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.

该论文发展了一种广义的低秩张量分解（GCP），使其可以适用于二进制或计数数据，其中除了平方误差损失函数外，还可以使用逻辑损失或 Kullback-Leibler 散度损失函数，我们提供了基于统计动机的多种损失函数，为计算梯度和处理缺失数据提供了广义框架，从而可以使用标准优化方法来拟合模型，在社交网络，老鼠的神经活动和印度的月降雨数据等几个真实世界的例子中展示了 GCP 的灵活性。