Rough Hypercuboid Based Generalized and Robust IT2 Fuzzy C-Means Algorithm.

One of the important issues in pattern recognition and machine learning is how to find natural groups present in a dataset. In this regard, this paper presents a novel clustering algorithm, called rough hypercuboid-based interval type-2 fuzzy c -means (RIT2FCM). It judiciously integrates the merits of the rough hypercuboid approach, c -means algorithm, and interval type-2 fuzzy set, to address the uncertainty associated with real-life datasets. Using the concept of hypercuboid equivalence partition matrix (HEM) of rough hypercuboid approach, the lower approximation and boundary region of each cluster are implicitly defined, without using any prespecified threshold parameter. The interval-valued fuzzifier is applied to address the uncertainty coupled with different parameters of rough-fuzzy clustering algorithms, where the determination of the appropriate value of fuzzifier is a difficult task. An analytical formulation on the convergence analysis of the proposed RIT2FCM algorithm, along with a theoretical bound of its fuzzifier, is also introduced. The efficacy of the proposed RIT2FCM method is extensively compared with that of several existing clustering algorithms, using some cluster validity and classification rate indices on various real-life datasets. The proposed algorithm performs better than the state-of-the-art c -means algorithms in 92.59% cases, with respect to different cluster validity indices, in lesser computation time.