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.
Monitoring changes within the land surface and open water bodies is critical for natural resource management, conservation, and environmental policy. While the use of satellite imagery for these purposes is common, fine-scale change detection can be a technical challenge. Difficulties arise from variable atmospheric conditions and the problem of assigning pixels to individual objects. We examined the degree to which two machine learning approaches can better characterize change detection in the context of a current conservation challenge, artisanal small-scale gold mining (ASGM). We obtained Sentinel-2 imagery and consulted with domain experts to construct an open-source labeled land-cover change dataset. The focus of this dataset is the Madre de Dios (MDD) region in Peru, a hotspot of ASGM activity. We also generated datasets of active ASGM areas in other countries (Venezuela, Indonesia, and Myanmar) for out-of-sample testing. With these labeled data, we utilized a supervised (E-ReCNN) and semi-supervised (SVM-STV) approach to study binary and multi-class change within mining ponds in the MDD region. Additionally, we tested how the inclusion of multiple channels, histogram matching, and La*b* color metrics improved the performance of the models and reduced the influence of atmospheric effects. Empirical results show that the supervised E-ReCNN method on 6-Channel histogram-matched images generated the most accurate detection of change not only in the focal region (Kappa: 0.92 (± 0.04), Jaccard: 0.88 (± 0.07), F1: 0.88 (± 0.05)) but also in the out-of-sample prediction regions (Kappa: 0.90 (± 0.03), Jaccard: 0.84 (± 0.04), and F1: 0.77 (± 0.04)). While semi-supervised methods did not perform as accurately on 6- or 10-channel imagery, histogram matching and the inclusion of La*b* metrics generated accurate results with low memory and resource costs. These results show that E-ReCNN is capable of accurately detecting specific and object-oriented environmental changes related to ASGM. E-ReCNN is scalable to areas outside the focal area and is a method of change detection that can be extended to other forms of land-use modification.
The insertion of a suitably designed phase plate in the pupil of an imaging system makes it possible to encode the depth dimension of an extended three-dimensional scene by means of an approximately shift-invariant PSF. The so-encoded image can then be deblurred digitally by standard image recovery algorithms to recoup the depth dependent detail of the original scene. A similar strategy can be adopted to compensate for certain monochromatic aberrations of the system. Here we consider two approaches to optimizing the design of the phase plate that are somewhat complementary -one based on Fisher information that attempts to reduce the sensitivity of the phase encoded image to misfocus and the other based on a minimax formulation of the sum of singular values of the system blurring matrix that attempts to maximize the resolution in the final image. Comparisons of these two optimization approaches are discussed. Our preliminary demonstration of the use of such pupil-phase engineering to successfully control system aberrations, particularly spherical aberration, is also presented.
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