Model-based von Mises-Fisher Co-clustering with a Conscience
Aghiles Salah, Mohamed Nadif · Society for Industrial and Applied Mathematics eBooks · 2017
Co-clustering has proven effective to deal with high dimensional sparse data, such as document-term matrices encountered in text mining. Apart from being high dimensional and sparse, the data sets from the aforementioned domain are also directional in nature. Most existing co-clustering approaches are, however, based on popular modelling assumptions, such as Gaussian or Multinomial, which are inadequate for directional data. Moreover, it is well known that, due to high dimensionality and sparsity, co-clustering approaches, like one-sided clustering methods, tend to generate highly skewed solutions with very unbalanced or even empty clusters, especially when the number of required clusters is large. In this paper, we rely on the recently proposed block von Mises-Fisher mixture model (dbmovMFs), which constitutes a general framework for co-clustering directional data distributed on the surface of a unit hypersphere, i.e, L2 normalized data. In order to overcome the above difficulties, we propose to modify dbmovMFs in a principled way by introducing a conscience mechanism which discourages bad local solutions having empty or very small/large clusters. This gives rise to a new scalable co-clustering algorithm which is guaranteed to increase monotonically a spherical k-means like criterion by intertwining row and column clusterings at each step. Moreover, empirical results, on several real-world datasets, provide strong support for the effectiveness of the proposed approach.