ailzy/tensor-learning

Python codes for tensor factorization, tensor completion, and tensor regression techniques.

Tensor Learning (张量学习)

Made by Xinyu Chen • 🌐 https://twitter.com/chenxy346

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

• geotensor | Image inpainting
• transdim | Spatiotemporal traffic data imputation and prediction
• Recommender systems
• mats | Multivariate time series imputation and forecasting

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

Our Research

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We conduct extensive experiments on some real-world data sets:

• Large-scale PeMS traffic speed data set registers traffic speed time series from 11160 sensors over 4/8/12 weeks (for PeMS-4W/PeMS-8W/PeMS-12W) with 288 time points per day (i.e., 5-min frequency) in California, USA. You can download this data set and place it at the folder of datasets.

  • Data path example: ../datasets/California-data-set/pems-4w.csv.

mats

mats is a project in the tensor learning repository, and it aims to develop machine learning for multivariate time series forecasting.

Low-Rank Autoregressive Tensor Completion for Multivariate Time Series Forecasting.
[arXiv]

Figure 1: Illustration of our proposed Low-Rank Tensor Completion (LATC) imputer/predictor with a prediction window τ (green nodes: observed values; white nodes: missing values; red nodes/panel: prediction; blue panel: training data to construct the tensor).

In this work, we develop a Low-Rank Autoregressive Tensor Completion for multivariate time series forecasting in the presence of missing values. To overcome the challenge of missing time series values, our LATC model takes into account:

• autoregressive process on the matrix structure to capture local temporal states,
• and low-rank assumption on the tensor structure to capture global low-rank patterns simultaneously.

Python codes for reproducing experiments are provided in the ../mats folder. Since these Python codes were written on the Jupyter Notebook, you could also view them on the nbviewer. Please open

• LATC-imputer.ipynb
• LATC-predictor.ipynb

If you find these codes useful, please star (★) this repository.

📖 Tutorial

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We summarize some preliminaries for better understanding tensor learning. They are given in the form of tutorial as follows.

• Foundations of Python Numpy Programming

  • Generating random numbers in Matlab and Numpy [Jupyter notebook] [blog post]

• Foundations of Tensor Computations

  • Kronecker product

• Singular Value Decomposition (SVD)

  • Randomized singular value decomposition [Jupyter notebook] [blog post]
  • Tensor singular value decomposition

Helpful Learning Material

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• Ruye Wang (2010). Introduction to Orthogonal Transforms with Applications in Data Processing and Analysis. Cambridge University Press. [PDF]

Quick Run

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

Citing

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This repository is from the following paper, please cite our paper if it helps your research.

• Xinyu Chen, Lijun Sun (2020). Low-rank autoregressive tensor completion for multivariate time series forecasting. arXiv: 2006.10436. [preprint] [data & Python code]

Acknowledgements

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This research is supported by the Institute for Data Valorization (IVADO).

License

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This work is released under the MIT license.