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A bimodality test in high dimensions. (English) Zbl 1290.68111
Summary: 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 the correct clusters more difficult. In addition to the original conservative test, we propose a practical test with the same asymptotic behavior that performs well for a moderate number of points and moderate dimensionality.
##### MSC:
 68T10 Pattern recognition, speech recognition 62H30 Classification and discrimination; cluster analysis (statistical aspects) 68T05 Learning and adaptive systems in artificial intelligence
##### Keywords:
clustering; bimodality; multidimensional space; asymptotic test