Tutorials

Scope and intention

This page presents a collection of tutorial written by the authors of mprod package and intended to help newcomers in incorporating the machinery offered by the library in their analysis workflows.

The main (and only) data-scientific tool currently implemented is the TCAM dimensionality reduction algorithm 1. We intend to keep expanding the package content by adding \(\star_{\mathbf{M}}\)-product based tools (such as tensor-PLS, tensor-CCA), and we encourage any form of collaboration, hoping to get good responses, feedback and help from the data-science community.

Target audience

We do not expect expertise in Machine Learning, or data science, in order to use this package. In fact, it is aimed at non-experts

That said, the library is not - by any means - meant to serve as a black magic tensor package for dummies. Just like with almost everything in machine-learning, using this library for ML related tasks require some general mathematical understanding of ML concepts. The implementation of dimensionality reduction methods (currently TCAM), is made consistent with scikit-learn library to the maximum possible extent, in order to enable smooth integration within the pythonic ML ecosystem. For this reason, the users are assumed to know the scikit-learn library. Scikit-learn package offers fantastic documentation, tutorials and examples that are more than enough in order to get started with machine learning in no time.

Note

We acknowledge that many potential users might find R more familiar. However, we urge them to take the time and try the alternative.

In addition, deep understanding of the mathematical theory underlying mprod based tensor algorithms is always a good idea. Bellow, you can find a short Brief Intro section about the idea behind tensor-tensor algebra via the \(\star_{\bf{M}}\) -product framework (For a thorough introduction, we refer the interested readers to 2)

The TCAM section contains tutorials for working with mprod.dimensionality_reduction.TCAM. For construction and showcase of TCAM refer to 1

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TCAM

• Minimal working example
  • Load files
  • Data normalization and mode-mapping
  • Transform
• Supervised learning
  • The case of matrix valued inputs
  • ML workflows
  • TCAM as dimensionality reduction step
  • Concrete example
  • Dataset
  • Making the ML workflow
    • Model evaluation

⚙ Background

• The M-product
• TSVDM
• Tensor ranks and truncations
• The effect of choosing different transforms

1(1,2)

Uria Mor, Yotam Cohen, Rafael Valdes-Mas, Denise Kviatcovsky, Eran Elinav, and Haim Avron. Dimensionality reduction of longitudinal ‘omics data using modern tensor factorization. 2021. arXiv:2111.14159.

2

Misha E. Kilmer, Lior Horesh, Haim Avron, and Elizabeth Newman. Tensor-tensor algebra for optimal representation and compression of multiway data. Proceedings of the National Academy of Sciences, 118(28):e2015851118, jul 2021. URL: https://www.pnas.org/content/118/28/e2015851118 https://www.pnas.org/content/118/28/e2015851118.abstract, doi:10.1073/PNAS.2015851118.