  In this paper, we propose a new time-aware dissimilarity measure that takes
into account the temporal dimension. Observations that are close in the
description space, but distant in time are considered as dissimilar. We also
propose a method to enforce the segmentation contiguity, by introducing, in the
objective function, a penalty term inspired from the Normal Distribution
Function. We combine the two propositions into a novel time-driven constrained
clustering algorithm, called TDCK-Means, which creates a partition of coherent
clusters, both in the multidimensional space and in the temporal space. This
algorithm uses soft semi-supervised constraints, to encourage adjacent
observations belonging to the same entity to be assigned to the same cluster.
We apply our algorithm to a Political Studies dataset in order to detect
typical evolution phases. We adapt the Shannon entropy in order to measure the
entity contiguity, and we show that our proposition consistently improves
temporal cohesion of clusters, without any significant loss in the
multidimensional variance.
