A Parallel Projection Method for Metric Constrained Optimization

Ruggles, Cameron; Veldt, Nate; Gleich, David F.

doi:10.48550/arxiv.1901.10084

Cited by 2 publications

(14 citation statements)

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“…Computing the LambdaCC linear programming relaxation can be challenging due to the size of the constraint set. For our smaller graphs we apply Gurobi optimization software, and for larger problems we use recently developed memory-efficient projection methods [37,31]. For the local-flow objective we use a fast Julia implementation we developed in recent work [39].…”

Section: Methodsmentioning

confidence: 99%

“…We note for example that the resolution parameter corresponding to modularity is λ = 1/(2|E|), which is also inversely proportional to |E|. Computing all of the LP bounds is the bottleneck in our computations, and takes just under 2.5 hours using a recently developed parallel solver for the correlation clustering relaxation [31].…”

Section: Meta-data and Global Clusteringmentioning

confidence: 99%

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Learning Resolution Parameters for Graph Clustering

Veldt

Gleich

Wirth

2019

The World Wide Web Conference

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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.

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Section: Methodsmentioning

confidence: 99%

Section: Meta-data and Global Clusteringmentioning

confidence: 99%

Learning Resolution Parameters for Graph Clustering

Veldt

Gleich

Wirth

2019

The World Wide Web Conference

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“…Hence solving the LP for large n becomes infeasible quickly in terms of both memory and time. Veldt et al (2019) showed that for instances with n ≈ 4000, standard solvers such as Gurobi ran out of memory on a 100 GB machine. Veldt et al (2019) develop a method for which they can feasibly solve the problem for n ≈ 11000.…”

Section: Dense Graphsmentioning

confidence: 99%

“…Veldt et al (2019) showed that for instances with n ≈ 4000, standard solvers such as Gurobi ran out of memory on a 100 GB machine. Veldt et al (2019) develop a method for which they can feasibly solve the problem for n ≈ 11000. To do so, they transformation problem 4.1 The red line is the mean running time for the algorithm from (Brickell et al, 2008).…”

Section: Dense Graphsmentioning

confidence: 99%

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Project and Forget: Solving Large-Scale Metric Constrained Problems

Sonthalia¹,

C.²

2020

Preprint

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Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, PROJECT AND FORGET, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of PROJECT AND FORGET and prove that our algorithm converges to the global optimal solution and that the L 2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

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A Parallel Projection Method for Metric Constrained Optimization

Cited by 2 publications

References 0 publications

Learning Resolution Parameters for Graph Clustering

Learning Resolution Parameters for Graph Clustering

Project and Forget: Solving Large-Scale Metric Constrained Problems

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