Madsen, Kristoffer Hougaard3; Hansen, Lars Kai4; Mørup, Morten5
1 Cognitive Systems, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 University of Copenhagen4 Copenhagen Center for Health Technology, Center, Technical University of Denmark5 Department of Applied Mathematics and Computer Science, Technical University of Denmark
We propose the Time Frequency Gradient Method (TFGM) which forms a framework for optimization of models that are constrained in the time domain while having efficient representations in the frequency domain. Since the constraints in the time domain in general are not transparent in a frequency representation we demonstrate how the class of objective functions that are separable in either time or frequency instances allow the gradient in the time or frequency domain to be converted to the opposing domain. We further demonstrate the usefulness of this framework for three different models; Shifted Non-negative Matrix Factorization, Convolutive Sparse Coding as well as Smooth and Sparse Matrix Factorization. Matlab implementation of the proposed algorithms are available for download at www.erpwavelab.org.