PARAFAC2: A Core Perspective
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Statistical Analysis and Data Mining
A new method is introduced for combining information from multiple sources to support one-class classification. The contributing sources may represent measurements taken by different sensors of the same physical entity, repeated measurements by a single sensor, or numerous features computed from a single measured image or signal. The approach utilizes the theory of statistical hypothesis testing, and applies Fisher's technique for combining p-values, modified to handle nonindependent sources. Classifier outputs take the form of fused p-values, which may be used to gauge the consistency of unknown entities with one or more class hypotheses. The approach enables rigorous assessment of classification uncertainties, and allows for traceability of classifier decisions back to the constituent sources, both of which are important for high-consequence decision support. Application of the technique is illustrated in two challenge problems, one for skin segmentation and the other for terrain labeling. The method is seen to be particularly effective for relatively small training samples.
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Powder Diffraction
X-ray fluorescence (XRF) has been employed as one of several orthogonal means of screening materials to prevent counterfeit and adulterated products from entering the product stream. We document the use of principal component analysis (PCA) of XRF data on compositionally similar and dissimilar stainless steels for the purpose of testing the feasibility of employing XRF spectra to parse and bin these alloys as the same or significantly different alloy materials. The results indicate that XRF spectra can separate and assign alloys via PCA, but that important corrections for detector drift and scaling must be performed in order to achieve valid results.
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The purpose of this project is to prove (or disprove) that a reasonable number of simple tests can be used to provide a unique data signature for materials, changes in which could serve as a harbinger of material deviation, prompting further evaluations. The routine tests are mutually orthogonal to any currently required materials specification tests.
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Proceedings of SPIE - The International Society for Optical Engineering
In this paper, we describe the use of various methods of one-dimensional spectral compression by variable selection as well as principal component analysis (PCA) for compressing multi-dimensional sets of spectral data. We have examined methods of variable selection such as wavelength spacing, spectral derivatives, and spectral integration error. After variable selection, reduced transmission spectra must be decompressed for use. Here we examine various methods of interpolation, e.g., linear, cubic spline and piecewise cubic Hermite interpolating polynomial (PCHIP) to recover the spectra prior to estimating at-sensor radiance. Finally, we compressed multi-dimensional sets of spectral transmittance data from moderate resolution atmospheric transmission (MODTRAN) data using PCA. PCA seeks to find a set of basis spectra (vectors) that model the variance of a data matrix in a linear additive sense. Although MODTRAN data are intricate and are used in nonlinear modeling, their base spectra can be reasonably modeled using PCA yielding excellent results in terms of spectral reconstruction and estimation of at-sensor radiance. The major finding of this work is that PCA can be implemented to compress MODTRAN data with great effect, reducing file size, access time and computational burden while producing high-quality transmission spectra for a given set of input conditions.
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Tensor (multiway array) factorization and decomposition offers unique advantages for activity characterization in spatio-temporal datasets because these methods are compatible with sparse matrices and maintain multiway structure that is otherwise lost in collapsing for regular matrix factorization. This report describes our research as part of the PANTHER LDRD Grand Challenge to develop a foundational basis of mathematical techniques and visualizations that enable unsophisticated users (e.g. users who are not steeped in the mathematical details of matrix algebra and mulitway computations) to discover hidden patterns in large spatiotemporal data sets.
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Proposed for publication in Nano Letter .
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