Abstract | ||
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Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive tensor factorization model of such data, along with appropriate algorithms and theory. To do so, we propose that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution. Under a Poisson assumption, we fit a model to observed data using the negative log-likelihood score. We present a new algorithm for Poisson tensor factorization called CANDECOMP-PARAFAC alternating Poisson regression (CP-APR) that is based on a majorization-minimization approach. It can be shown that CP-APR is a generalization of the Lee-Seung multiplicative updates. We show how to prevent the algorithm from converging to non-KKT points and prove convergence of CP-APR under mild conditions. We also explain how to implement CP-APR for large-scale sparse tensors and present results on several data sets, both real and simulated. |
Year | DOI | Venue |
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2012 | 10.1137/110859063 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
nonnegative tensor factorization,nonnegative CANDECOMP-PARAFAC,Poisson tensor factorization,Lee-Seung multiplicative updates,majorization-minimization algorithms | Random variable,Mathematical optimization,Multiplicative function,Tensor,Gaussian,Count data,Poisson regression,Poisson distribution,Multilinear map,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 4 | 0895-4798 |
Citations | PageRank | References |
87 | 3.01 | 22 |
Authors | ||
2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Eric C. Chi | 1 | 93 | 6.89 |
Tamara G. Kolda | 2 | 5079 | 262.60 |