
Gao, Xin, Xu, Hong, Ye, Dong (2009)
International Journal of Mathematics and Mathematical Sciences
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Godbole, Anant P., Lamorte, Ben, Sandquist, Erik Jonathan (1997)
The Electronic Journal of Combinatorics [electronic only]
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Gérard Ben Arous, Ofer Zeitouni (1998)
ESAIM: Probability and Statistics
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