On Quantization Errors in Approximate and Sample Entropy

Approximate and sample entropies are acclaimed tools for quantifying the regularity and unpredictability of time series. This paper analyses the causes of their inconsistencies. It is shown that the major problem is a coarse quantization of matching probabilities, causing a large error between their estimated and true values. Error distribution is symmetric, so in sample entropy, where matching probabilities are directly summed, errors cancel each other. In approximate entropy, errors are accumulating, as sums involve logarithms of matching probabilities. Increasing the time series length increases the number of quantization levels, and errors in entropy disappear both in approximate and in sample entropies. The distribution of time series also affects the errors. If it is asymmetric, the matching probabilities are asymmetric as well, so the matching probability errors cease to be mutually canceled and cause a persistent entropy error. Despite the accepted opinion, the influence of self-matching is marginal as it just shifts the error distribution along the error axis by the matching probability quant. Artificial lengthening the time series by interpolation, on the other hand, induces large error as interpolated samples are statistically dependent and destroy the level of unpredictability that is inherent to the original signal.

Prediction of Ship Heave Motion Using Regularized BP Neural Network with Cross Entropy Error Function

Accurate prediction of ship’s heave motion can greatly enhance the safety of offshore operation. Due to its complexity and nonlinearity, however, ship’s heave motion prediction is a difficult task to be solved. In this paper, a new method for predicting ship’s heave motion is proposed based on an improved back propagation neural network (IBPNN). To overcome the gradient saturation phenomenon of traditional BPNN, the mean square error (MSE) loss function is replaced with a cross entropy (CE) loss function in IBPNN. Meanwhile, the weights of IBPNN is regularized by $$L_2$$ L 2 norm to enhance the generalization ability of traditional BPNN. Finally, conjugate gradient method is adopted to train IBPNN. The IBPNN is used to predict ship’s heave motion and the prediction results prove its effectiveness.

Methods of Estimating the Form of the Probability Distribution Density in Tasks of Processing Measurement Results

Issues associated with methods for estimating the shape of the probability distribution density curve are analyzed in order to classify them when processing measurement results. For example, such nonparametric methods as the method of histograms and frequency polygon, as well as the method of classification of distributions, are considered. It is shown that the values of the anticurtosis and entropy coefficient can be taken as independent features of the form of symmetric distributions. For probability distribution densities that have a one-sided character, such as multiplicative noise, a skewness coefficient should be added to the parameters to consider. Recurrent procedures for obtaining current estimates of numerical characteristics of analyzed random processes are given. The results of processing a random process based on recurrent procedures are presented. It is shown that when the number of samples increases, the estimates obtained by using recurrent and non-recurrent procedures converge. The scattering of estimates of probability distribution density parameters, such as variance, relative mean square error, and entropy error, is determined.

Machine learning based decipherment of Cell Population Data: a promising hospital front-door screening tool for COVID-19

Introduction/Objective Key challenges against early diagnosis of COVID-19 are its symptoms sharing nature and prolong SARS-CoV-2 PCR turnaround time. Hither machine learning (ML) tools experienced by routinely generated clinical data; potentially grant early prediction. Methods/Case Report Routine and earlier diagnostic data along demographic information were extracted for total of 21,672 subsequent presentations. Along conventional statistics, multilayer perceptron (MLP) and radial basis function (RBF) were applied to predict COVID-19 from pre-pandemic control. Three feature sets were prepared, and performance evaluated through stratified 10-fold cross validation. With differing predominance of COVID-19, multiple test sets were created and predictive efficiency was evaluated to simulate real-fashion performance against fluctuating course of pandemic. Models validation was also inducted in prospective manner on independent dataset, equating framework forecasting to conclusions from PCR. Results (if a Case Study enter NA) RBF model attained superior cross entropy error 20.761(7.883) and 20.782(3.991) for Q-Flags and Routine Items respectively while MLP outperformed for cell population data (CPD) parameters with value of 6.968(1.259) for ‘training(testing)’. Our CPD driven MLP framework in challenge of lower (<5%) COVID-19 predominance affords greater negative predictive values (NPV >99%). Higher accuracy (%correct 92.5) was offered during prospective validation using independent dataset. Sensitivity analysis advances illusive accuracy (%correct 94.1) and NPV (96.9%). LY-WZ, Blasts/Abn Lympho?, ‘HGB Interf?’, and ‘RBC Agglutination?’ are among novel enlightening study attributes. Conclusion CPD driven ML tools offer efficient screening of COVID-19 patients at presentation to hospital to backing early expulsion and directing patients’ flow-from amid the initial presentation to hospital.

Application of a multilayer perceptron artificial neural network for identification of peach cultivars based on physical characteristics

In the fresh fruit industry, identification of fruit cultivars and fruit quality is of vital importance. In the current study, nine peach cultivars (Dixon, Early Grande, Flordaprince, Flordastar, Flordaglo, Florda 834, TropicSnow, Desertred, and Swelling) were evaluated for differences in skin color, firmness, and size. Additionally, a multilayer perceptron (MLP) artificial neural network was applied for identification of the cultivars according to these attributes. The MLP was trained with an input layer including six input nodes, a single hidden layer with six hidden nodes, and an output layer with nine output nodes. A hyperbolic tangent activation function was used in the hidden layer and the cross entropy error was given because the softmax activation function was functional to the output layer. Results showed that the cross entropy error was 0.165. The peach identification process was significantly affected by the following variables in order of contribution (normalized importance): polar diameter (100%), L∗ (89.0), b∗ (88.0%), a∗ (78.5%), firmness (71.3%), and cross diameter (37.5.3%). The MLP was found to be a viable method of peach cultivar identification and classification because few identifying attributes were required and an overall classification accuracy of 100% was achieved in the testing phase. Measurements and quantitative discrimination of peach properties are provided in this research; these data may help enhance the processing efficiency and quality of processed peaches.

Spatial Information and Performance Evaluation in Coprime Array

In this paper, the mutual information between the received signals and the source in the coprime linear array is investigated. In Shannon’s information theory, the mutual information is used to quantify the reduction in the priori uncertainty of the transmitted message. Similarly, the spatial information in the coprime array is the mutual information between direction of arrival (DOA), source amplitude, and received signals. Such information content is composed of two parts. The first part is DOA information, and the second one is scattering information. In a single source scenario, we derive the theoretical expression and its asymptotic upper bound of DOA information. The corresponding expression of scattering information is also formulated theoretically. Besides, the application of spatial information is discussed. We can obtain the optimal array configuration by maximizing the DOA information of the coprime array. Similarly, the information is also used to quantify the performance difference between the coprime array and uniform array. In addition, the entropy error is employed to evaluate the estimation performance based on spatial information. Numerical simulation of the information content confirms our theoretical analysis. The results in this paper have important guiding significance for the design of the coprime array in the actual environment.

The Upper Bound of Multi-source DOA Information in Sensor Array and Its Application in Performance Evaluation

Direction of arrival (DOA) estimation has been discussed extensively in the array signal processing field. In this paper, we focus on the DOA information which is defined as the mutual information between the DOA and the received signal with complex additive white Gaussian noise. A theoretical expression of DOA information with multiple sources is presented in the uniform linear array. Specially, the upper bound of DOA information for sparse sources with high SNR is derived and compared with the information of single source. Moreover, the relationship between Cramer-Rao bound and the upper bound of DOA information is given. Finally, the paper investigate the performance evaluation of estimation based on the DOA information. We define the entropy error (EE) as a new performance evaluation index and find that EE is better than mean square error. Moreover, the lower bound of the EE can be regarded as the Generalized Cramer-Rao bound considering the sources' order in multi-source scenario.

Automation of Calculation of Entropy Error of Measurement

The mathematical model of calculating the entropy error of measurement is obtained in the article. Program listings are provided for calculating measurement errors under the normal and uniform law of distribution errors in the Python software environment.

Enhanced Artificial Social Cockroaches (EASC) for Modern Information Retrieval

This article deals on an improved version of the recently developed Artificial Social Cockroaches (ASC) algorithm based on several modifications. The EASC has as input a set of artificial cockroaches and N selected shelters. It is based on a random displacement step and a set of operators (selection cockroaches, shelter attraction, congener's attraction, shelter permutation). Each cockroach must be hidden in the shelter where it feels safer (evaluation function). In the recent years with the coming of the world wide web, the amount of unstructured documents available in the digital society increases and becomes easily accessible, all this has led that satisfy the needs of users in terms of relevant information has become a substantial problem in the scientific community. The second component of the authors' study is to apply the algorithm (EASC) as an information retrieval system using multilingual pre-processing and thesaurus to solve the problems of multilingual query and searching with synonymy. The relevant documents will be rendered as a list of ranked and classified documents from the most relevant to the least relevant. Lastly the authors apply the benchmark Medline and a series of valuation measures (precision, recall, f-measure, entropy, error, accuracy, specificity, TCR, ROC) for the experimentation, also they have compared their results with the outcomes of set of existed systems (social worker bees, taboo search, genetic algorithm, simulating annealing, naïve method). The third component of the authors' system is the visualization step that ensures the presentation of the result in the form of a cobweb with some realism to be understandable by users.