Towards unique solutions of non-negative matrix factorization problems by a determinant criterion

Authors:
R. Schachtner;G. Pöppel;E. W. Lang
Affiliations:
Infineon Technologies AG, 93049 Regensburg, Germany and Institute of Biophysics, University of Regensburg, 93040 Regensburg, Germany;Infineon Technologies AG, 93049 Regensburg, Germany;Institute of Biophysics, University of Regensburg, 93040 Regensburg, Germany
Venue:
Digital Signal Processing
Year:
2011

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Abstract

We propose a determinant criterion to constrain the solutions of non-negative matrix factorization problems and achieve unique and optimal solutions in a general setting, provided an exact solution exists. We demonstrate how optimal solutions are obtained by a heuristic named detNMF in an illustrative example and discuss the difference to sparsity constraints. Furthermore, an intuitive explanation of multi-layer techniques is discussed also.