Characterizing Complex Spatiotemporal Patterns from Entropy Measures.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy (SHp) and a new approach based on Tsallis Spectral Permutation Entropy (Sqs). Notably, our observations reveal the segregation of reaction terms in this SHp×Sqs space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns.

Land use and land cover (LULC) performance modeling using machine learning algorithms: a case study of the city of Melbourne, Australia.

Accurate spatial information on Land use and land cover (LULC) plays a crucial role in city planning. A widely used method of obtaining accurate LULC maps is a classification of the categories, which is one of the challenging problems. Attempts have been made considering spectral (Sp), statistical (St), and index-based (Ind) features in developing LULC maps for city planning. However, no work has been reported to automate LULC performance modeling for their robustness with machine learning (ML) algorithms. In this paper, we design seven schemes and automate the LULC performance modeling with six ML algorithms-Random Forest, Support Vector Machine with Linear kernel, Support Vector Machine with Radial basis function kernel, Artificial Neural Network, Naïve Bayes, and Generalised Linear Model for the city of Melbourne, Australia on Sentinel-2A images. Experimental results show that the Random Forest outperforms remaining ML algorithms in the classification accuracy (0.99) on all schemes. The robustness and statistical analysis of the ML algorithms (for example, Random Forest imparts over 0.99 F1-score for all five categories and p value [Formula: see text] 0.05 from Wilcoxon ranked test over accuracy measures) against varying training splits demonstrate the effectiveness of the proposed schemes. Thus, providing a robust measure of LULC maps in city planning.

Asymptotic Distribution of Certain Types of Entropy under the Multinomial Law.

We obtain expressions for the asymptotic distributions of the Rényi and Tsallis of order q entropies and Fisher information when computed on the maximum likelihood estimator of probabilities from multinomial random samples. We verify that these asymptotic models, two of which (Tsallis and Fisher) are normal, describe well a variety of simulated data. In addition, we obtain test statistics for comparing (possibly different types of) entropies from two samples without requiring the same number of categories. Finally, we apply these tests to social survey data and verify that the results are consistent but more general than those obtained with a χ2 test.

Dual views of the generalized degree of purity.

Several approaches and descriptors have been proposed to characterize the purity of coherency or density matrices describing physical states, including the polarimetric purity of 2D and 3D partially polarized waves. This work introduces two interpretations of the degree of purity: one derived from statistics and another from algebra. In the first one, the degree purity is expressed in terms of the mean and standard deviation of the eigenvalue spectrum of the density or coherency matrix of the corresponding state. The second one expresses the purity in terms of two specific measures obtained by decomposing the coherency matrix as a sum of traceless symmetric, antisymmetric, and scalar matrices. We believe these two approaches offer better insights into the purity measure. Furthermore, interesting relations with existing quantities in polarization optics also are described.

Entropy Estimators in SAR Image Classification.

Remotely sensed data are essential for understanding environmental dynamics, for their forecasting, and for early detection of disasters. Microwave remote sensing sensors complement the information provided by observations in the optical spectrum, with the advantage of being less sensitive to adverse atmospherical conditions and of carrying their own source of illumination. On the one hand, new generations and constellations of Synthetic Aperture Radar (SAR) sensors provide images with high spatial and temporal resolution and excellent coverage. On the other hand, SAR images suffer from speckle noise and need specific models and information extraction techniques. In this sense, the G0 family of distributions is a suitable model for SAR intensity data because it describes well areas with different degrees of texture. Information theory has gained a place in signal and image processing for parameter estimation and feature extraction. Entropy stands out as one of the most expressive features in this realm. We evaluate the performance of several parametric and non-parametric Shannon entropy estimators as input for supervised and unsupervised classification algorithms. We also propose a methodology for fine-tuning non-parametric entropy estimators. Finally, we apply these techniques to actual data.

Modeling dengue vector population with earth observation data and a generalized linear model.

Mosquitoes propagate many human diseases, some widespread and with no vaccines. The Ae. aegypti mosquito vector transmits Zika, Chikungunya, and Dengue viruses. Effective public health interventions to control the spread of these diseases and protect the population require models that explain the core environmental drivers of the vector population. Field campaigns are expensive, and data from meteorological sites that feed models with the required environmental data often lack detail. As a consequence, we explore temporal modeling of the population of Ae. aegypti mosquito vector species and environmental conditions- temperature, moisture, precipitation, and vegetation- have been shown to have significant effects. We use earth observation (EO) data as our source for estimating these biotic and abiotic environmental variables based on proxy features, namely: Normalized difference vegetation index, Normalized difference water index, Precipitation, and Land surface temperature. We obtained our response variable from field-collected mosquito population measured weekly using 791 mosquito traps in Vila Velha city, Brazil, for 36 weeks in 2017, and 40 weeks in 2018. Recent similar studies have used machine learning (ML) techniques for this task. However, these techniques are neither intuitive nor explainable from an operational point of view. As a result, we use a Generalized Linear Model (GLM) to model this relationship due to its fitness for count response variable modeling, its interpretability, and the ability to visualize the confidence intervals for all inferences. Also, to improve our model, we use the Akaike Information Criterion to select the most informative environmental features. Finally, we show how to improve the quality of the model by weighting our GLM. Our resulting weighted GLM compares well in quality with ML techniques: Random Forest and Support Vector Machines. These results provide an advancement with regards to qualitative and explainable epidemiological risk modeling in urban environments.

A detailed characterization of complex networks using Information Theory.

Understanding the structure and the dynamics of networks is of paramount importance for many scientific fields that rely on network science. Complex network theory provides a variety of features that help in the evaluation of network behavior. However, such analysis can be confusing and misleading as there are many intrinsic properties for each network metric. Alternatively, Information Theory methods have gained the spotlight because of their ability to create a quantitative and robust characterization of such networks. In this work, we use two Information Theory quantifiers, namely Network Entropy and Network Fisher Information Measure, to analyzing those networks. Our approach detects non-trivial characteristics of complex networks such as the transition present in the Watts-Strogatz model from k-ring to random graphs; the phase transition from a disconnected to an almost surely connected network when we increase the linking probability of Erdos-Rényi model; distinct phases of scale-free networks when considering a non-linear preferential attachment, fitness, and aging features alongside the configuration model with a pure power-law degree distribution. Finally, we analyze the numerical results for real networks, contrasting our findings with traditional complex network methods. In conclusion, we present an efficient method that ignites the debate on network characterization.

Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach.

In 2002, Bandt and Pompe [Phys. Rev. Lett. 88, 174102 (2002)] introduced a successfully symbolic encoding scheme based on the ordinal relation between the amplitude of neighboring values of a given data sequence, from which the permutation entropy can be evaluated. Equalities in the analyzed sequence, for example, repeated equal values, deserve special attention and treatment as was shown recently by Zunino and co-workers [Phys. Lett. A 381, 1883 (2017)]. A significant number of equal values can give rise to false conclusions regarding the underlying temporal structures in practical contexts. In the present contribution, we review the different existing methodologies for treating time series with tied values by classifying them according to their different strategies. In addition, a novel data-driven imputation is presented that proves to outperform the existing methodologies and avoid the false conclusions pointed by Zunino and co-workers.

Modeling Dengue vector population using remotely sensed data and machine learning.

Mosquitoes are vectors of many human diseases. In particular, Aedes ægypti (Linnaeus) is the main vector for Chikungunya, Dengue, and Zika viruses in Latin America and it represents a global threat. Public health policies that aim at combating this vector require dependable and timely information, which is usually expensive to obtain with field campaigns. For this reason, several efforts have been done to use remote sensing due to its reduced cost. The present work includes the temporal modeling of the oviposition activity (measured weekly on 50 ovitraps in a north Argentinean city) of Aedes ægypti (Linnaeus), based on time series of data extracted from operational earth observation satellite images. We use are NDVI, NDWI, LST night, LST day and TRMM-GPM rain from 2012 to 2016 as predictive variables. In contrast to previous works which use linear models, we employ Machine Learning techniques using completely accessible open source toolkits. These models have the advantages of being non-parametric and capable of describing nonlinear relationships between variables. Specifically, in addition to two linear approaches, we assess a support vector machine, an artificial neural networks, a K-nearest neighbors and a decision tree regressor. Considerations are made on parameter tuning and the validation and training approach. The results are compared to linear models used in previous works with similar data sets for generating temporal predictive models. These new tools perform better than linear approaches, in particular nearest neighbor regression (KNNR) performs the best. These results provide better alternatives to be implemented operatively on the Argentine geospatial risk system that is running since 2012.

Analysis of Machine Learning Algorithms for Diagnosis of Diffuse Lung Diseases.

Computational Intelligence Re-meets Medical Image Processing A Comparison of Some Nature-Inspired Optimization Metaheuristics Applied in Biomedical Image Registration BACKGROUND: Diffuse lung diseases (DLDs) are a diverse group of pulmonary disorders, characterized by inflammation of lung tissue, which may lead to permanent loss of the ability to breathe and death. Distinguishing among these diseases is challenging to physicians due their wide variety and unknown causes. Computer-aided diagnosis (CAD) is a useful approach to improve diagnostic accuracy, by combining information provided by experts with Machine Learning (ML) methods. OBJECTIVES: Exploring the potential of dimensionality reduction combined with ML methods for diagnosis of DLDs; improving the classification accuracy over state-of-the-art methods. METHODS: A data set composed of 3252 regions of interest (ROIs) was used, from which 28 features were extracted per ROI. We used Principal Component Analysis, Linear Discriminant Analysis, and Stepwise Selection - Forward, Backward, and Forward-Backward to reduce feature dimensionality. The feature subsets obtained were used as input to the following ML methods: Support Vector Machine, Gaussian Mixture Model, k-Nearest Neighbor, and Deep Feedforward Neural Network. We also applied a Deep Convolutional Neural Network directly to the ROIs. RESULTS: We achieved the maximum reduction from 28 to 5 dimensions using LDA. The best classification results were obtained by DFNN, with 99.60% of overall accuracy. CONCLUSIONS: This work contributes to the analysis and selection of features that can efficiently characterize the DLDs studied.

Classification and Verification of Handwritten Signatures with Time Causal Information Theory Quantifiers.

We present a new approach for handwritten signature classification and verification based on descriptors stemming from time causal information theory. The proposal uses the Shannon entropy, the statistical complexity, and the Fisher information evaluated over the Bandt and Pompe symbolization of the horizontal and vertical coordinates of signatures. These six features are easy and fast to compute, and they are the input to an One-Class Support Vector Machine classifier. The results are better than state-of-the-art online techniques that employ higher-dimensional feature spaces which often require specialized software and hardware. We assess the consistency of our proposal with respect to the size of the training sample, and we also use it to classify the signatures into meaningful groups.

Classification of complex Wishart matrices with a diffusion-reaction system guided by stochastic distances.

We propose a new method for polarimetric synthetic aperture radar (PolSAR) imagery classification based on stochastic distances in the space of random matrices obeying complex Wishart distributions. Given a collection of prototypes [Formula: see text] and a stochastic distance d(.,.), we classify any random matrix X using two criteria in an iterative set-up. First, we associate X with the class which minimizes the weighted stochastic distance w(m)d(X,Z(m)), where the positive weights w(m) are computed to max- imize the class discrimination power. Second, we improve the result by embedding the classification problem into a diffusion-reaction partial differential system where the diffusion term smooths the patches within the image, and the reaction term tends to move the pixel values towards the closest class prototype. In particular, the method inherits the benefits of speckle reduction by diffusion-like methods. Results on synthetic and real PolSAR data show the performance of the method.

Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph.

A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque et al., Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa et al., Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form [Formula: see text], in which [Formula: see text] is the node degree and [Formula: see text] is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to [Formula: see text] chaotic maps, 2 chaotic flows and [Formula: see text] different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study.

Deconvolution of vibroacoustic images using a simulation model based on a three dimensional point spread function.

Vibro-acoustography (VA) is a medical imaging method based on the difference-frequency generation produced by the mixture of two focused ultrasound beams. VA has been applied to different problems in medical imaging such as imaging bones, microcalcifications in the breast, mass lesions, and calcified arteries. The obtained images may have a resolution of 0.7-0.8mm. Current VA systems based on confocal or linear array transducers generate C-scan images at the beam focal plane. Images on the axial plane are also possible, however the system resolution along depth worsens when compared to the lateral one. Typical axial resolution is about 1.0cm. Furthermore, the elevation resolution of linear array systems is larger than that in lateral direction. This asymmetry degrades C-scan images obtained using linear arrays. The purpose of this article is to study VA image restoration based on a 3D point spread function (PSF) using classical deconvolution algorithms: Wiener, constrained least-squares (CLSs), and geometric mean filters. To assess the filters' performance on the restored images, we use an image quality index that accounts for correlation loss, luminance and contrast distortion. Results for simulated VA images show that the quality index achieved with the Wiener filter is 0.9 (when the index is 1.0 this indicates perfect restoration). This filter yielded the best result in comparison with the other ones. Moreover, the deconvolution algorithms were applied to an experimental VA image of a phantom composed of three stretched 0.5mm wires. Experiments were performed using transducer driven at two frequencies, 3075kHz and 3125kHz, which resulted in the difference-frequency of 50kHz. Restorations with the theoretical line spread function (LSF) did not recover sufficient information to identify the wires in the images. However, using an estimated LSF the obtained results displayed enough information to spot the wires in the images. It is demonstrated that the phase of the theoretical and the experimental PSFs are dissimilar. This fact prevents VA image restoration with the current theoretical PSF. This study is a preliminary step towards understanding the restoration of VA images through the application of deconvolution filters.

Data driven performance evaluation of Wireless Sensor Networks.

Wireless Sensor Networks are presented as devices for signal sampling and reconstruction. Within this framework, the qualitative and quantitative influence of (i) signal granularity, (ii) spatial distribution of sensors, (iii) sensors clustering, and (iv) signal reconstruction procedure are assessed. This is done by defining an error metric and performing a Monte Carlo experiment. It is shown that all these factors have significant impact on the quality of the reconstructed signal. The extent of such impact is quantitatively assessed.

Using fuzzy logic to enhance stereo matching in multiresolution images.

Stereo matching is an open problem in computer vision, for which local features are extracted to identify corresponding points in pairs of images. The results are heavily dependent on the initial steps. We apply image decomposition in multiresolution levels, for reducing the search space, computational time, and errors. We propose a solution to the problem of how deep (coarse) should the stereo measures start, trading between error minimization and time consumption, by starting stereo calculation at varying resolution levels, for each pixel, according to fuzzy decisions. Our heuristic enhances the overall execution time since it only employs deeper resolution levels when strictly necessary. It also reduces errors because it measures similarity between windows with enough details. We also compare our algorithm with a very fast multi-resolution approach, and one based on fuzzy logic. Our algorithm performs faster and/or better than all those approaches, becoming, thus, a good candidate for robotic vision applications. We also discuss the system architecture that efficiently implements our solution.

Image formation in vibro-acoustography with depth-of-field effects.

We study the image formation of vibro-acoustography systems based on a concave sector array transducer taking into account depth-of-field effects. The system point-spread function (PSF) is defined in terms of the acoustic emission of a point-target in response to the dynamic radiation stress of ultrasound. The PSF on the focal plane and the axis of the transducer are presented. To extend the obtained PSF to the 3D-space, we assume it is a separable function in the axial direction and the focal plane of the transducer. In this model, an image is formed through the 3D convolution of the PSF with an object function. Experimental vibro-acoustography images of a breast phantom with lesion-like inclusions were compared with simulated images. Results show that the experimental images are in good agreement with the proposed model.