Tensor Learning (张量学习)

Tutorials and Python codes for tensor factorization, tensor completion and tensor regression techniques with the following real-world applications:

• Image inpainting
• Spatiotemporal data imputation
• Recommender systems

In a hurry? Please check out our contents as follows.

Contents

• Part 1: Foundations

  • 1 Proximal Methods

    • 1.1 Iterative Shrinkage Thresholding Algorithm (ISTA)
    • 1.2 Singular Value Thresholding

  • 2 Bayesian Inference Methods

  • 3 Time Series Analysis

    • 1.1 Vector Autoregressive (VAR) Model

• Part 2: Matrix Factorization and Completion Techniques

  • 1 Low-Rank Matrix Completion

    • 1.1 Building on Nuclear Norm Regularization
    • 1.2 Building on Nonconvex Regularization

  • 2 Low-Rank Matrix Factorization

    • 2.1 A Gradient Descent Solution
    • 2.2 An Alternating Least Square Solution
    • 2.3 A Probabilistic Solution
    • 2.4 A Bayesian Solution

  • 3 Temporal Regularized Matrix Factorization

    • 3.1 An Alternating Least Square Solution
    • 3.2 A Probabilistic Solution

  • 4 Bayesian Temporal Matrix Factorization

    • 4.1 Incorporating Autoregressive (AR) Model
    • 4.2 Incorporating Vector Autoregressive (VAR) Model

• Part 3: Tensor Factorization Techniques

  • 1 Tensor Factorization with Alternating Least Square (ALS)

  • 2 Nonnegative Tensor Factorization

  • 3 Bayesian Gaussian Tensor Factorization

• Part 4: Low-Rank Tensor Completion Techniques [coming soon!]

  • 1 Tensor Robust Principal Component Analysis
    • 1.1 Modeling for Tensor Recovery Problem
    • 1.2 Modeling for Outlier Detection Problem

• Part 5: Multidimensional Tensor Regression [coming soon!]

Quick Run

• If you just want to read the tutorial, please follow the link of above contents directly.

• If you want to run the code, please

  • download (or clone) this repository,
  • open the .ipynb file using Jupyter notebook,
  • and run the code.