分布式PCA通过动态协作实现高效收敛，理论与实验均验证其有效性。
Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation
- 各节点并行求解不同特征向量，通过优于自身的同伴更新结果
- 异步更新下仍保证收敛，通信开销小且可扩展
- 首个理论证明此类分布式动态交互的收敛性，适合大规模数据场景
我们研究一种分布式主成分分析（PCA）框架，其中每个工作节点负责求解一个独立的特征向量，并通过来自被判定为“更优”的同伴提供的中间解进行迭代优化。受集中式特征值问题中降维法的启发，该方法打破传统降维步骤间的顺序依赖，支持工作节点的异步更新，同时仅引入少量通信开销。据我们所知，这类分布式、动态的工作节点交互缺乏理论基础。本文提供了理论分析，解释了为何、如何以及在何种条件下这些层级化的中间更新能够在分布式环境中实现有效且可证明的收敛。尽管是理论性工作，我们的原型实现表明，该分布式PCA算法能有效收敛且具备可扩展性：实验显示，其性能与当前最先进的模型并行PCA求解器EigenGame-μ相当。
原文摘要 · Abstract (English)
We study a distributed Principal Component Analysis (PCA) framework where each worker targets a distinct eigenvector and refines its solution by updating from intermediate solutions provided by peers deemed as "superior". Drawing intuition from the deflation method in centralized eigenvalue problems, our approach breaks the sequential dependency in the deflation steps and allows asynchronous updates of workers, while incurring only a small communication cost. To our knowledge, a gap in the literature -- the theoretical underpinning of such distributed, dynamic interactions among workers -- has remained unaddressed. This paper offers a theoretical analysis explaining why, how, and when these intermediate, hierarchical updates lead to practical and provable convergence in distributed environments. Despite being a theoretical work, our prototype implementation demonstrates that such a distributed PCA algorithm converges effectively and in scalable way: through experiments, our proposed framework offers comparable performance to EigenGame-$μ$, the state-of-the-art model-parallel PCA solver.
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