Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K-groups: A Generalization of K-means Clustering   We propose a new class of distribution-based clustering algorithms, called
k-groups, based on energy distance between samples. The energy distance
clustering criterion assigns observations to clusters according to a
multi-sample energy statistic that measures the distance between distributions.
The energy distance determines a consistent test for equality of distributions,
and it is based on a population distance that characterizes equality of
distributions. The k-groups procedure therefore generalizes the k-means method,
which separates clusters that have different means. We propose two k-groups
algorithms: k-groups by first variation; and k-groups by second variation. The
implementation of k-groups is partly based on Hartigan and Wong's algorithm for
k-means. The algorithm is generalized from moving one point on each iteration
(first variation) to moving $m$ $(m > 1)$ points. For univariate data, we prove
that Hartigan and Wong's k-means algorithm is a special case of k-groups by
first variation. The simulation results from univariate and multivariate cases
show that our k-groups algorithms perform as well as Hartigan and Wong's
k-means algorithm when clusters are well-separated and normally distributed.
Moreover, both k-groups algorithms perform better than k-means when data does
not have a finite first moment or data has strong skewness and heavy tails. For
non--spherical clusters, both k-groups algorithms performed better than k-means
in high dimension, and k-groups by first variation is consistent as dimension
increases. In a case study on dermatology data with 34 features, both k-groups
algorithms performed better than k-means.

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The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
9
The categories of this paper are: nlin
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The categories of this paper are: quant-ph