State-of-the-art hypergraph partitioners follow the multilevel paradigm that constructs multiple levels of progressively coarser hypergraphs that are used to drive cut refinements on each level of the hierarchy. Multilevel partitioners are subject to two limitations: (i) Hypergraph coarsening processes rely on local neighborhood structure without fully considering the global structure of the hypergraph. (ii) Refinement heuristics can stagnate on local minima. In this paper, we describe SpecPart, the first supervised spectral framework that directly tackles these two limitations. SpecPart solves a generalized eigenvalue problem that captures the balanced partitioning objective and global hypergraph structure in a low-dimensional vertex embedding while leveraging initial high-quality solutions from multilevel partitioners as hints. SpecPart further constructs a family of trees from the vertex embedding and partitions them with a tree-sweeping algorithm. Then, a novel overlay of multiple tree-based partitioning solutions, followed by lifting to a coarsened hypergraph, where an ILP partitioning instance is solved to alleviate local stagnation. We have validated SpecPart on multiple sets of benchmarks. Experimental results show that for some benchmarks, our SpecPart can substantially improve the cutsize by more than 50% with respect to the best published solutions obtained with leading partitioners hMETIS and KaHyPar.
more »
« less
Towards Scalable Spectral Embedding and Data Visualization via Spectral Coarsening
This paper proposes a scalable multilevel framework for the spectral embedding of large undirected graphs. The proposed method first computes much smaller yet sparse graphs while preserving the key spectral (structural) properties of the original graph, by exploiting a nearly-linear time spectral graph coarsening approach. Then, the resultant spectrally-coarsened graphs are leveraged for the development of much faster algorithms for multilevel spectral graph embedding (clustering) as well as visualization of large data sets. We conducted extensive experiments using a variety of large graphs and datasets and obtained very promising results. For instance, we are able to coarsen the "coPapersCiteseer" graph with 0.43 million nodes and 16 million edges into a much smaller graph with only 13K (32X fewer) nodes and 17K (950X fewer) edges in about 16 seconds; the spectrally-coarsened graphs allow us to achieve up to 1,100X speedup for multilevel spectral graph embedding (clustering) and up to 60X speedup for t-SNE visualization of large data sets.
more »
« less
- Award ID(s):
- 2021309
- NSF-PAR ID:
- 10252376
- Date Published:
- Journal Name:
- ACM International Conference on Web Search and Data Mining
- Page Range / eLocation ID:
- 869 to 877
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Recent spectral graph sparsification techniques have shown promising performance in accelerating many numerical and graph algorithms, such as iterative methods for solving large sparse matrices, spectral partitioning of undirected graphs, vectorless verification of power/thermal grids, representation learning of large graphs, etc. However, prior spectral graph sparsification methods rely on fast Laplacian matrix solvers that are usually challenging to implement in practice. This work, for the first time, introduces a solver-free approach (SF-GRASS) for spectral graph sparsification by leveraging emerging spectral graph coarsening and graph signal processing (GSP) techniques. We introduce a local spectral embedding scheme for efficiently identifying spectrally-critical edges that are key to preserving graph spectral properties, such as the first few Laplacian eigenvalues and eigenvectors. Since the key kernel functions in SF-GRASS can be efficiently implemented using sparse-matrix-vector-multiplications (SpMVs), the proposed spectral approach is simple to implement and inherently parallel friendly. Our extensive experimental results show that the proposed method can produce a hierarchy of high-quality spectral sparsifiers in nearly-linear time for a variety of real-world, large-scale graphs and circuit networks when compared with prior state-of-the-art spectral methods.more » « less
-
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called “higher-order interactions” that involve more than two nodes at a time. However, we have fewer rigorous methods that can provide insight from such representations. Here, we develop a computational framework for the problem of clustering hypergraphs with categorical edge labels — or different interaction types — where clusters corresponds to groups of nodes that frequently participate in the same type of interaction. Our methodology is based on a combinatorial objective function that is related to correlation clustering on graphs but enables the design of much more efficient algorithms that also seamlessly generalize to hypergraphs. When there are only two label types, our objective can be optimized in polynomial time, using an algorithm based on minimum cuts. Minimizing our objective becomes NP-hard with more than two label types, but we develop fast approximation algorithms based on linear programming relaxations that have theoretical cluster quality guarantees. We demonstrate the efficacy of our algorithms and the scope of the model through problems in edge-label community detection, clustering with temporal data, and exploratory data analysis.more » « less
-
Diffusion-based graph generative models are effective in generating high-quality small graphs. However, it is hard to scale them to large graphs that contain thousands of nodes. In this work, we propose EDGE, a new diffusion-based graph generative model that addresses generative tasks for large graphs. The model is developed by reversing a discrete diffusion process that randomly removes edges until obtaining an empty graph. It leverages graph sparsity in the diffusion process to improve computational efficiency. In particular, EDGE only focuses on a small portion of graph nodes and only adds edges between these nodes. Without compromising modeling ability, it makes much fewer edge predictions than previous diffusion-based generative models. Furthermore, EDGE can explicitly model the node degrees of training graphs and then gain performance improvement in capturing graph statistics. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by the proposed model have graph statistics more similar to those of training graphs.more » « less
-
Diffusion-based graph generative models are effective in generating high-quality small graphs. However, it is hard to scale them to large graphs that contain thousands of nodes. In this work, we propose EDGE, a new diffusion-based graph generative model that addresses generative tasks for large graphs. The model is developed by reversing a discrete diffusion process that randomly removes edges until obtaining an empty graph. It leverages graph sparsity in the diffusion process to improve computational efficiency. In particular, EDGE only focuses on a small portion of graph nodes and only adds edges between these nodes. Without compromising modeling ability, it makes much fewer edge predictions than previous diffusion-based generative models. Furthermore, EDGE can explicitly model the node degrees of training graphs and then gain performance improvement in capturing graph statistics. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by the proposed model have graph statistics more similar to those of training graphs.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3437963.3441767
