Asynchronous gossip principal components analysis

Jerome Fellus 1 David Picard 2 Philippe-Henri Gosselin 2
1 MIDI
ETIS - Equipes Traitement de l'Information et Systèmes
Abstract : This 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.
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Jerome Fellus, David Picard, Philippe-Henri Gosselin. Asynchronous gossip principal components analysis. Neurocomputing, Elsevier, 2015, pp.0. ⟨10.1016/j.neucom.2014.11.076⟩. ⟨hal-01148639⟩

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