  We would like to congratulate Lee, Nadler and Wasserman on their contribution
to clustering and data reduction methods for high $p$ and low $n$ situations. A
composite of clustering and traditional principal components analysis, treelets
is an innovative method for multi-resolution analysis of unordered data. It is
an improvement over traditional PCA and an important contribution to clustering
methodology. Their paper [arXiv:0707.0481] presents theory and supporting
applications addressing the two main goals of the treelet method: (1) Uncover
the underlying structure of the data and (2) Data reduction prior to
statistical learning methods. We will organize our discussion into two main
parts to address their methodology in terms of each of these two goals. We will
present and discuss treelets in terms of a clustering algorithm and an
improvement over traditional PCA. We will also discuss the applicability of
treelets to more general data, in particular, the application of treelets to
microarray data.
