Data Mining and Knowledge Discovery

, Volume 29, Issue 5, pp 1233–1257

Beyond rankings: comparing directed acyclic graphs

Article

DOI: 10.1007/s10618-015-0406-1

Cite this article as:
Malmi, E., Tatti, N. & Gionis, A. Data Min Knowl Disc (2015) 29: 1233. doi:10.1007/s10618-015-0406-1

Abstract

Defining appropriate distance measures among rankings is a classic area of study which has led to many useful applications. In this paper, we propose a more general abstraction of preference data, namely directed acyclic graphs (DAGs), and introduce a measure for comparing DAGs, given that a vertex correspondence between the DAGs is known. We study the properties of this measure and use it to aggregate and cluster a set of DAGs. We show that these problems are \(\mathbf {NP}\)-hard and present efficient methods to obtain solutions with approximation guarantees. In addition to preference data, these methods turn out to have other interesting applications, such as the analysis of a collection of information cascades in a network. We test the methods on synthetic and real-world datasets, showing that the methods can be used to, e.g., find a set of influential individuals related to a set of topics in a network or to discover meaningful and occasionally surprising clustering structure.

Keywords

Directed acyclic graphs Aggregation Clustering  Preferences Information cascades 

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.HIIT and Department of Computer ScienceAalto UniversityEspooFinland

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