Many practical applications in the fields of signal processing often preprocess input data using component analysis. Component analysis can reduce dimensionality, extract features, or discover underlying structures of the data.
Principal component analysis (PCA) and independent component analysis (ICA) are frequently employed for various tasks, such as feature discovery or object extraction. The statistical properties of PCA and ICA make them indispensable tools for machine learning applications.
Non-negative matrix factorization (NMF) can also be used for component analysis, Lee D. D., and Seung H. S., “Learning the parts of objects by non-negative matrix factorization,” Nature, Vol. 401, No. 6755, 21 Oct. 1999, pp. 788-791. Non-negativity is a valuable property for working only with positive data. Because a large majority of acoustic, image and text data operations deal with positive only data, NMF presents an appropriate alternative to PCA and ICA. A particular reason for the success of NMF is that using non-negative components, in combination with non-negative weights, often translates to a meaningful solution.
In contrast, methods that do not use non-negativity yield a set of bases that contain negative elements. Then, cross-cancellation between the non-negative elements must be employed to approximate the input. Components with negative elements are hard to interpret in a positive only data framework and are often used for their statistical properties and not for the insight they provide of the underlying data structure. In contrast, NMF provides meaningful components for variety of data types such as images, and acoustic magnitude spectra.
However, the downside of NMF is that it is defined in a purely non-statistical framework, which prohibits NMF to be applied to probabilistic applications.