A cute hack in the world of sparse matrix factorisation, where the goal is to decode an element-wise non-negative matrix into a product of two smaller matrices, which looks a lot like sparse coding if you squint at it.

David Austin gives a simple introduction, to the classic Non-negative matrix factorization for the American Mathematical Society.

This method is famous for decomposing things into parts in a sparse way using \(l_2\) loss. It can be made even sparser by exploring other losses. π

## Tools

NMF (R) π

Matlab: Chih-Jen Linβs nmf.m - βThis tool solves NMF by alternative non-negative least squares using projected gradients. It converges faster than the popular multiplicative update approach. β

In this repository, we offer both MPI and OPENMP implementation for MU, HALS and ANLS/BPP based NMF algorithms. This can run off the shelf as well easy to integrate in other source code. These are very highly tuned NMF algorithms to work on super computers. We have tested this software in NERSC as well OLCF cluster. The openmp implementation is tested on many different Linux variants with intel processors. The library works well for both sparse and dense matrix. (Fairbanks et al. 2015; Kannan, Ballard, and Park 2016; Kannan 2016)

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