Tue, 03 Nov 2020

14:00 - 15:00
Virtual

FFTA: A bi-directional approach to comparing the modular structure of networks

Mattie Landman
(Mathematical Institute)
Abstract

Here we propose a new method to compare the modular structure of a pair of node-aligned networks. The majority of current methods, such as normalized mutual information, compare two node partitions derived from a community detection algorithm yet ignore the respective underlying network topologies. Addressing this gap, our method deploys a community detection quality function to assess the fit of each node partition with respect to the other network's connectivity structure. Specifically, for two networks A and B, we project the node partition of B onto the connectivity structure of A. By evaluating the fit of B's partition relative to A's own partition on network A (using a standard quality function), we quantify how well network A describes the modular structure of B. Repeating this in the other direction, we obtain a two-dimensional distance measure, the bi-directional (BiDir) distance. The advantages of our methodology are three-fold. First, it is adaptable to a wide class of community detection algorithms that seek to optimize an objective function. Second, it takes into account the network structure, specifically the strength of the connections within and between communities, and can thus capture differences between networks with similar partitions but where one of them might have a more defined or robust community structure. Third, it can also identify cases in which dissimilar optimal partitions hide the fact that the underlying community structure of both networks is relatively similar. We illustrate our method for a variety of community detection algorithms, including multi-resolution approaches, and a range of both simulated and real world networks.

Fri, 25 Jun 2021

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Joel Dyer, Constantin Puiu, Markus Dablander
(Mathematical Institute)
Fri, 28 May 2021

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Anna Berryman, Georgia Brennan, Matthew Shirley,
(Mathematical Institute)
Fri, 30 Apr 2021

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Giancarlo Antonucci, Thomas Babb, Yu Tian, Sophie Abrahams
(Mathematical Institute)
Fri, 26 Mar 2021

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Huining Yang, Deqing Jiang, Joe Roberts
(Mathematical Institute)
Fri, 26 Feb 2021

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Zhen Shao, John Fitzgerald, Brady Metherall, James Harris
(Mathematical Institute)
Fri, 29 Jan 2021

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Rodrigo Leal Cervantes, Isabelle Scott, Meredith Ellis, Oliver Bond
(Mathematical Institute)
Fri, 11 Dec 2020

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Harry Renolds, Lingyi Yang, Alexandru Puiu, Arkady Wey
(Mathematical Institute)
Fri, 27 Nov 2020

11:45 - 13:15
Virtual

InFoMM CDT Group Meeting

Giuseppe Ughi, James Morrill, Rahil Sachak-Patwa, Nicolas Boulle
(Mathematical Institute)
Tue, 01 Dec 2020
14:30
Virtual

Binary matrix factorisation via column generation

Reka Kovacs
(Mathematical Institute)
Abstract

Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic. Due to the NP-hardness of this problem, most previous attempts rely on heuristic techniques. We formulate the problem as a mixed integer linear program and use a large scale optimisation technique of column generation to solve it without the need of heuristic pattern mining. Our approach focuses on accuracy and on the provision of optimality guarantees. Experimental results on real world datasets demonstrate that our proposed method is effective at producing highly accurate factorisations and improves on the previously available best known results for 16 out of 24 problem instances.

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