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Generalized Canonical Polyadic Tensor Decomposition

arXiv 1808.07452 ↗First posted 22 Aug 2018math.NA cs.LG cs.NAcited by 34

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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.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Aug 2018.

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Citing papers per year: 2021: 10; 2022: 8; 2023: 7; 2024: 4; 2025: 1; 2026: 4.

34 papers.

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  1. 2023Convergence of Alternating Gradient Descent for Matrix Factorizationcited by 12
  2. 2021Spatiotemporal Tensor Completion for Improved Urban Traffic Imputationcited by 9
  3. 2021TenIPS: Inverse Propensity Sampling for Tensor Completioncited by 7
  4. 2021Learning Good State and Action Representations via Tensor Decompositioncited by 7
  5. 2021ATD: Augmenting CP Tensor Decomposition by Self Supervisioncited by 7
  6. 2021Beyond the Signs: Nonparametric Tensor Completion via Sign Seriescited by 4
  7. 2021Stochastic Mirror Descent for Low-Rank Tensor Decomposition Under Non-Euclidean Lossescited by 4
  8. 2021MTC: Multiresolution Tensor Completion from Partial and Coarse Observationscited by 4
  9. 2022MEKER: Memory Efficient Knowledge Embedding Representation for Link Prediction and Question Answeringcited by 4
  10. 2022Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeroscited by 3
  11. 2022Application Performance Modeling via Tensor Completioncited by 3
  12. 2024Efficient Nonparametric Tensor Decomposition for Binary and Count Datacited by 3
22 more
  1. 2022TTML: tensor trains for general supervised machine learningcited by 2
  2. 2022MULTIPAR: Supervised Irregular Tensor Factorization with Multi-task Learningcited by 2
  3. 2024Personalized Coupled Tensor Decomposition for Multimodal Data Fusion: Uniqueness and Algorithmscited by 2
  4. 2026Near-Universal Multiplicative Updates for Nonnegative Einsum Factorizationcited by 2
  5. 2021Streaming Generalized Canonical Polyadic Tensor Decompositionscited by 1
  6. 2022Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularizationcited by 1
  7. 2023A generalizable framework for low-rank tensor completion with numerical priorscited by 1
  8. 2023Deep-Learning-Aided Alternating Least Squares for Tensor CP Decomposition and Its Application to Massive MIMO Channel Estimationcited by 1
  9. 2023Multi-Dictionary Tensor Decompositioncited by 1
  10. 2023SWoTTeD: An Extension of Tensor Decomposition to Temporal Phenotypingcited by 1
  11. 2024Tensor Decomposition with Unaligned Observationscited by 1
  12. 2021Communication Efficient Generalized Tensor Factorization for Decentralized Healthcare Networkscited by 0
  13. 2021Reconfigurable Low-latency Memory System for Sparse Matricized Tensor Times Khatri-Rao Product on FPGAcited by 0
  14. 2022GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completioncited by 0
  15. 2022SeKron: A Decomposition Method Supporting Many Factorization Structurescited by 0
  16. 2023Statistical and computational rates in high rank tensor estimationcited by 0
  17. 2023ADMM-MM Algorithm for General Tensor Decompositioncited by 0
  18. 2024Knowledge Translation: A New Pathway for Model Compressioncited by 0
  19. 2025Data Understanding Survey: Pursuing Improved Dataset Characterization Via Tensor-based Methodscited by 0
  20. 2026Generalized Canonical Polyadic Tensor Decompositions with General Symmetrycited by 0
  21. 2026Disentangled Mode-Specific Representations for Tensor Time Series via Contrastive Learningcited by 0
  22. 2026Heteroskedastic Canonical Polyadic Tensor Decompositioncited by 0