Continuous non-negative matrix factorization for time-dependent data

In many signal processing applications such as image analysis or spectral decomposition, non-negativity constrains are necessary to provide a physical reasonable interpretation. This constraint is exploited by non-negative matrix factorization (NMF) methods. The goal of NMF is to find low rank matrices A ≥ 0 and B ≥ 0 such that the positive data matrix X can be approximated by AB ≈ X. Most algorithms for this type of factorization are discrete-step iterative optimization procedures based on gradient descent or Quasi-Newton methods. Here we propose a continuous-time version of NMF based on dynamical systems with positive solutions, which allows time-dependent cost functions, e.g. due to time-dependent data.