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Results for “Discriminant Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Multivariate regression modelling for gender prediction using volatile organic compounds from hand odor profiles via HS-SPME-GC-MS

The efficacy of using human volatile organic compounds (VOCs) as a form of forensic evidence has been well demonstrated with canines for crime scene response, suspect identification, and location checking. Although the use of human scent evidence in the field is well established, the laboratory evaluation of human VOC profiles has been limited. This study used Headspace-Solid Phase Microextraction-Gas Chromatography-Mass Spectrometry (HS-SPME-GC-MS) to analyze human hand odor samples collected from 60 individuals (30 Females and 30 Males). The human volatiles collected from the palm surfaces of each subject were interpreted for classification and prediction of gender. The volatile organic compound (VOC) signatures from subjects’ hand odor profiles were evaluated with supervised dimensional reduction techniques: Partial Least Squares-Discriminant Analysis (PLS-DA), Orthogonal-Projections to Latent Structures Discriminant Analysis (OPLS-DA), and Linear Discriminant Analysis (LDA). The PLS-DA 2D model demonstrated clustering amongst male and female subjects. The addition of a third component to the PLS-DA model revealed clustering and minimal separation of male and female subjects in the 3D PLS-DA model. The OPLS-DA model displayed discrimination and clustering amongst gender groups with leave one out cross validation (LOOCV) and 95% confidence regions surrounding clustered groups without overlap. The LDA had a 96.67% accuracy rate for female and male subjects. The culminating knowledge establishes a working model for the prediction of donor class characteristics using human scent hand odor profiles.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Bolide Light-curve Analysis and Discrimination Explorer (BLADE)

SAND2025-09601O Bolide Light-curve Analysis and Discrimination Explorer (BLADE) is a robust, high-fidelity framework designed to analyze the light curves of bolides—objects detected from space. It automates the identification of fragmentation events and energy release modes, using advanced techniques like Savitzky-Golay filtering, prominence-based peak detection, and gradient analysis. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Silber, Elizabeth [Sandia National Lab. (SNL-CA), ↗
DOE OSTI2025

Linear Discriminant Analysis-Based Machine Learning and All-Atom Molecular Dynamics Simulations for Probing Electro-Osmotic Transport in Cationic-Polyelectrolyte-Brush-Grafted Nanochannels

Deciphering the correct mechanisms governing certain phenomena in polyelectrolyte (PE) brush grafted systems, revealed through atomistic simulations, is an extremely challenging problem. In a recent study, our all-atom molecular dynamics (MD) simulations revealed a non-linearly large electroosmotic (EOS) flow (in the presence of an applied electric field) in nanochannels grafted with PMETAC [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] brushes. Given the lack of any formal procedure that would have directed us to identify the correct factors responsible for such an occurrence, we needed to spend several months and devote significant analyses to unravel the involved mechanisms. In this paper, we propose a Linear Discriminant Analysis (LDA) based Machine Learning (ML) approach to address this gap. At first, we obtain data on certain basic features from the all-atom MD data. These basic features represent the number of atoms of certain species around one atom of another (or same) species. Here, we obtain such data on basic features for a reference case (case of an EOS flow in PMETAC-brush-grafted nanochannels with a smaller electric field) and a perturbed case (case of an EOS flow in PMETAC-brush-grafted nanochannels with a larger electric field) in bins in which the nanochannel half height has been divided into. These datasets are high-dimensional dataset, to which the LDA is applied. This leads to the projection of the data (between the reference and the perturbed states) in a highly separated form on a 1D line. From such LDA calculations, we are able to identify the relative importance of the different basic features in ensuring this separation of the data (between the reference and the perturbed states) on the 1D line. This relative importance of the different basic features is quantified as “importance scores” for the different features, which in turn tell us what to study and where to study. Such knowledge enables us to rapidly identify the key factors responsible for the non-linearly large EOS transport in PMETAC-brush-grafted nanochannels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1998

Effect of altered sensory conditions on multivariate descriptors of human postural sway

Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

NASA Discipline Neuroscience↗
DOE OSTI2018

Solvent effects on differentiation of mouse brain tissue using laser microdissection ‘cut and drop’ sampling with direct mass spectral analysis

Rationale: Laser microdissection-liquid vortex capture/electrospray ionization mass spectrometry (LMD-LVC/ESI-MS) has potential for on-line classification of tissue but an investigation into what analytical conditions provide best spectral differentiation has not been conducted. The effects of solvent, ionization polarity, and spectral acquisition parameters on differentiation of mouse brain tissue regions are described.Methods: Individual 40 × 40 μm microdissections from cortex, white, grey, granular, and nucleus regions of mouse brain tissue were analyzed using different capture/ESI solvents, in positive and negative ion mode ESI, using time-of-flight (TOF)-MS and sequential window acquisitions of all theoretical spectra (SWATH)-MS (a permutation of tandem-MS), and combinations thereof. Principal component analysis-linear discriminant analysis (PCA-LDA), applied to each mass spectral dataset, was used to determine the accuracy of differentiation of mouse brain tissue regions. Results: Mass spectral differences associated with capture/ESI solvent composition manifested as altered relative distributions of ions rather than the presence or absence of unique ions. In negative ion mode ESI, 80/20 (v/v) methanol/water yielded spectra with low signal/noise ratios relative to other solvents. PCA-LDA models acquired using 90/10 (v/v) methanol/chloroform differentiated tissue regions with 100% accuracy while data collected using methanol misclassified some samples. The combination of SWATH-MS and TOF-MS data improved differentiation accuracy.Conclusions: Combined TOF-MS and SWATH-MS data differentiated white, grey, granular, and nucleus mouse tissue regions with greater accuracy than when solely using TOF-MS data. Using 90/10 (v/v) methanol/chloroform, tissue regions were perfectly differentiated. Lastly, these results will guide future studies looking to utilize the potential of LMD-LVC/ESI-MS for tissue and disease differentiation.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

Hydroacoustic Assessment of Behavioral Responses by Fish Passing Near an Operating Tidal Turbine in the East River, New York

An important environmental issue facing the marine and hydrokinetic energy industry is whether fish that encounter underwater energy devices are likely to be struck and injured by moving components, primarily rotating turbine blades. The automated analysis of nearly 3 weeks of multibeam hydroacoustics data identified about 35,000 tracks of fish passing a tidal turbine in the East River, New York. These tracks included both individual fish and schools during periods with the turbine absent, the turbine present and operating, and the turbine present but not operating. The density of fish in the sampled area when the turbine was absent was roughly twice the density observed when the turbine was in place, particularly when the turbine was operating. This suggests that some avoidance occurred before fish were close enough to the turbine to be observed by the hydroacoustics system. Various measures of swimming behavior (direction, velocity, and linearity) were calculated for each track and evaluated for indication of behavioral responses to turbine presence and operation. Fish tracks were grouped based on tidal cycle, current velocity, and swimming direction and were evaluated with respect to turbine presence and operation and with respect to distance from the turbine. Nonparametric tests (Kolmogorov–Smirnov test) and multivariate analysis (canonical discriminant analysis) found significant differences among groups with respect to turbine presence and operation, suggesting that some fish responded to the turbine by adjusting swimming behavior, such as making small adjustments to swimming direction and velocity as they passed near the turbine. We found no evidence that fish were being struck by rotating blades, but there did appear to be large-scale avoidance initiated out of the range of the hydroacoustics detection system. Furthermore, more study is needed to determine whether such avoidance behavior has significant ramifications for normal fish movement patterns, bioenergetics, seasonal migrations, and predator exposure.

13 HYDRO ENERGY↗
DOE OSTI2018

Automated Optically Guided System for Chemical Analysis of Single Plant and Algae Cells Using Laser Microdissection/Liquid Vortex Capture/Mass Spectrometry

Current analytical methods are not capable of providing rapid, sensitive, and comprehensive chemical analysis of a wide range of cellular constitutes of single cells (e.g., lipids, metabolites, proteins, etc.) from dispersed cell suspensions and thin tissues. This capability is important for a number of critical applications, including discovery of cellular mechanisms for coping with chemical or environmental stress and cellular response to drug treatment, to name a few. Here we introduce an optically guided platform and methodology for rapid, automated recognition, sampling, and chemical analysis of surface confined individual cells utilizing a novel hybrid laser capture microdissection/liquid vortex capture/mass spectrometry system. The system enabled automated analysis of single cells by reliably detecting and sampling them either through laser ablation from a glass microscope slide or by cutting the entire cell out of a poly(ethylene naphthalate)-coated membrane substrate that the cellular sample is deposited on. Proof of principle experiments were performed using thin tissues of Allium cepa and cultured Euglena gracilis and Phacus cell suspensions as model systems for single cell analysis using the developed method. Reliable, hands-off laser ablation sampling coupled to liquid vortex capture/mass spectrometry analysis was conducted for hundreds of individual Allium cepa cells in connected tissue. In addition, more than 300 individual Euglena gracilis and Phacus cells were analyzed automatically and sampled using laser microdissection sampling with the same liquid vortex capture/mass spectrometry analysis system. Principal component analysis-linear discriminant analysis, applied to each mass spectral dataset, was used to determine the accuracy of differentiation of the different algae cell lines.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1996

Feature Selection for Classification of Polar Regions Using a Fuzzy Expert System

Labeling, feature selection, and the choice of classifier are critical elements for classification of scenes and for image understanding. This study examines several methods for feature selection in polar regions, including the list, of a fuzzy logic-based expert system for further refinement of a set of selected features. Six Advanced Very High Resolution Radiometer (AVHRR) Local Area Coverage (LAC) arctic scenes are classified into nine classes: water, snow / ice, ice cloud, land, thin stratus, stratus over water, cumulus over water, textured snow over water, and snow-covered mountains. Sixty-seven spectral and textural features are computed and analyzed by the feature selection algorithms. The divergence, histogram analysis, and discriminant analysis approaches are intercompared for their effectiveness in feature selection. The fuzzy expert system method is used not only to determine the effectiveness of each approach in classifying polar scenes, but also to further reduce the features into a more optimal set. For each selection method,features are ranked from best to worst, and the best half of the features are selected. Then, rules using these selected features are defined. The results of running the fuzzy expert system with these rules show that the divergence method produces the best set features, not only does it produce the highest classification accuracy, but also it has the lowest computation requirements. A reduction of the set of features produced by the divergence method using the fuzzy expert system results in an overall classification accuracy of over 95 %. However, this increase of accuracy has a high computation cost.

Penaloza, Mauel A.↗
NASA NTRSDate not supplied

Remote Sensing of Lineage Functional Types for Modeling and Monitoring Biodiversity

Hyperspectral remote sensing has the potential to continuously scale plant function and plant diversity information from landscape to global extents. Numerous studies have indicated that VSWIR (400-2500 nm) reflectance properties of vegetation capture evolutionarily conserved biochemical, structural, and other functional attributes of plant species. Spectral properties conserved in plants provide the opportunity to both 1) aggregate species into lineages with improved classification accuracy and 2) link those lineages directly to plant traits. Full realization of this goal will enable parameterization of Land Surface Models (LSMs) with remotely sensed information, e.g., canopy nitrogen, and better representations of biodiversity and functional diversity in biogeographic studies. In this study, we use hyperspectral AVIRIS data from the 2013 HyspIRI campaign over the Southern Sierra Nevada, California flight box to investigate the potential for incorporating evolutionary thinking into landcover classification. We link the airborne hyperspectral data with vegetation plot data from roughly 1372 surveys and a phylogeny representing 1361 species. We aggregate species into lineages ranging from species level groups down to similar number of Plant Functional Types as often used in LSMs. We assessed the ability of Random Forest and Partial Least Squares Discriminant Analysis to discriminate across these different phylogenetic scales and determine the optimal number of lineages to classify. Although there are some temporal and spatial differences in our training data, our best approaches achieved moderate classification accuracy (Kappa > 0.65). Given an optimal number of lineages, we explored approaches to improve classifications including machine learning and unmixing approaches. This work suggests that lineage-based methods may be a promising way to leverage the huge amounts of data that will come from high resolution and high return interval hyperspectral data planned for the Surface Biology and Geology mission with sparsely sampled existing ground-based ecological data.

Hyperspectral↗
DOE OSTI2021

Detection of the Metabolic Response to Drought Stress Using Hyperspectral Reflectance

Drought is the most important limitation on crop yield. Understanding and detecting drought stress in crops is vital for improving water use efficiency through effective breeding and management. Leaf reflectance spectroscopy offers a rapid, non-destructive alternative to traditional techniques for measuring plant traits involved in a drought response. We measured drought stress in six glasshouse-grown agronomic species using physiological, biochemical and spectral data. In contrast to physiological traits, leaf metabolite concentrations revealed drought stress before it was visible to the naked eye. We used full-spectrum leaf reflectance data to predict metabolite concentrations using partial least-squares regression, with validation R2 values of 0.49 to 0.87. We show for the first time that spectroscopy may be used for the quantitative estimation of proline and abscisic acid, demonstrating the first use of hyperspectral data to detect a phytohormone. We used linear discriminant analysis and partial least squares discriminant analysis to differentiate between droughted and watered plants based on measured traits (accuracy: 71%) and raw spectral data (66%). Finally, we validated our glasshouse-developed models in an independent field trial. We demonstrate that spectroscopy can detect drought stress via underlying biochemical changes, before visual differences occur, representing a powerful advance for measuring limitations on yield.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Applications of Fuzzy Clustering Techniques to Stratified by Tropopause MSU Temperature Retrievals

The fuzzy partitioned clustering method was applied to predict tropopause height only using microwave information with an eye towards using it on real data under cloudy conditions. In the second stage stratified by tropopause regression temperature retrievals included using only the three or four microwave channels for each 40 mb range. The first step in the experiment is the fuzzy partitioned clustering of the microwave brightness temperatures. This method is a combination of standard hard clustering and discriminant analysis. The fuzzy partitioned clustering uses all the generated probabilities of membership of each pattern vector in any of the given clusters. These probabilities are generated by discriminant analysis to locate the correct cluster. The ultimate goal of standard discriminant analysis is to provide the unique (correct) cluster to which the pattern vector belongs. It was only the maximum of all the generated probabilities. The method uses all the probabilities and weight the regressions generated within each cluster. These regression formulas predict the tropopause height from the microwave brightness temperatures. In the second step the microwave regression temperature retrievals are stratified by tropopause height every 40 mb. The control experiment is defined, the data are stratified by land/ocean, summer/winter, and latitude bands.

Munteanu, M. J.↗
DOE OSTI2020

Data-driven analysis of relight variability of jet fuels induced by turbulence

For safety purposes, reliable reignition of aircraft engines in the event of flame blow-out is a critical requirement. Typically, an external ignition source in the form of a spark is used to achieve a stable flame in the combustor. However, such forced turbulent ignition may not always successfully relight the combustor, mainly because the state of the combustor cannot be precisely determined. Uncertainty in the turbulent flow inside the combustor, inflow conditions, and spark discharge characteristics can lead to variability in sparking outcomes even for nominally identical operating conditions. Prior studies have shown that of all the uncertain parameters, turbulence is often dominant and can drastically alter ignition behavior. For instance, even when different fuels have similar ignition delay times, their ignition behavior in practical systems can be completely different. In practical operating conditions, it is challenging to understand why ignition fails and how much variation in outcomes can be expected. The focus of this work is to understand relight variability induced by turbulence for two different aircraft fuels, namely Jet-A and a variant named C1. A detailed, previously developed simulation approach is used to generate a large number of successful and failed ignition events. Using this data, the cause of misfire is evaluated based on a discriminant analysis that delineates the difference between turbulent initial conditions that lead to ignition or failure. From the discriminant analysis, a compressed sensing algorithm is then applied to help pinpoint the locations of relevant turbulent features. Findings from the discriminant analysis are confirmed with the time history of near kernel properties. Next, a clustering strategy is used to identify ignition and misfire modes. With this approach, it was determined that the cause of ignition failure is different for the two fuels. While it was found that Jet-A is influenced by fuel entrainment, C1 was found to be more sensitive to small scale turbulence features. Finally, a larger variability is found in the ignition modes of C1, which can be subject to extreme events induced by kernel breakdown.

42 ENGINEERING↗
NASA NTRS1974

Distinguishing between CAT and non-CAT areas by use of discriminant function analysis

The investigation considered is concerned with a method in which a statistical approach is employed to determine algebraic functions involving selected synoptic-scale parameters which would indicate areas and altitudes of CAT in the stratosphere over the western U.S. The statistical approach selected is based on discriminant function analysis. The functions are determined from combinations of synoptic-scale parameters and stratospheric turbulence data. It was found in the investigation that there is a relationship between selected combinations of synoptic-scale parameters of the upper troposphere and lower stratosphere and stratospheric clear-air turbulence.

Clark, T. L.↗
DOE OSTI2021

Structural Polymorphism of Chitin and Chitosan in Fungal Cell Walls From Solid-State NMR and Principal Component Analysis

Chitin is a major carbohydrate component of the fungal cell wall and a promising target for novel antifungal agents. However, it is technically challenging to characterize the structure of this polymer in native cell walls. Here, we recorded and compared 13 C chemical shifts of chitin using isotopically enriched cells of six Aspergillus, Rhizopus, and Candida strains, with data interpretation assisted by principal component analysis (PCA) and linear discriminant analysis (LDA) methods. The structure of chitin is found to be intrinsically heterogeneous, with peak multiplicity detected in each sample and distinct fingerprints observed across fungal species. Fungal chitin exhibits partial similarity to the model structures of α- and γ-allomorphs; therefore, chitin structure is not significantly affected by interactions with other cell wall components. Addition of antifungal drugs and salts did not significantly perturb the chemical shifts, revealing the structural resistance of chitin to external stress. In addition, the structure of the deacetylated form, chitosan, was found to resemble a relaxed two-fold helix conformation. This study provides high-resolution information on the structure of chitin and chitosan in their cellular contexts. The method is applicable to the analysis of other complex carbohydrates and polymer composites.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1993

Multivariate statistical analysis: Principles and applications to coorbital streams of meteorite falls

Multivariate statistical analysis techniques (linear discriminant analysis and logistic regression) can provide powerful discrimination tools which are generally unfamiliar to the planetary science community. Fall parameters were used to identify a group of 17 H chondrites (Cluster 1) that were part of a coorbital stream which intersected Earth's orbit in May, from 1855 - 1895, and can be distinguished from all other H chondrite falls. Using multivariate statistical techniques, it was demonstrated that a totally different criterion, labile trace element contents - hence thermal histories - or 13 Cluster 1 meteorites are distinguishable from those of 45 non-Cluster 1 H chondrites. Here, we focus upon the principles of multivariate statistical techniques and illustrate their application using non-meteoritic and meteoritic examples.

Wolf, S. F.↗
DOE OSTI2016

Mapping Cheatgrass Across the Range of the Greater Sage-Grouse: Linking Biophysical, Climate and Remote Sensing Data to Predict Cheatgrass Occurrence

Increasing spread of invasive annual grasses, such as Bromus tectorum (cheatgrass), can contribute to increased fire frequency and hinder the reestablishment of native sagebrush, forbs, and grasses in subsequent years. Knowledge of the current distribution of cheatgrass on the landscape is a key component in planning and executing strategies to protect sagebrush ecosystems and sensitive wildlife species such as the Greater sage-grouse (Centrocercus urophasianus). Pacific Northwest National Laboratory (PNNL) worked with US Fish and Wildlife Service (FWS) to assemble and derive information to map cheatgrass occurrence across the historic range of sage-grouse. The information and map products described in this report can help land managers prioritize conservation efforts at the species’ range scale. We constructed an ecological model based on a suite of climatic and biophysical variables and satellite measures of peak NDVI (normalized difference vegetation index) – an index of vegetation greenness – to predict cheatgrass occurrence across the historic range of sage-grouse in the United States. More than 24,000 field measurements of cheatgrass cover across the study area were acquired from various agencies and research groups and reviewed for use in the modeling efforts. A subset of 6650 field measurement points were identified and verified for use in statistical analyses. For each measurement location we derived a suite of 50 biophysical and NDVI variables correlated with cheatgrass occurrence. Pairwise correlation of variables was examined to remove highly-correlated variables from the model. A total of 13 variables were retained for use in forward-stepping discriminant analysis and modeling. Discriminant scores were used to determine probability of cheatgrass occurrence, which was broken into two relative cover classes: 0% to 2% cover and > 2% cheatgrass cover. This report describes the data and methods used to develop the model and the cheatgrass occurrence map. We provide a brief discussion of the accuracy of classification, and describe the appropriate scale of use for map results. The range-wide map of occurrence will be made available online for FWS and partner agencies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Comparing gas composition from fast pyrolysis of live foliage measured in bench-scale and fire-scale experiments

Background: Fire models have used pyrolysis data from oxidising and non-oxidising environments for flaming combustion. In wildland fires pyrolysis, flaming and smouldering combustion typically occur in an oxidising environment (the atmosphere). Aims: Using compositional data analysis methods, determine if the composition of pyrolysis gases measured in non-oxidising and ambient (oxidising) atmospheric conditions were similar. Methods: Permanent gases and tars were measured in a fuel-rich (non-oxidising) environment in a flat flame burner (FFB). Permanent and light hydrocarbon gases were measured for the same fuels heated by a fire flame in ambient atmospheric conditions (oxidising environment). Log-ratio balances of the measured gases common to both environments (CO, CO 2 , CH 4 , H 2 , C 6 H 6 O (phenol), and other gases) were examined by principal components analysis (PCA), canonical discriminant analysis (CDA) and permutational multivariate analysis of variance (PERMANOVA). Key results: Mean composition changed between the non-oxidising and ambient atmosphere samples. PCA showed that flat flame burner (FFB) samples were tightly clustered and distinct from the ambient atmosphere samples. CDA found that the difference between environments was defined by the CO-CO 2 log-ratio balance. PERMANOVA and pairwise comparisons found FFB samples differed from the ambient atmosphere samples which did not differ from each other. Conclusion: Relative composition of these pyrolysis gases differed between the oxidising and non-oxidising environments. This comparison was one of the first comparisons made between bench-scale and field scale pyrolysis measurements using compositional data analysis. Implications: These results indicate the need for more fundamental research on the early time-dependent pyrolysis of vegetation in the presence of oxygen.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1992

Extracting galactic structure parameters from multivariated density estimation

Multivariate statistical analysis, including includes cluster analysis (unsupervised classification), discriminant analysis (supervised classification) and principle component analysis (dimensionlity reduction method), and nonparameter density estimation have been successfully used to search for meaningful associations in the 5-dimensional space of observables between observed points and the sets of simulated points generated from a synthetic approach of galaxy modelling. These methodologies can be applied as the new tools to obtain information about hidden structure otherwise unrecognizable, and place important constraints on the space distribution of various stellar populations in the Milky Way. In this paper, we concentrate on illustrating how to use nonparameter density estimation to substitute for the true densities in both of the simulating sample and real sample in the five-dimensional space. In order to fit model predicted densities to reality, we derive a set of equations which include n lines (where n is the total number of observed points) and m (where m: the numbers of predefined groups) unknown parameters. A least-square estimation will allow us to determine the density law of different groups and components in the Galaxy. The output from our software, which can be used in many research fields, will also give out the systematic error between the model and the observation by a Bayes rule.

Chen, B.↗