# Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data

arXiv: https://arxiv.org/abs/2309.03439 · HTML: https://mlsanity.com/paper/2309.03439/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 66 references that are in the map.
- First posted on arXiv 7 Sep 2023.

## Builds on (most cited first, 18 of 18)

- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction](https://mlsanity.com/paper/1912.05693/) (2019)
- [The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning](https://mlsanity.com/paper/2111.05326/) (2021)
- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [A novel approach for fusion of heterogeneous sources of data](https://mlsanity.com/paper/1803.00138/) (2018)
- [Dynamic Tensor Clustering](https://mlsanity.com/paper/1708.07259/) (2017)
- [Structured Point Cloud Data Analysis via Regularized Tensor Regression for Process Modeling and Optimization](https://mlsanity.com/paper/1807.10278/) (2018)
- [Tensor-based algorithms for image classification](https://mlsanity.com/paper/1910.02150/) (2019)
- [General Tensor Spectral Co-clustering for Higher-Order Data](https://mlsanity.com/paper/1603.00395/) (2016)
- [Smooth Robust Tensor Completion for Background/Foreground Separation with Missing Pixels: Novel Algorithm with Convergence Guarantee](https://mlsanity.com/paper/2203.16328/) (2022)
- [Real-time Detection of Clustered Events in Video-imaging data with Applications to Additive Manufacturing](https://mlsanity.com/paper/2004.10977/) (2020)
- [Tensor Analysis with n-Mode Generalized Difference Subspace](https://mlsanity.com/paper/1909.01954/) (2019)
- [Deep Spatio-temporal Sparse Decomposition for Trend Prediction and Anomaly Detection in Cardiac Electrical Conduction](https://mlsanity.com/paper/2109.09317/) (2021)
- [Rapid Detection of Hot-spots via Tensor Decomposition with applications to Crime Rate Data](https://mlsanity.com/paper/2004.11710/) (2020)
- [Adaptive Partially-Observed Sequential Change Detection and Isolation](https://mlsanity.com/paper/2208.08855/) (2022)
- [Multi-View Clustering via Semi-non-negative Tensor Factorization](https://mlsanity.com/paper/2303.16748/) (2023)

## Built on by (most cited first, 2 of 2)

- [Federated Multilinear Principal Component Analysis with Applications in Prognostics](https://mlsanity.com/paper/2312.06050/) (2023)
- [Personalized Federated Hierarchical Gaussian Processes for Privacy-Preserving Modeling of Heterogeneous Distributed Systems](https://mlsanity.com/paper/2609.19337/) (2026)

## Abstract (arXiv)

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global components and personalized local components. We introduce a mode orthogonality assumption and develop a proximal gradient regularized block coordinate descent algorithm that is guaranteed to converge to a stationary point. By learning unique and common representations across datasets, we demonstrate perTucker's effectiveness in anomaly detection, client classification, and clustering through a simulation study and two case studies on solar flare detection and tonnage signal classification.