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Open Access Methodology article

LS-NMF: A modified non-negative matrix factorization algorithm utilizing uncertainty estimates

Guoli Wang, Andrew V Kossenkov and Michael F Ochs*

Author Affiliations

Division of Population Science, Fox Chase Cancer Center, Philadelphia, PA, USA

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BMC Bioinformatics 2006, 7:175  doi:10.1186/1471-2105-7-175

Published: 28 March 2006



Non-negative matrix factorisation (NMF), a machine learning algorithm, has been applied to the analysis of microarray data. A key feature of NMF is the ability to identify patterns that together explain the data as a linear combination of expression signatures. Microarray data generally includes individual estimates of uncertainty for each gene in each condition, however NMF does not exploit this information. Previous work has shown that such uncertainties can be extremely valuable for pattern recognition.


We have created a new algorithm, least squares non-negative matrix factorization, LS-NMF, which integrates uncertainty measurements of gene expression data into NMF updating rules. While the LS-NMF algorithm maintains the advantages of original NMF algorithm, such as easy implementation and a guaranteed locally optimal solution, the performance in terms of linking functionally related genes has been improved. LS-NMF exceeds NMF significantly in terms of identifying functionally related genes as determined from annotations in the MIPS database.


Uncertainty measurements on gene expression data provide valuable information for data analysis, and use of this information in the LS-NMF algorithm significantly improves the power of the NMF technique.