Title: Data-Driven Tree Transforms and Metrics,
Abstract: We consider the analysis of high dimensional data given in the form of a
matrix with columns consisting of observations and rows consisting of features.
Often the data is such that the observations do not reside on a regular grid,
and the given order of the features is arbitrary and does not convey a notion
of locality. Therefore, traditional transforms and metrics cannot be used for
data organization and analysis. In this paper, our goal is to organize the data
by defining an appropriate representation and metric such that they respect the
smoothness and structure underlying the data. We also aim to generalize the
joint clustering of observations and features in the case the data does not
fall into clear disjoint groups. For this purpose, we propose multiscale
data-driven transforms and metrics based on trees. Their construction is
implemented in an iterative refinement procedure that exploits the
co-dependencies between features and observations. Beyond the organization of a
single dataset, our approach enables us to transfer the organization learned
from one dataset to another and to integrate several datasets together. We
present an application to breast cancer gene expression analysis: learning
metrics on the genes to cluster the tumor samples into cancer sub-types and
validating the joint organization of both the genes and the samples. We
demonstrate that using our approach to combine information from multiple gene
expression cohorts, acquired by different profiling technologies, improves the
clustering of tumor samples.