Supervised multiway factorization

Abstract

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 describe a 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 https://github.com/lockEF/SupCP .

31 pages, 6 figures, 7 tables

References in corpus (6)

• Tensor Regression with Applications in Neuroimaging Data Analysis
• Projected principal component analysis in factor models
• Multilinear tensor regression for longitudinal relational data
• Separable factor analysis with applications to mortality data
• Supervised multiway factorization
• Discriminating sample groups with multi-way data

Cited by in corpus (7)

• Tensor-on-tensor regression
• Supervised multiway factorization
• Supervised tensor decomposition with features on multiple modes
• Regularized and Smooth Double Core Tensor Factorization for Heterogeneous Data
• Integrative Factor Regression and Its Inference for Multimodal Data Analysis
• Sparse covariate-driven factorization of high-dimensional brain connectivity with application to site effect correction
• Latent Functional PARAFAC for modeling multidimensional longitudinal data