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\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 443-464

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2010.148

\vspace{3pc} \normalsize \centerline{\large\bf CLUSTERING HIGH
DIMENSION, LOW SAMPLE SIZE } \vspace{2pt} \centerline{\large\bf DATA
USING THE MAXIMAL DATA PILING DISTANCE} \vspace{.25cm}
\author{Jeongyoun Ahn, Myung Hee
Lee and Young Joo Yoon} \vspace{.4cm} \centerline{\it University of
Georgia, Colorado State University and Konkuk University}

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\begin{quotation}
\noindent {\it Abstract:} We propose a new hierarchical clustering
method for high dimension, low sample size (HDLSS) data. The method
utilizes the fact that each individual data vector accounts for
exactly one dimension in the subspace generated by HDLSS data. The
linkage that is used for measuring the distance between clusters is
the orthogonal distance between affine subspaces generated by each
cluster. The ideal implementation would be to consider all possible
binary splits of the data and choose the one that maximizes the
distance in between. Since this is not computationally feasible in
general, we use the singular value decomposition for its
approximation. We provide theoretical justification of the method by
studying high dimensional asymptotics. Also we obtain the
probability distribution of the  distance measure under the null
hypothesis of no split, which we use to propose a criterion for
determining the number of clusters. Simulation and data analysis
with microarray data show competitive clustering performance of the
proposed method.\par\vspace{9pt} \noindent {\it Key words and
phrases:} Hierarchical clustering, high dimension, low sample size
data, maximal data piling, singular value decomposition
\par \par
\end{quotation}

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