Automatic factorization of biological signals by using Boltzmann non-negative matrix factorization

We propose an automatic factorization method for time series signals that follow Boltzmann distribution. Generally time series signals are fitted by using a model function for each sample. To analyze many samples automatically, we have to apply a factorization method. When the energy dynamics are measured in thermal equilibrium, the energy distribution can be modeled by Boltzmann distribution law. The measured signals are factorized as the non-negative sum of the probability density function of Boltzmann distribution. If these signals are composed from several components, then they can be decomposed by using the idea of non-negative matrix factorization (NMF). In this paper, we modify the original NMF to introduce the probability density function modeled by Boltzmann distribution. Also the number of components in samples is estimated by using model selection method. We applied our proposed method to actual data that was measured by fluorescence correlation spectroscopy (FCS). The experimental results show that our method can automatically factorize the signals into the correct components.