Improved Locality Preserving Projection for Hyperspectral Image Classification in Probabilistic Framework

Unlabeled samples and transformation matrix are two main parts of unsupervised and semi-supervised feature extraction (FE) algorithms. In this manuscript, a semi-supervised FE method, locality preserving projection in the probabilistic framework (LPPPF), to find a sufficient number of reliable and unmixed unlabeled samples from all classes and constructing an optimal projection matrix is proposed. The LPPPF has two main steps. In the first step, a number of reliable unlabeled samples are selected based on the training samples, spectral features, and spatial information in the probabilistic framework. In this way, the spectral and spatial probability distribution function is calculated for each unlabeled sample. Therefore, the spectral features and spatial information are integrated together with a joint probability distribution function. Finally, a sufficient number of unlabeled samples with the highest joint probability distribution are selected. In the second step, the selected unlabeled samples are applied to construct the transformation matrix based on the spectral and spatial information of the unlabeled samples. The adjacency graph is improved by using new weights based on spectral and spatial information. This method is evaluated on three data sets: Indian Pines, Pavia University, and Kennedy Space Center (KSC) and compared with some recent and well-known supervised, semi-supervised, and unsupervised FE methods. Various experiments demonstrate the efficiency of the LPPPF in comparison with the other FE methods. LPPPF has also considerable performance with limited training samples.

SFEM Analysis of Beams with Scaled Lengths including Spatially Varying and Cross-Correlated Concrete Properties

This paper presents the results obtained for plain concrete beams under four-point bending with spatially varying material properties. Beams of increasing length but constant depth were analyzed using the stochastic finite element method. Spatial fluctuation of a uniaxial tensile strength, fracture energy and elastic modulus was defined within cross-correlated random fields. The symmetrical Gauss probability distribution function was applied for the material properties. The shape of the probability distribution function was modified by changing the coefficient of variation in order to find its right value. The correctness of the numerical solution was verified against the experimental results of Koide et al. (1998, 2000). The stochastic FEM analysis was performed with an autocorrelation length of 40 mm and material coefficients of variation of 0.12, 0.14, 0.16, 0.20 and 0.24. The comparison between numerical outcomes and experimental results demonstrated that the coefficient of variation of 0.24 gave the best agreement when referring to the experimental mean values. On the other hand, the variation of results was better captured with the coefficient of variation of 0.16. The findings indicate that the Gauss probability distribution function with cov = 0.24 correctly reproduced the statistical size effect, but its tails needed modification in order to project experimental result variation.

Rainfall models – a study over Gangtok

In this paper, the Pearsonian system of curves were fitted to the monthly rainfalls from January to December, in addition to the seasonal as well as annual rainfalls totalling to 14 data sets of the period 1957-2005 with 49 years of duration for the station Gangtok to determine the probability distribution function of these data sets. The study indicated that the monthly rainfall of July and summer monsoon seasonal rainfall did not fit in to any of the Pearsonian system of curves, but the monthly rainfalls of other months and the annual rainfalls of Gangtok station indicated to fit into Pearsonian type-I distribution which in other words is an uniform distribution. Anderson-Darling test was applied to for null hypothesis. The test indicated the acceptance of null-hypothesis. The statistics of the data sets and their probability distributions are discussed in this paper.

sígame v3: Gas Fragmentation in Postprocessing of Cosmological Simulations for More Accurate Infrared Line Emission Modeling

We present an update to the framework called Simulator of Galaxy Millimeter/submillimeter Emission (sígame). sígame derives line emission in the far-infrared (FIR) for galaxies in particle-based cosmological hydrodynamics simulations by applying radiative transfer and physics recipes via a postprocessing step after completion of the simulation. In this version, a new technique is developed to model higher gas densities by parameterizing the probability distribution function (PDF) of the gas density in higher-resolution simulations run with the pseudo-Lagrangian, Voronoi mesh code arepo. The parameterized PDFs are used as a look-up table, and reach higher densities than in previous work. sígame v3 is tested on redshift z = 0 galaxies drawn from the simba cosmological simulation for eight FIR emission lines tracing vastly different phases of the interstellar medium. This version of sígame includes dust radiative transfer with Skirt and high-resolution photoionization models with Cloudy, the latter sampled according to the density PDF of the arepo simulations to augment the densities in the cosmological simulation. The quartile distributions of the predicted line luminosities overlap with the observed range for nearby galaxies of similar star formation rate (SFR) for all but two emission lines: [O i]63 and CO(3–2), which are overestimated by median factors of 1.3 and 1.0 dex, respectively, compared to the observed line–SFR relation of mixed-type galaxies. We attribute the remaining disagreement with observations to the lack of precise attenuation of the interstellar light on sub-grid scales (≲200 pc) and differences in sample selection.

A Probabilistic Model for Maximum Rainfall Frequency Analysis

As determining the probability of the exceedance of maximum precipitation over a specified duration is critical to hydrotechnical design, particularly in the context of climate change, a model was developed to perform a frequency analysis of maximum precipitation of a specified duration. The PMAXΤP model (Precipitation MAXimum Time (duration) Probability) harbors a pair of computational modules fulfilling different roles: (i) statistical analysis of precipitation series, and (ii) estimation of maximum precipitation for a specified duration and its probability of exceedance. The input data consist of homogeneous 30-element series of precipitation values for 16 different durations: 5, 10, 15, 30, 45, 60, 90, 120, 180, 360, 720, 1080, 1440, 2160, 2880, and 4320 min, obtained through Annual Maximum Precipitation (AMP) and Peaks-Over-Threshold (POT) approaches. The statistical analysis of the precipitation series includes: (i) detecting outliers using the Grubbs–Beck test; (ii) checking for the random variable’s independence using the Wald–Wolfowitz test and the Anderson serial correlation coefficient test; (iii) checking the random variable’s stationarity using nonparametric tests, e.g., the Kruskal–Wallis test and Spearman rank correlation coefficient test for trends of mean and variance; (iv) identifying the trend of the random variables using correlation and regression analysis, including an evaluation of the form of the trend function; and (v) checking for the internal correlation of the random variables using the Anderson autocorrelation coefficient test. To estimate maximum precipitations of a specified duration and with a specified probability of exceedance, three-parameter theoretical probability distributions were used: a shifted gamma distribution (Pearson type III), a log-normal distribution, a Weibull distribution (Fisher–Tippett type III), a log-gamma distribution, as well as a two-parameter Gumbel distribution. The best distribution was selected by: (i) maximum likelihood estimation of parameters; (ii) tests of the hypothesis of goodness of fit of the theoretical probability distribution function with the empirical distribution using Pearson’s χ2 test; (iii) selection of the best-fitting function within each type according to the criterion of minimum Kolmogorov distance; (iv) selection of the most credible probability distribution function from the set of various types of best-fitting functions according to the Akaike information criterion; and (v) verification of the most credible function using single-dimensional tests of goodness of fit: the Kolmogorov–Smirnov test, the Anderson–Darling test, the Liao–Shimokawa test, and Kuiper’s test. The PMAXTP model was tested on data from two meteorological stations in northern Poland (Chojnice and Bialystok) drawn from a digital database of high-resolution precipitation records for the period of 1986 to 2015, available for 100 stations in Poland (i.e., the Polish Atlas of Rainfall Intensities (PANDa)). Values of maximum precipitation with a specified probability of exceedance obtained from the PMAXTP model were compared with values obtained from the probabilistic Bogdanowicz–Stachý model. The comparative analysis was based on the standard error of fit, graphs of the density function for the probability of exceedance, and estimated quantile errors. The errors of fit were lower for the PMAXTP compared to the Bogdanowicz–Stachý model. For both stations, the smallest errors were obtained for the quantiles determined on the basis of maximum precipitation POT using PMAXTP.