  Cluster analysis and outlier detection are strongly coupled tasks in data
mining area. Cluster structure can be easily destroyed by few outliers; on the
contrary, outliers are defined by the concept of cluster, which are recognized
as the points belonging to none of the clusters. Unfortunately, most existing
studies do not notice the coupled relationship between these two task and
handle them separately. In light of this, we consider the joint cluster
analysis and outlier detection problem, and propose the Clustering with Outlier
Removal (COR) algorithm. Generally speaking, the original space is transformed
into the binary space via generating basic partitions in order to define
clusters. Then an objective function based Holoentropy is designed to enhance
the compactness of each cluster with a few outliers removed. With further
analyses on the objective function, only partial of the problem can be handled
by K-means optimization. To provide an integrated solution, an auxiliary binary
matrix is nontrivally introduced so that COR completely and efficiently solves
the challenging problem via a unified K-means-- with theoretical supports.
Extensive experimental results on numerous data sets in various domains
demonstrate the effectiveness and efficiency of COR significantly over
state-of-the-art methods in terms of cluster validity and outlier detection.
Some key factors in COR are further analyzed for practical use. Finally, an
application on flight trajectory is provided to demonstrate the effectiveness
of COR in the real-world scenario.
