Introducing Sparsity in Possibilistic Clustering: A Unified Framework and a Line Detection Paradigm
Konstantinos Koutroumbas · IEEE Transactions on Fuzzy Systems · 2018
The contribution of this paper is twofold. First, it introduces a generalized framework where sparsity is imposed to a well-known class of cost-function optimization possibilistic algorithms. In addition, under mild conditions, the algorithms in this framework have the ability to determine the number of the true clusters, starting from an overestimation of it. Second, it proposes a new algorithm that is proved to belong to the above framework, which is able to cope with linearly shaped clusters in the two-dimensional space. The algorithm employs (finite) line segments as cluster representatives and the distance of a data point from a cluster is defined as its distance from the corresponding representative line segment. In contrast to several relative algorithms, the proposed algorithm is able to identify intersecting linear clusters as well as to discriminate between collinear clusters. Finally, the experimental results that assess the performance of the proposed algorithm are provided.