A Linearly Convergent Algorithm for Distributed Principal Component Analysis

Abstract

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are uncorrelated. Furthermore, the ever-increasing volume of data in the modern world often requires storage of data samples across multiple machines, which precludes the use of centralized PCA algorithms. This paper focuses on the dual objective of PCA, namely, dimensionality reduction and decorrelation of features, but in a distributed setting. This requires estimating the eigenvectors of the data covariance matrix, as opposed to only estimating the subspace spanned by the eigenvectors, when data is distributed across a network of machines. Although a few distributed solutions to the PCA problem have been proposed recently, convergence guarantees and/or communications overhead of these solutions remain a concern. With an eye towards communications efficiency, this paper introduces a feedforward neural network-based one time-scale distributed PCA algorithm termed Distributed Sanger's Algorithm (DSA) that estimates the eigenvectors of the data covariance matrix when data is distributed across an undirected and arbitrarily connected network of machines. Furthermore, the proposed algorithm is shown to converge linearly to a neighborhood of the true solution. Numerical results are also provided to demonstrate the efficacy of the proposed solution.

34 pages; final version of journal paper accepted for publication in a special issue of EURASIP J. Signal Processing

References in corpus (4)

• Adversary-resilient Distributed and Decentralized Statistical Inference and Machine Learning: An Overview of Recent Advances Under the Byzantine Threat Model
• Scaling-up Distributed Processing of Data Streams for Machine Learning
• Distributed Stochastic Algorithms for High-rate Streaming Principal Component Analysis
• Exit Time Analysis for Approximations of Gradient Descent Trajectories Around Saddle Points

Cited by in corpus (5)

• Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function
• FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis
• Distributed Principal Subspace Analysis for Partitioned Big Data: Algorithms, Analysis, and Implementation
• A Communication-Efficient and Privacy-Aware Distributed Algorithm for Sparse PCA
• Decentralized Riemannian Gradient Descent on the Stiefel Manifold