  How to extract useful insights from data is always a challenge, especially if
the data is multidimensional. Often, the data can be organized according to
certain hierarchical structure that are stemmed either from data collection
process or from the information and phenomena carried by the data itself. The
current study attempts to discover and visualize these underlying hierarchies.
By regarding each observation in the data as a draw from a (hypothetical)
multidimensional joint density, our first goal is to approximate this unknown
density with a piecewise constant function via binary partition, our
non-parametric approach makes no assumptions on the form of the density. Given
the piecewise constant density function and its corresponding binary partition,
our second goal is to construct a connected graph and build up a tree
representation of the data by level sets. To demonstrate that our method is a
general data mining and visualization tool which can provide "multi-resolution"
summaries and reveal different levels of information of the data, we apply it
to two real data sets from Flow Cytometry and Social Network.
