Generalized Canonical Polyadic Tensor Decomposition


Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor decomposition that allows other loss functions besides squared error. For instance, we can use logistic loss or Kullback-Leibler divergence, enabling tensor decomposition for binary or count data. We present a variety of statistically-motivated loss functions for various scenarios. We provide a generalized framework for computing gradients and handling missing data that enables the use of standard optimization methods for fitting the model. We demonstrate the flexibility of GCP on several real-world examples including interactions in a social network, neural activity in a mouse, and monthly rainfall measurements in India.

SIAM Review
D. Hong, T. G. Kolda, J. A. Duersch. Generalized Canonical Polyadic Tensor Decomposition. SIAM Review, Vol. 62, No. 1, pp. 133-163, 2020.


canonical polyadic (CP) tensor decomposition, CANDECOMP, PARAFAC, Poisson tensor factorization, Bernoulli tensor factorization, missing data


author = {David Hong and Tamara G. Kolda and Jed A. Duersch}, 
title = {Generalized Canonical Polyadic Tensor Decomposition}, 
journal = {SIAM Review}, 
volume = {62}, 
number = {1}, 
pages = {133-163}, 
year = {2020},
doi = {10.1137/18M1203626},
eprint = {1808.07452},