Reconciliation k-median: Clustering with Non-polarized Representatives

Abstract

We propose a new variant of the k-median problem, where the objective function models not only the cost of assigning data points to cluster representatives, but also a penalty term for disagreement among the representatives. We motivate this novel problem by applications where we are interested in clustering data while avoiding selecting representatives that are too far from each other. For example, we may want to summarize a set of news sources, but avoid selecting ideologically-extreme articles in order to reduce polarization.To solve the proposed k-median formulation we adopt the localsearch algorithm of Arya et al. [2], We show that the algorithm provides a provable approximation guarantee, which becomes constant under a mild assumption on the minimum number of points for each cluster. We experimentally evaluate our problem formulation and proposed algorithm on datasets inspired by the motivating applications. In particular, we experiment with data extracted from Twitter, the US Congress voting records, and popular news sources. The results show that our objective can lead to choosing less polarized groups of representatives without significant loss in representation fidelity.

Visualizing Structural Balance in Signed Networks

“…The layout produced by Structural-balance-viz has the following characteristics that are useful in a variety of network analysis tasks: (i) it shows whether the input network is balanced or not and, in the second case, how close the network is to be balanced; (ii) by nodes' x-coordinate, it provides an indication of the contribute to the balance structure of the network and, also, of the individual balance/polarization of each node (such information might be exploited, e.g., for the task of finding non-polarized representatives [19]); (iii) it identifies two factions of nodes on the basis of their polarization which finds applications in clustering problems, e.g., 2-correlation-clustering [7,2]; (iv) the scale represented by the x-axis shows cumulative characteristics of the identified factions, e.g., size or internal clustering coefficient; and, (v) the resulting visualization are reproducible (desirable feature but not common to all network layouts, e.g., force based) and easy to compare in terms of balance structure. We verify such characteristics by running Structural-balance-viz on synthetic networks and a real-world dataset representing political debates.…”