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2018 Supervised multiway factorization
Eric F. Lock, Gen Li
Electron. J. Statist. 12(1): 1150-1180 (2018). DOI: 10.1214/18-EJS1421


We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order array. Such data are increasingly encountered in biomedical research and other fields. We use a novel likelihood-based latent variable representation of the CP factorization, in which the latent variables are informed by additional covariates. We give conditions for identifiability, and develop an EM algorithm for simultaneous estimation of all model parameters. SupCP can be used for dimension reduction, capturing latent structures that are more accurate and interpretable due to covariate supervision. Moreover, SupCP specifies a full probability distribution for a multiway data observation with given covariate values, which can be used for predictive modeling. We conduct comprehensive simulations to evaluate the SupCP algorithm. We apply it to a facial image database with facial descriptors (e.g., smiling / not smiling) as covariates, and to a study of amino acid fluorescence. Software is available at


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Eric F. Lock. Gen Li. "Supervised multiway factorization." Electron. J. Statist. 12 (1) 1150 - 1180, 2018.


Received: 1 April 2017; Published: 2018
First available in Project Euclid: 27 March 2018

zbMATH: 1388.62176
MathSciNet: MR3780043
Digital Object Identifier: 10.1214/18-EJS1421

Keywords: Dimension reduction , Faces in the wild , latent variables , parafac/candecomp , Singular value decomposition , tensors


Vol.12 • No. 1 • 2018
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