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Nonnegative matrix factorization for spectral data analysis. (English) Zbl 1096.65033

Summary: 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.

65F30Other matrix algorithms
15A23Factorization of matrices
85A35Statistical astronomy
62-07Data analysis (statistics)
65C60Computational problems in statistics
62G35Nonparametric robustness