mlsanityData to 7 Oct 2026

Network Lasso: Clustering and Optimization in Large Graphs

arXiv 1507.00280 ↗First posted 1 Jul 2015cs.SI math.OC stat.APcited by 42

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Abstract (arXiv)

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the network lasso, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jul 2015.

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Citing papers per year: 2021: 10; 2022: 9; 2023: 5; 2024: 6; 2025: 7; 2026: 5.

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  1. 2022Efficient Distribution Similarity Identification in Clustered Federated Learning via Principal Angles Between Client Data Subspacescited by 36
  2. 2021A New Look and Convergence Rate of Federated Multi-Task Learning with Laplacian Regularizationcited by 27
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  5. 2021Temporal Graph Signal Decompositioncited by 8
  6. 2021Clustered Federated Learning via Generalized Total Variation Minimizationcited by 7
  7. 2023The Contextual Lasso: Sparse Linear Models via Deep Neural Networkscited by 6
  8. 2022Improving Your Graph Neural Networks: A High-Frequency Boostercited by 4
  9. 2022Clustered Federated Learning based on Nonconvex Pairwise Fusioncited by 4
  10. 2021On Convex Clustering Solutionscited by 3
  11. 2023Multi-Task Learning Regression via Convex Clusteringcited by 3
  12. 2021Model-Agnostic Graph Regularization for Few-Shot Learningcited by 2
30 more
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  5. 2021Time-varying Graph Learning Under Structured Temporal Priorscited by 1
  6. 2021A Bayesian approach to multi-task learning with network lassocited by 1
  7. 2022flow-based clustering and spectral clustering: a comparisoncited by 1
  8. 2022Binary Representation via Jointly Personalized Sparse Hashingcited by 1
  9. 2024Analysis of Total Variation Minimization for Clustered Federated Learningcited by 1
  10. 2025Decentralized Optimization with Topology-Independent Communicationcited by 1
  11. 2025Federated k-Means over Networkscited by 1
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  13. 2021Approximate Frank-Wolfe Algorithms over Graph-structured Support Setscited by 0
  14. 2022Inference of Multiscale Gaussian Graphical Modelcited by 0
  15. 2023Online Heavy-tailed Change-point detectioncited by 0
  16. 2024A Unified Framework for Center-based Clustering of Distributed Datacited by 0
  17. 2024Decentralised Traffic Incident Detection via Network Lassocited by 0
  18. 2024Multi-task learning via robust regularized clustering with non-convex group penaltiescited by 0
  19. 2024Your Data, My Model: Learning Who Really Helps in Federated Learningcited by 0
  20. 2024MARINA-P: Superior Performance in Non-smooth Federated Optimization with Adaptive Stepsizescited by 0
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  22. 2025Learning under Latent Group Sparsity via Diffusion on Networkscited by 0
  23. 2025Data-driven Trust Bootstrapping for Mobile Edge Computing-based Industrial IoT Servicescited by 0
  24. 2025Fused Lasso Improves Accuracy of Co-occurrence Network Inference in Grouped Samplescited by 0
  25. 2025A non-smooth regularization framework for learning over multitask graphscited by 0
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  27. 2026A Unified Framework for Structure-Aware Clustering and Heterogeneous Causal Graph Learningcited by 0
  28. 2026TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matchingcited by 0
  29. 2026Decentralized Multitask Learning over Learned Task Graphscited by 0
  30. 2026Multitask Regression with Pairwise Fusioncited by 0