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Non-negative matrix factorization via archetypal analysis

Non-negative matrix factorization via archetypal analysis

An approach to non-negative matrix factorization that does not require data to be separable and provides a generally unique decomposition.

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Jude Gomila
Jude Gomila approved a suggestion from Golden's AI on 19 Mar 2019 6:25 pm
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Unlike the original archetypal analysis method developed by Cutler and Breiman, NMF via archetypal analysis does not require the data in a given data setdata set to be separable. The method aims to optimize the trade-off between two objectives:

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Daniel Frumkin"Wrote article"
Daniel Frumkin edited on 12 Mar 2019 1:48 pm
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Non-negative matrix factorization via archetypal analysis is named after two well-known techniques of statistics and unsupervised learning, non-negative matrix factorization (NMF) and archetypal analysis (AA).



Unlike the original archetypal analysis method developed by Cutler and Breiman, NMF via archetypal analysis does not require the data in a given data set to be separable. The method aims to optimize the trade-off between two objectives:

  • Minimizing the distance of the data points from the convex envelope of archetypes (which can be interpreted as an empirical risk); and
  • Minimizing the distance of the the archetypes from the convex envelope of data (which can be interpreted as a data-dependent regularization).



NMF via archetypal analysis introduces a 'uniqueness condition' on the data which is necessary for exactly recovering the archetypes from noiseless data. The approach requires solving a non-convex optimization problem, but early experiments showed that the standard optimization methods succeeded in finding good solutions.

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Edits on 10 Mar 2019
Daniel Frumkin
Daniel Frumkin edited on 10 Mar 2019 12:59 pm
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Non-negative matrix factorization via archetypal analysis

An approach to non-negative matrix factorizationnon-negative matrix factorization that does not require data to be separable and provides a generally unique decomposition.

Further reading

Title
Author
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Type

A geometric approach to archetypal analysis and non-negative matrix factorization

Anil Damle, Yuekai Sun

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Fast and Robust Archetypal Analysis for Representation Learning

Yuansi Chen, Julien Mairal, Zaid Harchaoui

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Edits on 9 Mar 2019
Daniel Frumkin"Created page"
Daniel Frumkin edited on 9 Mar 2019 8:45 pm
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Non-negative matrix factorization via archetypal analysis

An approach to non-negative matrix factorization that does not require data to be separable and provides a generally unique decomposition.

Further reading

Title
Author
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Type

Archetypal analysis for machine learning

Morten Morup, Lars Kai Hansen

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Non-negative Matrix Factorization via Archetypal Analysis

Hamid Javadi, Andrea Montanari

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Daniel Frumkin"Initial topic creation"
Daniel Frumkin created this topic on 9 Mar 2019 8:37 pm
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 Non-negative matrix factorization via archetypal analysis

An approach to non-negative matrix factorization that does not require data to be separable and provides a generally unique decomposition.

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