Combinatorial Optimization Techniques for Network-Based Data Mining

Shirokikh, Oleg; Stozhkov, Vladimir; Boginski, Vladimir

doi:10.1007/978-1-4419-7997-1_6

Cited by 1 publication

(1 citation statement)

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“…The first model, referred to as (M1), addresses the well-studied graph coloring problem [17]. The problem inherently requires finding the minimum number of colors to assign the nodes of the network such that no adjacent nodes have the same color.…”

Section: Pure and Mixed-integer Linear Programming Modelsmentioning

confidence: 99%

Clustering Network Data Using Mixed Integer Linear Programming

Pirim¹,

Aghalari²,

Marufuzzaman³

2022

Recent Applications in Graph Theory

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Network clustering provides insights into relational data and feeds certain machine learning pipelines. We present five integer or mixed-integer linear programming formulations from literature for a crisp clustering. The first four clustering models employ an undirected, unweighted network; the last one employs a signed network. All models are coded in Python and solved using Gurobi solver. Codes for one of the models are explained. All codes and datasets are made available. The aim of this chapter is to compare some of the integer or mixed-integer programming network clustering models and to provide access to Python codes to replicate the results. Mathematical programming formulations are provided, and experiments are run on two different datasets. Results are reported in terms of computational times and the best number of clusters. The maximum diameter minimization model forms compact clusters including members with a dominant affiliation. The model generates a few clusters with relatively larger size. Additional constraints can be included to force bounds on the cluster size. The NP-hard nature of the problem limits the size of the dataset, and one of the models is terminated after 6 days. The models are not practical for networks with hundreds of nodes and thousands of edges or more. However, the diversity of models suggests different practical applications in social sciences.

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Section: Pure and Mixed-integer Linear Programming Modelsmentioning

confidence: 99%