# Generalized Canonical Polyadic Tensor Decomposition

arXiv: https://arxiv.org/abs/1808.07452 · HTML: https://mlsanity.com/paper/1808.07452/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2018.

## Built on by (most cited first, 30 of 34)

- [Convergence of Alternating Gradient Descent for Matrix Factorization](https://mlsanity.com/paper/2305.06927/) (2023)
- [Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation](https://mlsanity.com/paper/2103.08323/) (2021)
- [TenIPS: Inverse Propensity Sampling for Tensor Completion](https://mlsanity.com/paper/2101.00323/) (2021)
- [Learning Good State and Action Representations via Tensor Decomposition](https://mlsanity.com/paper/2105.01136/) (2021)
- [ATD: Augmenting CP Tensor Decomposition by Self Supervision](https://mlsanity.com/paper/2106.07900/) (2021)
- [Beyond the Signs: Nonparametric Tensor Completion via Sign Series](https://mlsanity.com/paper/2102.00384/) (2021)
- [Stochastic Mirror Descent for Low-Rank Tensor Decomposition Under Non-Euclidean Losses](https://mlsanity.com/paper/2104.14562/) (2021)
- [MTC: Multiresolution Tensor Completion from Partial and Coarse Observations](https://mlsanity.com/paper/2106.07135/) (2021)
- [MEKER: Memory Efficient Knowledge Embedding Representation for Link Prediction and Question Answering](https://mlsanity.com/paper/2204.10629/) (2022)
- [Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros](https://mlsanity.com/paper/2201.10014/) (2022)
- [Application Performance Modeling via Tensor Completion](https://mlsanity.com/paper/2210.10184/) (2022)
- [Efficient Nonparametric Tensor Decomposition for Binary and Count Data](https://mlsanity.com/paper/2401.07711/) (2024)
- [TTML: tensor trains for general supervised machine learning](https://mlsanity.com/paper/2203.04352/) (2022)
- [MULTIPAR: Supervised Irregular Tensor Factorization with Multi-task Learning](https://mlsanity.com/paper/2208.00993/) (2022)
- [Personalized Coupled Tensor Decomposition for Multimodal Data Fusion: Uniqueness and Algorithms](https://mlsanity.com/paper/2412.01102/) (2024)
- [Near-Universal Multiplicative Updates for Nonnegative Einsum Factorization](https://mlsanity.com/paper/2602.02759/) (2026)
- [Streaming Generalized Canonical Polyadic Tensor Decompositions](https://mlsanity.com/paper/2110.14514/) (2021)
- [Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularization](https://mlsanity.com/paper/2205.03059/) (2022)
- [A generalizable framework for low-rank tensor completion with numerical priors](https://mlsanity.com/paper/2302.05881/) (2023)
- [Deep-Learning-Aided Alternating Least Squares for Tensor CP Decomposition and Its Application to Massive MIMO Channel Estimation](https://mlsanity.com/paper/2305.13947/) (2023)
- [Multi-Dictionary Tensor Decomposition](https://mlsanity.com/paper/2309.09717/) (2023)
- [SWoTTeD: An Extension of Tensor Decomposition to Temporal Phenotyping](https://mlsanity.com/paper/2310.01201/) (2023)
- [Tensor Decomposition with Unaligned Observations](https://mlsanity.com/paper/2410.14046/) (2024)
- [Communication Efficient Generalized Tensor Factorization for Decentralized Healthcare Networks](https://mlsanity.com/paper/2109.01718/) (2021)
- [Reconfigurable Low-latency Memory System for Sparse Matricized Tensor Times Khatri-Rao Product on FPGA](https://mlsanity.com/paper/2109.08874/) (2021)
- [GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion](https://mlsanity.com/paper/2205.03749/) (2022)
- [SeKron: A Decomposition Method Supporting Many Factorization Structures](https://mlsanity.com/paper/2210.06299/) (2022)
- [Statistical and computational rates in high rank tensor estimation](https://mlsanity.com/paper/2304.04043/) (2023)
- [ADMM-MM Algorithm for General Tensor Decomposition](https://mlsanity.com/paper/2312.11763/) (2023)
- [Knowledge Translation: A New Pathway for Model Compression](https://mlsanity.com/paper/2401.05772/) (2024)

## Abstract (arXiv)

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.