Structuring Typical Evolutions Using Temporal-Driven Constrained Clustering

Abstract

Abstract-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.

ClusPath: a temporal-driven clustering to infer typical evolution paths

“…TDCK-Means [Rizoiu et al(2012)Rizoiu, Velcin, and Lallich] was introduced to detect typical evolution phases in a population of entities. The main contributions of this work were i) proposing a temporal-aware dissimilarity measure, used to assess the similarity between two observations, both in the multidimensional descriptive and temporal spaces and ii) assuring a contiguous segmentation by imposing semi-supervised must-link constraints [Wagstaff et al(2001)Wagstaff, Cardie, Rogers, and Schroedl] and a continuous timedependent penalty function for breaking the constraints.…”

“…ClusPath fulfills the aforementioned objectives by a) translating them into several objectives and combining them into an overall objective function J and b) applying a gradient descent optimization method, in which J is minimized, using a K-Means-like iterative relocation framework. To optimize Obj 1, we use the temporal-aware dissimilarity measure proposed by [Rizoiu et al(2012)Rizoiu, Velcin, and Lallich]:…”

“…3.1. The first three objectives are evaluated using measures proposed by [Rizoiu et al(2012) Rizoiu, Velcin, and Lallich]. The coherence of the obtained partition in the descriptive and temporal dimensions are measured using the classical variance on, respectively, the multidimensional component (MDvar measure) and the temporal component (Tvar measure).…”

http://ria.revuesonline.com/article.jsp?articleId=19006

“…L'objectif est de déterminer des partitions cohérentes, à la fois sur l'espace des variables et sur l'espace temporel. C'est le cas de l'algorithme TDCK-Means (Rizoiu et al, 2012) incluant une mesure de dissemblance temporelle qui, tout en introduisant le temps dans le clustering, ne réduit pas la pertinence des partitions sur l'espace des variables. L'intérêt croissant pour l'étude des réseaux sociaux a donné également lieu à un nombre important d'algorithmes d'analyse de la dynamique de clusters.…”