mlsanityData to 7 Oct 2026

DeEPCA: Decentralized Exact PCA with Linear Convergence Rate

arXiv 2102.03990 ↗First posted 8 Feb 2021cs.LG math.OCcited by 18

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Abstract (arXiv)

Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the problem of decentralized Principal components analysis (PCA), which is a statistical method widely used for data analysis. We introduce a technique called subspace tracking to reduce the communication cost, and apply it to power iterations. This leads to a decentralized PCA algorithm called textttDeEPCA, which has a convergence rate similar to that of the centralized PCA, while achieving the best communication complexity among existing decentralized PCA algorithms. textttDeEPCA is the first decentralized PCA algorithm with the number of communication rounds for each power iteration independent of target precision. Compared to existing algorithms, the proposed method is easier to tune in practice, with an improved overall communication cost. Our experiments validate the advantages of textttDeEPCA empirically.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 8 of its 31 references that are in the map. First posted on arXiv 8 Feb 2021.

Builds on

8 of 31 references.

References · 8

  1. 2019Advances and Open Problems in Federated Learningcited by 3,021
  2. 2017Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descentcited by 496
  3. 2014SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectivescited by 401
  4. 2014EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimizationcited by 160
  5. 2013On the Convergence of Decentralized Gradient Descentcited by 158
  6. 2013The Noisy Power Method: A Meta Algorithm with Applicationscited by 58
  7. 2020Multi-consensus Decentralized Accelerated Gradient Descentcited by 20
  8. 2014Cloud K-SVD: A Collaborative Dictionary Learning Algorithm for Big, Distributed Datacited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 0; 2023: 4; 2024: 4; 2025: 3; 2026: 2.

18 papers.

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  1. 2023Improving the Model Consistency of Decentralized Federated Learningcited by 45
  2. 2021Decentralized Riemannian Gradient Descent on the Stiefel Manifoldcited by 33
  3. 2021Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Functioncited by 11
  4. 2024Decentralized Directed Collaboration for Personalized Federated Learningcited by 9
  5. 2023Towards More Suitable Personalization in Federated Learning via Decentralized Partial Model Trainingcited by 8
  6. 2023Decentralized Riemannian Conjugate Gradient Method on the Stiefel Manifoldcited by 7
  7. 2024Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Datacited by 5
  8. 2021FedPower: Privacy-Preserving Distributed Eigenspace Estimationcited by 4
  9. 2021Distributed Principal Subspace Analysis for Partitioned Big Data: Algorithms, Analysis, and Implementationcited by 4
  10. 2024Riemannian Federated Learning via Averaging Gradient Streamscited by 4
  11. 2025DeMuon: A Decentralized Muon for Matrix Optimization over Graphscited by 4
  12. 2021FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysiscited by 3
6 more
  1. 2023Decentralized Weakly Convex Optimization Over the Stiefel Manifoldcited by 1
  2. 2025Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Trackingcited by 1
  3. 2025Unveiling the Power of Multiple Gossip Steps: A Stability-Based Generalization Analysis in Decentralized Trainingcited by 1
  4. 2024Rapid Grassmannian Averaging with Chebyshev Polynomialscited by 0
  5. 2026Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCAcited by 0
  6. 2026Incremental Aggregation on the Grassmannian for Asynchronous Eigenspace Computationcited by 0