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.
A geometric approach to archetypal analysis and non-negative matrix factorization
Anil Damle, Yuekai Sun
Archetypal analysis for machine learning
Morten Morup, Lars Kai Hansen
Fast and Robust Archetypal Analysis for Representation Learning
Yuansi Chen, Julien Mairal, Zaid Harchaoui
Non-negative Matrix Factorization via Archetypal Analysis
Hamid Javadi, Andrea Montanari
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