Minimizing Localized Ratio Cut Objectives in Hypergraphs

Veldt, Nate; Benson, Austin R.; Kleinberg, Jon

doi:10.1145/3394486.3403222

Cited by 39 publications

(74 citation statements)

References 20 publications

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“…Nevertheless, for many instances of semi-supervised learning problems, it produces results with much larger F1 scores than alternative methods. In particular, it is much faster and performs much better with extremely limited label information than a recently proposed flow-based method [33].…”

Section: Introductionmentioning

confidence: 96%

“…and (ii) Given some limited label information on the nodes of the graph, what can be inferred about missing labels? These statements correspond to the clustering and semi-supervised learning problems respectively, and while there exists a strong state of the art in algorithms for these problems on graphs [3, 13,19,29,34,35,37,42], research on these problems is currently highly active for hypergraphs [8,17,27,33,38,40,41] building on new types of results [15,26,32] compared to prior approaches [1,20,43]. The lack of flexible, diverse, and scalable hypergraph algorithms for these problems limits the opportunities to investigate rich structure in data.…”

Section: Introductionmentioning

confidence: 99%

“…Hypergraphs, indeed, enable a flexible and rich data model that has the potential to capture subtle insights that are difficult or impossible to find with traditional graph-based analysis [5,27,33,38,40]. But, hypergraph generalizations of graph-based algorithms often struggle with scalability and interpretation [1,15] with ongoing questions of whether particular models capture the higher-order information in hypergraphs.…”

Section: Introductionmentioning

confidence: 99%

“…Strongly local algorithms are those whose runtime depends on the size of the output rather than the size of the graph. This was only recently addressed for various hypergraph clustering and semi-supervised learning frameworks [17,33]. This property enables fast (seconds to minutes) evaluation even for massive graphs with hundreds of millions of nodes and edges [3] (compared with hours).…”

Section: Introductionmentioning

confidence: 99%

“…Then we localize the computation in the reduced graph using a general strategy to build strongly local computations. This involves a particular modification often called a "localized cut" graph or hypergraph [4,11,28,33]. We then use a squared 2-norm (i.e.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning

Liu¹,

Veldt

Song³

et al. 2021

Proceedings of the Web Conference 2021

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Hypergraph-based machine learning methods are now widely recognized as important for modeling and using higher-order and multiway relationships between data objects. Local hypergraph clustering and semi-supervised learning specifically involve finding a well-connected set of nodes near a given set of labeled vertices. Although many methods for local graph clustering exist, there are relatively few for localized clustering in hypergraphs. Moreover, those that exist often lack flexibility to model a general class of hypergraph cut functions or cannot scale to large problems. To tackle these issues, this paper proposes a new diffusion-based hypergraph clustering algorithm that solves a quadratic hypergraph cut based objective akin to a hypergraph analog of Andersen-Chung-Lang personalized PageRank clustering for graphs. We prove that, for graphs with fixed maximum hyperedge size, this method is strongly local, meaning that its runtime only depends on the size of the output instead of the size of the hypergraph and is highly scalable. Moreover, our method enables us to compute with a wide variety of cardinality-based hypergraph cut functions. We also prove that the clusters found by solving the new objective function satisfy a Cheeger-like quality guarantee. We demonstrate that on large real-world hypergraphs our new method finds better clusters and runs much faster than existing approaches. Specifically, it runs in a few seconds for hypergraphs with a few million hyperedges compared with minutes for a flow-based technique. We furthermore show that our framework is general enough that can also be used to solve other p-norm based cut objectives on hypergraphs. CCS CONCEPTS• Mathematics of computing → Hypergraphs; • Theory of computation → Semi-supervised learning; • Computing methodologies → Cluster analysis.

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Section: Introductionmentioning

confidence: 96%