Generalized Canonical Polyadic Tensor Decomposition

TL;DR

This paper introduces a flexible tensor decomposition framework that allows various loss functions beyond squared error, enabling applications to binary, count, and other data types with improved adaptability.

Contribution

It develops a generalized canonical polyadic tensor decomposition method supporting diverse loss functions, facilitating broader applications in data science.

Findings

Successfully applied to social network interactions

Analyzed neural activity data in mice

Modeled monthly rainfall measurements in India

Abstract

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 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.