A Clustering Model for Uncertain Preferences Based on Belief Functions

Community detection is a popular topic in network science field. In social network analysis, preference is often applied as an attribute for individuals’ representation. In some cases, uncertain and imprecise preferences may appear. Moreover, conflicting preferences can arise from multiple sources. From a model for imperfect preferences we proposed earlier, we study the clustering quality in case of perfect preferences as well as imperfect ones based on weak orders (orders that are complete, reflexive and transitive). The model for uncertain preferences is based on the theory of belief functions with an appropriate dissimilarity measure when performing the clustering steps. To evaluate the quality of clustering results, we used Adjusted Rand Index (ARI) and silhouette score on synthetic data as well as on Sushi preference data set collected from real world. The results show that our model has an equivalent quality with traditional preference representations for certain cases while it has better quality confronting imperfect cases.

[1]  Haluk Bingol,et al.  Community detection using preference networks , 2017, ArXiv.

[2]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[3]  Yiru Zhang,et al.  An Empirical Study to Determine the Optimal k in Ek-NNclus Method , 2018, BELIEF.

[4]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[5]  Katarzyna Musial,et al.  Adaptive community detection incorporating topology and content in social networks✰ , 2018, Knowl. Based Syst..

[6]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Thierry Denoeux,et al.  Modelling and predicting partial orders from pairwise belief functions , 2016, Soft Comput..

[8]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[9]  Yiru Zhang,et al.  Preference fusion and Condorcet's paradox under uncertainty , 2017, 2017 20th International Conference on Information Fusion (Fusion).

[10]  Ronald Fagin,et al.  Comparing and aggregating rankings with ties , 2004, PODS '04.

[11]  Jure Leskovec,et al.  Community Detection in Networks with Node Attributes , 2013, 2013 IEEE 13th International Conference on Data Mining.

[12]  Grégory Smits,et al.  A Distance-Based Decision in the Credal Level , 2014, AISC.

[13]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[14]  Anne-Laure Jousselme,et al.  Distances in evidence theory: Comprehensive survey and generalizations , 2012, Int. J. Approx. Reason..

[15]  Shotaro Akaho,et al.  Efficient Clustering for Orders , 2006, ICDM Workshops.

[16]  L. Hubert,et al.  Comparing partitions , 1985 .

[17]  Shotaro Akaho,et al.  Efficient Clustering for Orders , 2006, Sixth IEEE International Conference on Data Mining - Workshops (ICDMW'06).

[18]  Toshihiro Kamishima,et al.  Nantonac collaborative filtering: recommendation based on order responses , 2003, KDD '03.