Exact multiplicative updates for convolutional $β$-NMF in 2D
This work addresses an incremental improvement in nonnegative matrix factorization methods for signal processing or machine learning applications.
The authors tackled the problem of extending convolutional β-NMF to two dimensions by deriving exact multiplicative updates for its factors, which generalize and correct previous work, and demonstrated through simulation that these updates lead to monotonically decreasing β-divergence with consistent convergence curves across common β values.
In this paper, we extend the $β$-CNMF to two dimensions and derive exact multiplicative updates for its factors. The new updates generalize and correct the nonnegative matrix factor deconvolution previously proposed by Schmidt and Mørup. We show by simulation that the updates lead to a monotonically decreasing $β$-divergence in terms of the mean and the standard deviation and that the corresponding convergence curves are consistent across the most common values for $β$.