Explaining Neural Network Predictions for Functional Data Using Principal Component Analysis and Feature Importance.
Abstract not provided.
Goode, Katherine Jean↗
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Explaining Neural Network Predictions for Functional Data Using Principal Component Analysis and Feature Importance.
Abstract not provided.
Goode, Katherine Jean↗
Seeking regularity from irregularity: unveiling the synthesis–nanomorphology relationships of heterogeneous nanomaterials using unsupervised machine learning
Nanoscale morphology of functional materials determines their chemical and physical properties. However, despite increasing use of transmission electron microscopy (TEM) to directly image nanomorphology, it remains challenging to quantify the information embedded in TEM data sets, and to use nanomorphology to link synthesis and processing conditions to properties. We develop an automated, descriptor-free analysis workflow for TEM data that utilizes convolutional neural networks and unsupervised learning to quantify and classify nanomorphology, and thereby reveal synthesis–nanomorphology relationships in three different systems. While TEM records nanomorphology readily in two-dimensional (2D) images or three-dimensional (3D) tomograms, we advance the analysis of these images by identifying and applying a universal shape fingerprint function to characterize nanomorphology. After dimensionality reduction through principal component analysis, this function then serves as the input for morphology grouping through unsupervised learning. We demonstrate the wide applicability of our workflow to both 2D and 3D TEM data sets, and to both inorganic and organic nanomaterials, including tetrahedral gold nanoparticles mixed with irregularly shaped impurities, hybrid polymer-patched gold nanoprisms, and polyamide membranes with irregular and heterogeneous 3D crumple structures. In each of these systems, unsupervised nanomorphology grouping identifies both the diversity and the similarity of the nanomaterial across different synthesis conditions, revealing how synthetic parameters guide nanomorphology development. Our work opens possibilities for enhancing synthesis of nanomaterials through artificial intelligence and for understanding and controlling complex nanomorphology, both for 2D systems and in the far less explored case of 3D structures, such as those with embedded voids or hidden interfaces.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Augmenting machine learning of Grad–Shafranov equilibrium reconstruction with Green's functions
This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using principal component analysis of plasma toroidal current densities (J t ) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for the poloidal flux (ψ) and diagnostics generated from the toroidal current (J t ). Similar to the idea of a physics-informed neural network (NN), this physically enforces consistency between ψ, J t , and the synthetic diagnostics. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. The results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J t with median R 2 = 0.9993 and R 2 = 0.978, respectively. A comprehensive NN using a network architecture search is also employed to predict the coefficients of the basis functions. The NN demonstrates significantly better performance compared to the least squares method with median R 2 = 0.9997 and 0.9916 for J t and ψ, respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Principal Component Analysis for Extremes and Application to U.S. Precipitation
Here, we propose a method for analyzing extremal behavior through the lens of a most efficient basis of vectors. The method is analogous to principal component analysis, but is based on methods from extreme value analysis. Specifically, rather than decomposing a covariance or correlation matrix, we obtain our basis vectors by performing an eigendecomposition of a matrix that describes pairwise extremal dependence. We apply the method to precipitation observations over the contiguous United States. We find that the time series of large coefficients associated with the leading eigenvector shows very strong evidence of a positive trend, and there is evidence that large coefficients of other eigenvectors have relationships with El Niño–Southern Oscillation.
54 ENVIRONMENTAL SCIENCES↗
Machine learning inversion from scattering for mechanically driven polymers
A machine learning inversion method is developed for analyzing scattering functions of mechanically driven polymers and extracting the corresponding feature parameters, which include energy parameters and conformation variables. The polymer is modeled as a chain of fixed-length bonds constrained by bending energy, and it is subject to external forces such as stretching and shear. We generate a data set consisting of random combinations of energy parameters, including bending modulus, stretching and shear force, along with Monte Carlo-calculated scattering functions and conformation variables such as end-to-end distance, radius of gyration and off-diagonal component of the gyration tensor. The effects of the energy parameters on the polymer are captured by the scattering function, and principal component analysis ensures the feasibility of the machine learning inversion. Finally, we train a Gaussian process regressor using part of the data set as a training set and validate the trained regressor for inversion using the rest of the data. The regressor successfully extracts the feature parameters.
Gaussian process regressors↗
Modeling pair distribution functions of rare-earth phosphate glasses using principal component analysis
The use of principal component analysis (PCA) to statistically infer features of local structure from experimental pair distribution function (PDF) data is assessed on a case study of rare-earth phosphate glasses (REPGs). Such glasses, co-doped with two rare-earth ions (R and R’) of different sizes and optical properties, are of interest to the laser industry. The determination of structure-property relationships in these materials is an important aspect of their technological development. Yet, realizing the local structure of co-doped REPGs presents significant challenges relative to their singly-doped counterparts; specifically, R and R’ are difficult to distinguish in terms of establishing relative material compositions, identifying atomic pairwise correlation profiles in a PDF that are associated with each ion, and resolving peak overlap of such profiles in PDFs. This study demonstrates that PCA can be employed to help overcome these structural complications, by statistically inferring trends in PDFs that exist for a restricted set of experimental data on REPGs, and using these as training data to predict material compositions and PDF profiles in unknown co-doped REPGs. The application of these PCA methods to resolve individual atomic pairwise correlations in t(r) signatures is also presented. The training methods developed for these structural predictions are pre-validated by testing their ability to reproduce known physical phenomena, such as the lanthanide contraction, on PDF signatures of the structurally simpler singly-doped REPGs. The intrinsic limitations of applying PCA to analyze PDFs relative to the quality control of source data, data processing, and sample definition, are also considered. Furthermore, while this case study is limited to lanthanide-doped REPGs, this type of statistical inference may easily be extended to other inorganic solid-state materials, and be exploited in large-scale data-mining efforts that probe many t(r) functions.
36 MATERIALS SCIENCE↗
Factors correlating with significant differences between X-ray structures of myoglobin
Conformational differences between myoglobin structures are studied. Most structural differences in whale myoglobin beyond the uncertainty threshold can be correlated with a few specific structural factors. There are always exceptions and a search for additional factors is needed. The results might have serious implications for biological insights from conformational differences. Validation of general ideas about the origins of conformational differences in proteins is critical in order to arrive at meaningful functional insights. Here, principal component analysis (PCA) and distance difference matrices are used to validate some such ideas about the conformational differences between 291 myoglobin structures from sperm whale, horse and pig. Almost all of the horse and pig structures form compact PCA clusters with only minor coordinate differences and outliers that are easily explained. The 222 whale structures form a few dense clusters with multiple outliers. A few whale outliers with a prominent distortion of the GH loop are very similar to the cluster of horse structures, which all have a similar GH-loop distortion apparently owing to intermolecular crystal lattice hydrogen bonds to the GH loop from residues near the distal histidine His64. The variations of the GH-loop coordinates in the whale structures are likely to be owing to the observed alternative intermolecular crystal lattice bond, with the change to the GH loop distorting bonds correlated with the binding of specific ‘unusual’ ligands. Such an alternative intermolecular bond is not observed in horse myoglobins, obliterating any correlation with the ligands. Intermolecular bonds do not usually cause significant coordinate differences and cannot be validated as their universal cause. Most of the native-like whale myoglobin structure outliers can be correlated with a few specific factors. However, these factors do not always lead to coordinate differences beyond the previously determined uncertainty thresholds. The binding of unusual ligands by myoglobin, leading to crystal-induced distortions, suggests that some of the conformational differences between the apo and holo structures might not be ‘functionally important’ but rather artifacts caused by the binding of ‘unusual’ substrate analogs. The causes of P6 symmetry in myoglobin crystals and the relationship between crystal and solution structures are also discussed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Description of sunspot cycles by orthogonal functions
Based on the principal component analysis technique and evidence for a 22-yr double-sunspot cycle periodicity. The time series of sunspot numbers is represented as a sum of mutually orthogonal eigenvectors in the time domain. It is shown that the first two eigenvectors account for about 90 percent of the cumulative 'signal power,' and that this is sufficient for reconstruction of the raw data curve. It is also noted that the second eigenvector behaves as the time derivative of the first, and that a phase-plane plot of these eigenvectors (i.e. a plot of a variable vs. its rate of change) suggests that the sun's sunspot cycle is driven by an oscillator; the implication is that, embedded within the sun, a chronometer is at work (e.g. Dicke, 1979).
Teuber, D. L.↗
Uncertainty Quantification for Smooth Functional Data with Application to Material Properties
This document outlines a method for processing functional output (i.e., curves) for the ultimate purpose of sampling curves under specified input conditions for use in modeling and simulation uncertainty quantification (UQ) studies. A set of benchmark curves sufficiently representative of the relevant scenario(s) being simulated are provided to the process and formatted as described in Section 1. Principal Component Analysis (PCA) is utilized to discover the components of uncertainty in the benchmark curves and is outlined in Section 2. Section 3 describes the application of uncertainty quantification to the PCA results for the purpose of sampling curves to be used in UQ analysis. Section 4 applies these techniques to an example benchmark dataset. Concluding remarks are provided in the final section.
36 MATERIALS SCIENCE↗
Relative effectiveness of kinetic analysis vs single point readings for classifying environmental samples based on community-level physiological profiles (CLPP)
The relative effectiveness of average-well-color-development-normalized single-point absorbance readings (AWCD) vs the kinetic parameters mu(m), lambda, A, and integral (AREA) of the modified Gompertz equation fit to the color development curve resulting from reduction of a redox sensitive dye from microbial respiration of 95 separate sole carbon sources in microplate wells was compared for a dilution series of rhizosphere samples from hydroponically grown wheat and potato ranging in inoculum densities of 1 x 10(4)-4 x 10(6) cells ml-1. Patterns generated with each parameter were analyzed using principal component analysis (PCA) and discriminant function analysis (DFA) to test relative resolving power. Samples of equivalent cell density (undiluted samples) were correctly classified by rhizosphere type for all parameters based on DFA analysis of the first five PC scores. Analysis of undiluted and 1:4 diluted samples resulted in misclassification of at least two of the wheat samples for all parameters except the AWCD normalized (0.50 abs. units) data, and analysis of undiluted, 1:4, and 1:16 diluted samples resulted in misclassification for all parameter types. Ordination of samples along the first principal component (PC) was correlated to inoculum density in analyses performed on all of the kinetic parameters, but no such influence was seen for AWCD-derived results. The carbon sources responsible for classification differed among the variable types with the exception of AREA and A, which were strongly correlated. These results indicate that the use of kinetic parameters for pattern analysis in CLPP may provide some additional information, but only if the influence of inoculum density is carefully considered. c2001 Elsevier Science Ltd. All rights reserved.
NASA Center KSC↗
Regional climate change predictions from the Goddard Institute for Space Studies high resolution GCM
A new diagnostic tool is developed for examining relationships between the synoptic scale circulation and regional temperature distributions in GCMs. The 4 x 5 deg GISS GCM is shown to produce accurate simulations of the variance in the synoptic scale sea level pressure distribution over the U.S. An analysis of the observational data set from the National Meteorological Center (NMC) also shows a strong relationship between the synoptic circulation and grid point temperatures. This relationship is demonstrated by deriving transfer functions between a time-series of circulation parameters and temperatures at individual grid points. The circulation parameters are derived using rotated principal components analysis, and the temperature transfer functions are based on multivariate polynomial regression models. The application of these transfer functions to the GCM circulation indicates that there is considerable spatial bias present in the GCM temperature distributions. The transfer functions are also used to indicate the possible changes in U.S. regional temperatures that could result from differences in synoptic scale circulation between a 1XCO2 and a 2xCO2 climate, using a doubled CO2 version of the same GISS GCM.
Crane, Robert G.↗
Comparing simulated emission from molecular clouds using experimental design
We propose a new approach to comparing simulated observations that enables us to determine the significance of the underlying physical effects. We utilize the methodology of experimental design, a subfield of statistical analysis, to establish a framework for comparing simulated position-position-velocity data cubes to each other. We propose three similarity metrics based on methods described in the literature: principal component analysis, the spectral correlation function, and the Cramer multi-variate two-sample similarity statistic. Using these metrics, we intercompare a suite of mock observational data of molecular clouds generated from magnetohydrodynamic simulations with varying physical conditions. Using this framework, we show that all three metrics are sensitive to changing Mach number and temperature in the simulation sets, but cannot detect changes in magnetic field strength and initial velocity spectrum. We highlight the shortcomings of one-factor-at-a-time designs commonly used in astrophysics and propose fractional factorial designs as a means to rigorously examine the effects of changing physical properties while minimizing the investment of computational resources.
79 ASTRONOMY AND ASTROPHYSICS↗
TH-E-BRF-07: Raman Spectroscopy for Radiation Treatment Response Assessment in a Lung Metastases Mouse Model
Purpose: Raman spectroscopy is an optical spectroscopic method used to probe chemical information about a target tissue. Our goal was to investigate whether Raman spectroscopy is able to distinguish lung tumors from normal lung tissue and whether this technique can identify the molecular changes induced by radiation. Methods: 4T1 mouse breast cancer cells were implanted subcutaneously into the flanks of 6 Balb/C female mice. Four additional mice were used as “normal lung” controls. After 14 days, 3 mice bearing tumors received 6Gy to the left lung with 6MV photons and the other three were treated as “unirradiated tumor” controls. At a 24-hour time point, lungs were excised and the specimens were sectioned using a cryostat; alternating sections were either stained with hematoxylin and eosin (H and E) for evaluation by a pathologist or unstained for Raman measurements. 240 total Raman spectra were collected; 84 from normal lung controls; 63 from unirradiated tumors and 64 from tumors irradiated with 6Gy in a single fraction. Raman spectra were also collected from normal lung tissues of mice with unirradiated tumors. Principal component analysis (PCA) and discriminant function analysis (DFA) were performed to analyze the data. Results: Raman bands assignable to DNA/RNA showed prominent contributions in tumor tissues while Raman bands associated with hemoglobin showed strong contributions in normal lung tissue. PCA/DFA analysis identified normal lung tissue and tumor with 100% and 98.4% accuracy, respectively, relative to pathologic scoring. Additionally, normal lung tissues from unirradiated mice bearing tumors were classified as normal with 100% accuracy. In a model consisting of unirradiated and irradiated tumors identification accuracy was 79.4% and 93.8% respectively, relative to pathologic assessment. Conclusion: Initial results demonstrate the promise for Raman spectroscopy in the diagnosis normal vs. lung metastases as well as the assessment of radiation therapy response. Further investigations are needed to validate these results. This study was supported in part by a research grant from Varian Medical Systems, Palo Alto, CA.
60 APPLIED LIFE SCIENCES↗
SpecDis: Value Added Distance Catalog for 4 Million Stars from DESI Year-1 Data
We present the SpecDis value-added stellar distance catalog accompanying DESI Data Release 1. SpecDis trains a feed-forward neural network (NN) with Gaia parallaxes and gets the distance estimates. To build up an unbiased training sample, we do not apply selections on parallax error or signal-to-noise (S/N) of the stellar spectra, and instead, we incorporate parallax error into the loss function. Moreover, we employ principal component analysis to reduce the noise and dimensionality of stellar spectra. Validated by independent external samples of member stars with precise distances from globular clusters, dwarf galaxies, stellar streams, combined with blue horizontal branch stars, we demonstrate that our distance measurements show no significant bias up to 100 kpc, and are much more precise than Gaia parallax beyond 7 kpc. The median distance uncertainties are 23%, 19%, 11%, and 7% for S/N < 20, 20 ≤ S/N < 60, 60 ≤ S/N < 100, and S/N ≥ 100. Selecting stars with ${\mathrm{log}}\,g\lt 3.8$ and distance uncertainties smaller than 25%, we have more than 74,000 giant candidates within 50 kpc of the Galactic center and 1500 candidates beyond this distance. Additionally, we develop a Gaussian mixture model to identify unresolvable equal-mass binaries by modeling the discrepancy between the NN-predicted and the geometric absolute magnitudes from Gaia parallaxes and identify 120,000 equal-mass binary candidates. Our final catalog provides distances and distance uncertainties for >4 million stars, offering a valuable resource for Galactic astronomy.
astronomy data analysis↗
AN EXPLORATION OF THE STATISTICAL SIGNATURES OF STELLAR FEEDBACK
All molecular clouds are observed to be turbulent, but the origin, means of sustenance, and evolution of the turbulence remain debated. One possibility is that stellar feedback injects enough energy into the cloud to drive observed motions on parsec scales. Recent numerical studies of molecular clouds have found that feedback from stars, such as protostellar outflows and winds, injects energy and impacts turbulence. We expand upon these studies by analyzing magnetohydrodynamic simulations of molecular clouds, including stellar winds, with a range of stellar mass-loss rates and magnetic field strengths. We generate synthetic {sup 12}CO(1–0) maps assuming that the simulations are at the distance of the nearby Perseus molecular cloud. By comparing the outputs from different initial conditions and evolutionary times, we identify differences in the synthetic observations and characterize these using common astrostatistics. We quantify the different statistical responses using a variety of metrics proposed in the literature. We find that multiple astrostatistics, including the principal component analysis, the spectral correlation function, and the velocity coordinate spectrum (VCS), are sensitive to changes in stellar mass-loss rates and/or time evolution. A few statistics, including the Cramer statistic and VCS, are sensitive to the magnetic field strength. These findings demonstrate that stellar feedback influences molecular cloud turbulence and can be identified and quantified observationally using such statistics.
79 ASTRONOMY AND ASTROPHYSICS↗
A unified development of several techniques for the representation of random vectors and data sets
Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.
Bundick, W. T.↗
A Distal Disulfide Bridge in OXA-1 β-Lactamase Stabilizes the Catalytic Center and Alters the Dynamics of the Specificity Determining Ω Loop
Widespread antibiotic resistance, particularly when mediated by broad-spectrum β-lactamases, has major implications for public health. Substitutions in the active site often allow broad-spectrum enzymes to accommodate diverse types of β-lactams. Substitutions observed outside the active site are thought to compensate for the loss of thermal stability. The OXA-1 clade of class D β-lactamases contains a pair of conserved cysteines located outside the active site that forms a disulfide bond in the periplasm. In this paper, the effect of the distal disulfide bond on the structure and dynamics of OXA-1 was investigated via 4 μs molecular dynamics simulations. The results reveal that the disulfide promotes the preorganized orientation of the catalytic residues and affects the conformation of the functionally important Ω loop. Furthermore, principal component analysis reveals differences in the global dynamics between the oxidized and reduced forms, especially in the motions involving the Ω loop. A dynamical network analysis indicates that, in the oxidized form, in addition to its role in ligand binding, the KTG family motif is a central hub of the global dynamics. Finally, as activity of OXA-1 has been measured only in the reduced form, we suggest that accurate assessment of its functional profile would require oxidative conditions mimicking periplasm.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗