标题： FAST-PCA：一种快速且精确的分布式主成分分析算法 显示英文标题

标题： FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis

摘要： 主成分分析（PCA）是机器学习领域中一种基本的数据预处理工具。 虽然PCA通常被视为一种降维方法，但实际上PCA的目的有两个：降维和不相关特征学习。 此外，现代数据集中的维度和样本量的巨大规模使得集中式PCA解决方案无法使用。 在这方面，本文重新考虑了当数据样本分布在任意连接的网络节点上时的PCA问题。 虽然存在一些分布式PCA的解决方案，但这些方案要么忽略了PCA的不相关特征学习方面，要么通信开销较高，使其效率低下，或者缺乏“精确”或“全局”的收敛保证。 为了解决上述问题，本文提出了一种称为FAST-PCA（快速且精确的分布式PCA）的分布式PCA算法。 该算法在通信方面是高效的，并被证明可以线性且精确地收敛到主成分，从而实现降维以及不相关特征。 这些主张得到了实验结果的进一步支持。 显示英文摘要

摘要： Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction and uncorrelated feature learning. Furthermore, the enormity of the dimensions and sample size in the modern day datasets have rendered the centralized PCA solutions unusable. In that vein, this paper reconsiders the problem of PCA when data samples are distributed across nodes in an arbitrarily connected network. While a few solutions for distributed PCA exist, those either overlook the uncorrelated feature learning aspect of the PCA, tend to have high communication overhead that makes them inefficient and/or lack `exact' or `global' convergence guarantees. To overcome these aforementioned issues, this paper proposes a distributed PCA algorithm termed FAST-PCA (Fast and exAct diSTributed PCA). The proposed algorithm is efficient in terms of communication and is proven to converge linearly and exactly to the principal components, leading to dimension reduction as well as uncorrelated features. The claims are further supported by experimental results.