Asynchronous gossip principal components analysis

International audienceThis paper deals with Principal Components Analysis (PCA) of data spread over a network where central coordination and synchronous communication between networking nodes are forbidden. We propose an asynchronous and decentralized PCA algorithm dedicated to large scale problems, where " large " simultaneously applies to dimensionality, number of observations and network size. It is based on the integration of a dimension reduction step into a Gossip consensus protocol. Unlike other approaches, a straightforward dual formulation makes it suitable when observed dimensions are distributed. We theoretically show its equivalence with a centralized PCA under a low-rank assumption on training data. An experimental analysis reveals that it achieves a good accuracy with a reasonable communication cost even when the low-rank assumption is relaxed