Non-negative factorization of non-negative matrices

John Gruninger

doi:10.1117/12.738381

24 October 2007 Non-negative factorization of non-negative matrices

John Gruninger

Proceedings Volume 6748, Image and Signal Processing for Remote Sensing XIII; 67480H (2007) https://doi.org/10.1117/12.738381
Event: SPIE Remote Sensing, 2007, Florence, Italy

Abstract

A new non-negative factorization method has been developed. The method is based on the concept of non-negative rank (NNR). Bounds for the NNR of certain non-negative matrices are determined relative to the rank of the matrix, with the lower bound being equal to the rank. The method requires that the data matrix be non-negative and have a large first singular value. Unlike other non-negative factorization methods, the approach does not assume or require that the factors be linearly independent and no assumption of statistical independence is required. The rank of the matrix provides the number of linearly independent components present in the data while the non-negative rank provides the number of non-negative independent components present in the data. The method is described and illustrated in application to hyperspectral data sets.

Citation Download Citation

John Gruninger "Non-negative factorization of non-negative matrices", Proc. SPIE 6748, Image and Signal Processing for Remote Sensing XIII, 67480H (24 October 2007); https://doi.org/10.1117/12.738381

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