Heteroskedastic Matrix Factorization is great but many problems are bound to only non-negative weight values (e.g., astronomy light curves). This module provides a straightforward implementation of weighted non-negative matrix factorization, or weighted NMF. Weighted NMF is a matrix factorization method similar to principal components analysis (PCA) except that it enforces a non-negativity constraint on the produced basis vectors (rather than orthogonality) and it is naturally suited to handle non-homogenous uncertainties and missing data. Our implementation provies a multiplicative weights iterative update technique which minimizes a Frobenius norm objective function.
Given data X and weights S of shape (n_samples, n_features),
m = nmf_factorization(X, S, options...)
Returns a model object m from which you can inspect the vector factors, coefficients, reconstructed model, and original inputs, e.g.,
pylab.plot(m.vectors[0])
pylab.plot(m.model[0])
pylab.plot(m.data[0])
Note that missing data is simply the limit of weight=0.
For ease of understanding the implementation, an unrolled, non-vectorized version of weighted NMF is also implemented.
Ruhi Doshi (@rdoshi99), Spring 2022
To install this package, you can run the following commands in your terminal.
First, clone into this repository.
git clone https://github.com/rdoshi99/weighted_nmf.git
And move inside the current directory.
cd weighted_nmf
Then run the setup.py file.
python setup.py install
That completes the installation process for this package and its dependencies.
Only requires numpy (as of version v1.0)
The work is based on this paper by Tsalmantza & Hogg, 2012 (1), which outlines the underlying mathematical basis. It is available here: https://arxiv.org/pdf/1201.3370.pdf. Additionally, the algorithm specified by Blanton & Roweis (2) provides clearer explicit update rules for each iteration (available at https://arxiv.org/pdf/astro-ph/0606170.pdf).
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Tsalmantza, P. and Hogg, D., 2012. A DATA-DRIVEN MODEL FOR SPECTRA: FINDING DOUBLE REDSHIFTS IN THE SLOAN DIGITAL SKY SURVEY. The Astrophysical Journal, [online] 753(2), p.122. Available at: https://arxiv.org/pdf/1201.3370.pdf.
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M. Blanton and S. Roweis., (2007). K-corrections and filter transformations in the ultraviolet, optical, and near infrared. The Astronomical Journal 133, [online]734-754(2). Available at https://arxiv.org/abs/astro-ph/0606170.
Thank you to Stephen Bailey (@sbailey) for the significant guidance and support in improving the original algorithms and iterating throughout the research process.