Affiliations: [a] School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece | [b] Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Greece
Abstract: Several well known clustering algorithms have their own online counterparts, in order to deal effectively with the big data issue, as well as with the case where the data become available in a streaming fashion. However, very few of them follow the stochastic gradient descent philosophy, despite the fact that the latter enjoys certain practical advantages (such as the possibility of (a) running faster than their batch processing counterparts and (b) escaping from local minima of the associated cost function), while, in addition, strong theoretical convergence results have been established for it. In this paper a novel stochastic gradient descent possibilistic clustering algorithm, called O-PCM2 is introduced. The algorithm is presented in detail and it is rigorously proved that the gradient of the associated cost function tends to zero in the L2 sense, based on general convergence results established for the family of the stochastic gradient descent algorithms. Furthermore, an additional discussion is provided on the nature of the points where the algorithm may converge. Finally, the performance of the proposed algorithm is tested against other related algorithms, on the basis of both synthetic and real data sets.
