Learning Resolution Parameters for Graph Clustering

Abstract

Finding clusters of well-connected nodes in a graph is an extensively studied problem in graph-based data analysis. Because of its many applications, a large number of distinct graph clustering objective functions and algorithms have already been proposed and analyzed. To aid practitioners in determining the best clustering approach to use in different applications, we present new techniques for automatically learning how to set clustering resolution parameters. These parameters control the size and structure of communities that are formed by optimizing a generalized objective function. We begin by formalizing the notion of a parameter fitness function, which measures how well a fixed input clustering approximately solves a generalized clustering objective for a specific resolution parameter value. Under reasonable assumptions, which suit two key graph clustering applications, such a parameter fitness function can be efficiently minimized using a bisection-like method, yielding a resolution parameter that fits well with the example clustering. We view our framework as a type of single-shot hyperparameter tuning, as we are able to learn a good resolution parameter with just a single example. Our general approach can be applied to learn resolution parameters for both local and global graph clustering objectives. We demonstrate its utility in several experiments on real-world data where it is helpful to learn resolution parameters from a given example clustering.

Strongly local p-norm-cut algorithms for semi-supervised learning and local graph clustering

“…Finally, we note that there are more general constructions possible. For instance, differential penalties for S and S in the localized cut graph can be used for a variety of effects [Orecchia and Zhu, 2014;Veldt et al, 2019b]. For 1-norm objectives, optimal parameters for γ and κ can also be chosen to model desierable clusters [Veldt et al, 2019b] -similar ideas may be possible for these p-norm generalizations.…”

“…For instance, differential penalties for S and S in the localized cut graph can be used for a variety of effects [Orecchia and Zhu, 2014;Veldt et al, 2019b]. For 1-norm objectives, optimal parameters for γ and κ can also be chosen to model desierable clusters [Veldt et al, 2019b] -similar ideas may be possible for these p-norm generalizations. We view the structured flexibility of these ideas as a key advantage because ideas are easy to compose.…”

“…The second experiment uses the class-year metadata on Facebook [Traud et al, 2012], which is known to have good conductance structure for at least class year 2009 [Veldt et al, 2019b] that should be identifiable with many methods. Other class years are harder to detect with conductance.…”

Graph Clustering in All Parameter Regimes

“…In follow up work [10], the same authors showed that the LambdaCC LP relaxation has an O(log n) integrality gap. They also later proved new results for how learn the best value of λ to use in practice [34].…”

“…Our ability to approximate the LP relaxation of a clustering objective in all parameter regimes is useful even when LP solutions are not rounded to produce approximate clusterings. Solutions to the LP provide lower bounds for evaluating the performance of heuristic clustering techniques, and can also be useful for learning how to set graph clustering resolution parameters in practice [34].…”