Non-negative matrix factorization (NMF) is a well-known unsupervised learningmethod that has been successfully used for blind source separation ofnon-negative additive signals.NMF method requires the number of the originalsources to be known a priori. Recently, we reported a method, we called NMFk,which by coupling the original NMF multiplicative algorithm with a customsemi-supervised clustering allows us to estimate the number of the sourcesbased on the robustness of the reconstructed solutions. Here, an extension ofNMFk is developed, called ShiftNMFk, which by combining NMFk with previouslyformulated ShiftNMF algorithm, Akaike Information Criterion (AIC), and a customprocedure for estimating the source locations is capable of identifying: (a)the number of the unknown sources, (b) the eventual delays in the signalpropagation, (c) the locations of the sources, and (d) the speed of propagationof each of the signals in the medium. Our new method is a natural extension ofNMFk that can be used for sources identification based only on observationaldata. We demonstrate how our novel method identifies the components ofsynthetic data sets, discuss its limitations, and present a Julia languageimplementation of ShiftNMFk algorithm.
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