NDLI: Gossip PCA

Content Provider	ACM Digital Library
Author	Korada, Satish Babu Montanari, Andrea Oh, Sewoong
Abstract	Eigenvectors of data matrices play an important role in many computational problems, ranging from signal processing to machine learning and control. For instance, algorithms that compute positions of the nodes of a wireless network on the basis of pairwise distance measurements require a few leading eigenvectors of the distances matrix. While eigenvector calculation is a standard topic in numerical linear algebra, it becomes challenging under severe communication or computation constraints, or in absence of central scheduling. In this paper we investigate the possibility of computing the leading eigenvectors of a large data matrix through gossip algorithms. The proposed algorithm amounts to iteratively multiplying a vector by independent random sparsification of the original matrix and averaging the resulting normalized vectors. This can be viewed as a generalization of gossip algorithms for consensus, but the resulting dynamics is significantly more intricate. Our analysis is based on controlling the convergence to stationarity of the associated Kesten-Furstenberg Markov chain.
Starting Page	169
Ending Page	180
Page Count	12
File Format	PDF
ISSN	01635999
DOI	10.1145/2007116.2007136
Journal	ACM SIGMETRICS Performance Evaluation Review (PERV)
Volume Number	39
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Gossip algorithm Pca
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Hardware and Architecture Software

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