  This paper presents a clustering technique that reduces the susceptibility to
data noise by learning and clustering the data-distribution and then assigning
the data to the cluster of its distribution. In the process, it reduces the
impact of noise on clustering results. This method involves introducing a new
distance among distributions, namely the expectation distance (denoted, ED),
that goes beyond the state-of-art distribution distance of optimal mass
transport (denoted, $W_2$ for $2$-Wasserstein): The latter essentially depends
only on the marginal distributions while the former also employs the
information about the joint distributions. Using the ED, the paper extends the
classical $K$-means and $K$-medoids clustering to those over data-distributions
(rather than raw-data) and introduces $K$-medoids using $W_2$. The paper also
presents the closed-form expressions of the $W_2$ and ED distance measures. The
implementation results of the proposed ED and the $W_2$ distance measures to
cluster real-world weather data as well as stock data are also presented, which
involves efficiently extracting and using the underlying data distributions --
Gaussians for weather data versus lognormals for stock data. The results show
striking performance improvement over classical clustering of raw-data, with
higher accuracy realized for ED. Also, not only does the distribution-based
clustering offer higher accuracy, but it also lowers the computation time due
to reduced time-complexity.
