  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. This paper focuses on this dual objective of PCA, namely,
dimensionality reduction and decorrelation of features, which requires
estimating the eigenvectors of a data covariance matrix, as opposed to only
estimating the subspace spanned by the eigenvectors. 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.
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 a data covariance matrix when data are 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 shown to demonstrate the efficacy of the
proposed solution.
