Solving NMF with smoothness and sparsity constraints using PALM
This work provides an incremental improvement for researchers and practitioners in fields like data compression and audio processing by enabling NMF with specific constraints.
The authors tackled the problem of non-negative matrix factorization (NMF) by adapting the PALM minimization scheme to incorporate smoothness and sparsity constraints, resulting in a method that can produce solutions with these desired properties.
Non-negative matrix factorization is a problem of dimensionality reduction and source separation of data that has been widely used in many fields since it was studied in depth in 1999 by Lee and Seung, including in compression of data, document clustering, processing of audio spectrograms and astronomy. In this work we have adapted a minimization scheme for convex functions with non-differentiable constraints called PALM to solve the NMF problem with solutions that can be smooth and/or sparse, two properties frequently desired.