Journal of Pattern Recognition Research

A supervised learning algorithm for the separation of seismic sources in a single channel is presented. The proposed algorithm employs non-negative matrix factorization (NMF) technique in the feature space, called Kernel NMF (KNMF). The algorithm is based on factorizing the magnitude spectrogram of an input signal into a sum of components, each of which has a fixed magnitude spectrum and a time-varying gain. The algorithm presented in this paper is used to separate human footstep signatures from horse footstep signatures. KNMF extracts discriminative spectral features from the spectrogram, a time-frequency representation of seismic data. The main benefit of the proposed technique is its ability to decompose a complex signal automatically into objects that have a meaningful interpretation. In this paper, the original NMF1 algorithm is extended to KNMF. The advantages of KNMF over NMF are: 1) it could extract more useful features hidden in the original data through some kernel-induced nonlinear mappings, 2) it can deal with data where only relationships (similarities or dissimilarities) between objects are known. KNMF is developed and implemented on seismic data of human and horse footsteps. The performance of this method is very promising as demonstrated by the experimental results.