Combining clusterings in the belief function framework

International audienceIn this paper, we propose a clustering ensemble method based on Dempster-Shafer Theory. In the first step, base partitions are generated by evidential clustering algorithms such as the evidential c-means or EVCLUS. Base credal partitions are then converted to their relational representations, which are combined by averaging. The combined relational representation is then made transitive using the theory of intuitionistic fuzzy relations. Finally, the consensus solution is obtained by minimizing an error function. Experiments with simulated and real datasets show the good performances of this method

Median evidential c-means algorithm and its application to community detection

Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical framework of belief functions is proposed. The median variant relaxes the restriction of a metric space embedding for the objects but constrains the prototypes to be in the original data set. Due to these properties, MECM could be applied to graph clustering problems. A community detection scheme for social networks based on MECM is investigated and the obtained credal partitions of graphs, which are more refined than crisp and fuzzy ones, enable us to have a better understanding of the graph structures. An initial prototype-selection scheme based on evidential semi-centrality is presented to avoid local premature convergence and an evidential modularity function is defined to choose the optimal number of communities. Finally, experiments in synthetic and real data sets illustrate the performance of MECM and show its difference to other methods

Clustering is difficult only when it does not matter

Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the great importance of clustering, we still do not have a satisfactory mathematical theory of clustering. In order to properly understand clustering, it is clearly necessary to develop a solid theoretical basis for the area. For example, from the perspective of computational complexity theory the clustering problem seems very hard. Numerous papers introduce various criteria and numerical measures to quantify the quality of a given clustering. The resulting conclusions are pessimistic, since it is computationally difficult to find an optimal clustering of a given data set, if we go by any of these popular criteria. In contrast, the practitioners' perspective is much more optimistic. Our explanation for this disparity of opinions is that complexity theory concentrates on the worst case, whereas in reality we only care for data sets that can be clustered well. We introduce a theoretical framework of clustering in metric spaces that revolves around a notion of "good clustering". We show that if a good clustering exists, then in many cases it can be efficiently found. Our conclusion is that contrary to popular belief, clustering should not be considered a hard task

Structural Regularities in Text-based Entity Vector Spaces

Entity retrieval is the task of finding entities such as people or products in response to a query, based solely on the textual documents they are associated with. Recent semantic entity retrieval algorithms represent queries and experts in finite-dimensional vector spaces, where both are constructed from text sequences. We investigate entity vector spaces and the degree to which they capture structural regularities. Such vector spaces are constructed in an unsupervised manner without explicit information about structural aspects. For concreteness, we address these questions for a specific type of entity: experts in the context of expert finding. We discover how clusterings of experts correspond to committees in organizations, the ability of expert representations to encode the co-author graph, and the degree to which they encode academic rank. We compare latent, continuous representations created using methods based on distributional semantics (LSI), topic models (LDA) and neural networks (word2vec, doc2vec, SERT). Vector spaces created using neural methods, such as doc2vec and SERT, systematically perform better at clustering than LSI, LDA and word2vec. When it comes to encoding entity relations, SERT performs best.Comment: ICTIR2017. Proceedings of the 3rd ACM International Conference on the Theory of Information Retrieval. 201