Gossip algorithms for principal component analysis in networks

Abstract

This paper deals with the issues of the dimensionality reduction and the extraction of the structure of data using principal component analysis for the multivariable data in large-scale networks. In order to overcome the high computational complexity of this technique, we derive several in-network strategies to estimate the principal axes without the need for computing the sample covariance matrix. To this aim, we propose to combine Oja's iterative rule with average gossiping algorithms. Gossiping is used as a solution for communication between asynchronous nodes. The performance of the proposed approach is illustrated on time series acquisition in wireless sensor networks.

Eigenvector Computation and Community Detection in Asynchronous Gossip Models

“…However, the computation of graph eigenvectors in fully asynchronous and gossip-based message passing systems, in which nodes communicate with a single neighbor at a time in an asynchronous fashion, is not well-understood. While a number of algorithms have been proposed, which give convergence to the true eigenvectors as the number of iterations goes to infinity, strong finite iteration approximation bounds are not known [16,27]. Our contributions In this work, we give state-of-the-art algorithms for graph eigenvector computation in asynchronous systems with randomized schedulers, including the classic gossip model [8,14] and population protocol model [2].…”

“…where in the final bound we assume 1 − ǫ ≥ 1/2 which is without loss of generality, since we can always scale ǫ down by a 1/2 factor. We similarly use the perturbation bound of ( 28), the scale bound of ( 27) and our eigenvalue calculations for BB T to argue that that λ 1 (D+W) ≤ 16 n and that λ 2 (I−1/2D+1/2W) ≤ 1− q 2n(p+q)…”