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 the GCP decomposition on several real-world examples including interactions in a social network, neural activity in a mouse, and monthly rainfall measurements in India.