Generalized Canonical Polyadic Tensor Decomposition
This work addresses the problem of handling non-Gaussian data in tensor decomposition for researchers and practitioners in data science, though it is incremental as it extends existing methods with new loss functions.
The paper tackles the limitation of standard tensor decomposition methods by introducing a generalized canonical polyadic (GCP) decomposition that supports various loss functions like logistic loss and Kullback-Leibler divergence, enabling applications to binary or count data, and demonstrates its flexibility on real-world datasets such as social networks and neural activity.
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.