# Incorporating spatial context into fuzzy-possibilistic clustering using Bayesian inference

Data clustering is the generic process of splitting a set of datums into a number of homogenous sets. Nevertheless, although a clustering process inputs datums as a set of separate mathematical objects, these entities are in fact correlated within a spatial context specific to the problem class in hand. For example, when the data acquisition process yields a 2D matrix of regularly sampled measurements, as it is the case with image sensors which utilize different modalities, adjacent datums are highly correlated. Hence, the clustering process must take into consideration the spatial context of the datums. A review of the literature, however, reveals that a significant majority of the well-established clustering techniques in the literature ignore spatial context. Other approaches, which do consider spatial context, however, either utilize pre- or post-processing operations or engineer into the cost function one or more regularization terms which reward spatial contiguity. We argue that employing cost functions and constraints based on heuristics and intuition is a hazardous approach from an epistemological perspective. This is in addition to the other shortcomings of those approaches. Instead, in this paper, we apply Bayesian inference on the clustering problem and construct a mathematical model for data clustering which is aware of the spatial context of the datums. This model utilizes a robust loss function and is independent of the notion of homogeneity relevant to any particular problem class. We then provide a solution strategy and assess experimental results generated by the proposed method in comparison with the literature and from the perspective of computational complexity and spatial contiguity.