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In this paper we discuss the development and use of low-rank approximate nonnegative matrix factorization (NMF) algorithms for feature extraction and identification in the fields of text mining and spectral data analysis. The evolution and convergence properties of hybrid methods based on both sparsity and smoothness constraints for the resulting nonnegative matrix factors are discussed. The interpretability of NMF outputs in specific contexts are provided along with opportunities for future work in the modification of NMF algorithms for large-scale and time-varying datasets.

Data analysis is pervasive throughout business, engineering and science. Very often the data to be analyzed is nonnegative, and it is often preferable to take this constraint into account in the analysis process. Here we are concerned with the application of analyzing data obtained using astronomical spectrometers, which provide spectral data which is inherently nonnegative. The identification and classification of space objects that cannot be imaged in the normal way with telescopes is an important but difficult problem for tracking thousands of objects, including satellites, rocket bodies, debris, and asteroids, in orbit around the earth. In this paper we develop an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification purposes. Promising numerical results are presented using laboratory and simulated datasets.

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