Discussion of: Treelets--An adaptive multi-scale basis for sparse   unordered data
  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. 
Catherine Tuglus, Mark J. van der Laan