# Streaming Generalized Canonical Polyadic Tensor Decompositions

arXiv: https://arxiv.org/abs/2110.14514 · HTML: https://mlsanity.com/paper/2110.14514/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [Stochastic Gradients for Large-Scale Tensor Decomposition](https://mlsanity.com/paper/1906.01687/) (2019)
- [Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors](https://mlsanity.com/paper/1404.4667/) (2014)
- [Rank regularization and Bayesian inference for tensor completion and extrapolation](https://mlsanity.com/paper/1301.7619/) (2013)
- [Identifying and Alleviating Concept Drift in Streaming Tensor Decomposition](https://mlsanity.com/paper/1804.09619/) (2018)
- [Variational Bayesian Inference for Robust Streaming Tensor Factorization and Completion](https://mlsanity.com/paper/1809.02153/) (2018)
- [SamBaTen: Sampling-based Batch Incremental Tensor Decomposition](https://mlsanity.com/paper/1709.00668/) (2017)

## Built on by (most cited first, 1 of 1)

- [GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion](https://mlsanity.com/paper/2205.03749/) (2022)

## Abstract (arXiv)

In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data. GCP differs from traditional canonical polyadic (CP) tensor decompositions as it allows for arbitrary objective functions which the CP model attempts to minimize. This approach can provide better fits and more interpretable models when the observed tensor data is strongly non-Gaussian. In the streaming case, tensor data is gradually observed over time and the algorithm must incrementally update a GCP factorization with limited access to prior data. In this work, we extend the GCP formalism to the streaming context by deriving a GCP optimization problem to be solved as new tensor data is observed, formulate a tunable history term to balance reconstruction of recently observed data with data observed in the past, develop a scalable solution strategy based on segregated solves using stochastic gradient descent methods, describe a software implementation that provides performance and portability to contemporary CPU and GPU architectures and integrates with Matlab for enhanced useability, and demonstrate the utility and performance of the approach and software on several synthetic and real tensor data sets.