Bayesian semi non-negative matrix factorisation

Non-negative Matrix Factorisation (NMF) has become a standard method for source identification when data, sources and mixing coefficients are constrained to be positive-valued. The method has recently been extended to allow for negative-valued data and sources in the form of Semi-and Convex-NMF. In this paper, we re-elaborate Semi-NMF within a full Bayesian framework. This provides solid foundations for parameter estimation and, importantly, a principled method to address the problem of choosing the most adequate number of sources to describe the observed data. The proposed Bayesian Semi-NMF is preliminarily evaluated here in a real neuro-oncology problem.Peer ReviewedPostprint (published version

A MAP approach for convex non-negative matrix factorization in the diagnosis of brain tumors

Convex non-negative matrix factorization is a blind signal separation technique that has previously demonstrated to be well-suited for the task of human brain tumor diagnosis from magnetic resonance spectroscopy data. This is due to its ability to retrieve interpretable sources of mixed sign that highly correlate with tissue type prototypes. The current study provides a Bayesian formulation for such problem and derives a maximum a posteriori estimate based on a gradient descent algorithm specifically designed to deal with matrices with different sign restrictions. Its applicability to neuro-oncology diagnosis was experimentally assessed and the results were found to be comparable to those achieved by state of the art methods in tumor type discrimination and consistently better in source extraction.Peer ReviewedPostprint (published version

A MAP approach for convex non-negative matrix factorization in the diagnosis of brain tumors

Convex non-negative matrix factorization is a blind signal separation technique that has previously demonstrated to be well-suited for the task of human brain tumor diagnosis from magnetic resonance spectroscopy data. This is due to its ability to retrieve interpretable sources of mixed sign that highly correlate with tissue type prototypes. The current study provides a Bayesian formulation for such problem and derives a maximum a posteriori estimate based on a gradient descent algorithm specifically designed to deal with matrices with different sign restrictions. Its applicability to neuro-oncology diagnosis was experimentally assessed and the results were found to be comparable to those achieved by state of the art methods in tumor type discrimination and consistently better in source extraction.Peer Reviewe