Multi-Layer Reconstruction Errors Autoencoding and Density Estimate for Network Anomaly Detection

Anomaly detection is an important method for intrusion detection.In recent years,unsupervised methods have been widely researched because they do not require labeling.For example,a nonlinear autoencoder can use reconstruction errors to attain the discrimination threshold.This method is not effective when the model complexity is high or the data contains noise.The method for detecting the density of compressed features in a hidden layer can be used to reduce the influence of noise on the selection of the threshold because the density of abnormal data in hidden layers is smaller than normal data.However,compressed features may lose some of the high-dimensional distribution information of the original data.In this paper,we present an efficient anomaly detection framework for unsupervised anomaly detection,which includes network data capturing,processing,feature extraction,and anomaly detection.We employ a deep autoencoder to obtain compressed features and multi-layer reconstruction errors,and feeds them the same to the Gaussian mixture model to estimate the density.The proposed approach is trained and tested on multiple current intrusion detection datasets and real network scenes,and performance indicators,namely accuracy,recall,and F1-score,are better than other autoencoder models.

Enhancing microseismic/acoustic emission source localization accuracy with an outlier-robust kernel density estimation approach

Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust localization method that integrates kernel density estimation(KDE)with damping linear correction to enhance the precision of microseismic/acoustic emission(MS/AE)source positioning.Our approach systematically addresses abnormal arrival times through a three-step process:initial location by 4-arrival combinations,elimination of outliers based on three-dimensional KDE,and refinement using a linear correction with an adaptive damping factor.We validate our method through lead-breaking experiments,demonstrating over a 23%improvement in positioning accuracy with a maximum error of 9.12 mm(relative error of 15.80%)—outperforming 4 existing methods.Simulations under various system errors,outlier scales,and ratios substantiate our method’s superior performance.Field blasting experiments also confirm the practical applicability,with an average positioning error of 11.71 m(relative error of 7.59%),compared to 23.56,66.09,16.95,and 28.52 m for other methods.This research is significant as it enhances the robustness of MS/AE source localization when confronted with data anomalies.It also provides a practical solution for real-world engineering and safety monitoring applications.

A Weakly-Supervised Crowd Density Estimation Method Based on Two-Stage Linear Feature Calibration

In a crowd density estimation dataset,the annotation of crowd locations is an extremely laborious task,and they are not taken into the evaluation metrics.In this paper,we aim to reduce the annotation cost of crowd datasets,and propose a crowd density estimation method based on weakly-supervised learning,in the absence of crowd position supervision information,which directly reduces the number of crowds by using the number of pedestrians in the image as the supervised information.For this purpose,we design a new training method,which exploits the correlation between global and local image features by incremental learning to train the network.Specifically,we design a parent-child network(PC-Net)focusing on the global and local image respectively,and propose a linear feature calibration structure to train the PC-Net simultaneously,and the child network learns feature transfer factors and feature bias weights,and uses the transfer factors and bias weights to linearly feature calibrate the features extracted from the Parent network,to improve the convergence of the network by using local features hidden in the crowd images.In addition,we use the pyramid vision transformer as the backbone of the PC-Net to extract crowd features at different levels,and design a global-local feature loss function(L2).We combine it with a crowd counting loss(LC)to enhance the sensitivity of the network to crowd features during the training process,which effectively improves the accuracy of crowd density estimation.The experimental results show that the PC-Net significantly reduces the gap between fullysupervised and weakly-supervised crowd density estimation,and outperforms the comparison methods on five datasets of Shanghai Tech Part A,ShanghaiTech Part B,UCF_CC_50,UCF_QNRF and JHU-CROWD++.

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

An Enhanced Multiview Transformer for Population Density Estimation Using Cellular Mobility Data in Smart City

This paper addresses the problem of predicting population density leveraging cellular station data.As wireless communication devices are commonly used,cellular station data has become integral for estimating population figures and studying their movement,thereby implying significant contributions to urban planning.However,existing research grapples with issues pertinent to preprocessing base station data and the modeling of population prediction.To address this,we propose methodologies for preprocessing cellular station data to eliminate any irregular or redundant data.The preprocessing reveals a distinct cyclical characteristic and high-frequency variation in population shift.Further,we devise a multi-view enhancement model grounded on the Transformer(MVformer),targeting the improvement of the accuracy of extended time-series population predictions.Comparative experiments,conducted on the above-mentioned population dataset using four alternate Transformer-based models,indicate that our proposedMVformer model enhances prediction accuracy by approximately 30%for both univariate and multivariate time-series prediction assignments.The performance of this model in tasks pertaining to population prediction exhibits commendable results.

Maternal dietary patterns associated with bone density in Chinese lactating women and infants at 6 months postpartum:a prospective study using data from 2018-2019

This cohort study was designed to explore the relationship between maternal dietary patterns(DPs)and bone health in Chinese lactating mothers and infants.We recruited 150 lactating women at 1-month postpartum.The estimated bone mineral density(eBMD)of subjects’calcanei and the information on dietary intake were collected.After 5-month follow-up,the eBMD of mothers and their infants were measured again.Factor analysis was applied to determine maternal DPs.General linear models were used to evaluate the association between maternal DPs and maternal eBMD loss or infants’eBMD.With all potential covariates adjusted,Factor 2(high intake of whole grains,tubers,mixed beans,soybeans and soybean products,seaweeds,and nuts)showed a positive association with the changes of maternal eBMD(β=0.16,95%CI:0.005,0.310).Factor 3(high intake of soft drinks,fried foods,and puffed foods)was inversely correlated with the changes of maternal eBMD(β=-0.22,95%CI:-0.44,0.00).The changes of maternal eBMD were positively associated with 6-month infants’eBMD(β=0.34,95%CI:0.017,0.652).In conclusion,Factor 2 might contribute to the maintenance of eBMD in lactating women,while Factor 3 could exacerbate maternal eBMD loss.Additionally,the changes of maternal eBMD presented a positive correlation with 6-month infants’eBMD.

Bayesian Classifier Based on Robust Kernel Density Estimation and Harris Hawks Optimisation

In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.

Covariate balancing based on kernel density estimates for controlled experiments

Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes.A completely randomised design is usually used to randomly assign treatment levels to experimental units.When covariates of the experimental units are available,the experimental design should achieve covariate balancing among the treatment groups,such that the statistical inference of the treatment effects is not confounded with any possible effects of covariates.However,covariate imbalance often exists,because the experiment is carried out based on a single realisation of the complete randomisation.It is more likely to occur and worsen when the size of the experimental units is small or moderate.In this paper,we introduce a new covariate balancing criterion,which measures the differences between kernel density estimates of the covariates of treatment groups.To achieve covariate balance before the treatments are randomly assigned,we partition the experimental units by minimising the criterion,then randomly assign the treatment levels to the partitioned groups.Through numerical examples,weshow that the proposed partition approach can improve the accuracy of the difference-in-mean estimator and outperforms the complete randomisation and rerandomisation approaches.

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.

ESSENTIAL RELATIONSHIP BETWEEN DOMAIN-BASED ONE-CLASS CLASSIFIERS AND DENSITY ESTIMATION

One-class support vector machine （OCSVM） and support vector data description （SVDD） are two main domain-based one-class （kernel） classifiers. To reveal their relationship with density estimation in the case of the Gaussian kernel, OCSVM and SVDD are firstly unified into the framework of kernel density estimation, and the essential relationship between them is explicitly revealed. Then the result proves that the density estimation induced by OCSVM or SVDD is in agreement with the true density. Meanwhile, it can also reduce the integrated squared error （ISE）. Finally, experiments on several simulated datasets verify the revealed relationships.

Spatiotemporal Patterns of Road Network and Road Development Pri-ority in Three Parallel Rivers Region in Yunnan,China:An Evaluation Based on Modified Kernel Distance Estimate

Road network is a critical component of public infrastructure,and the supporting system of social and economic development.Based on a modified kernel density estimate(KDE)algorithm,this study evaluated the road service capacity provided by a road network composed of multi-level roads(i.e.national,provincial,county and rural roads),by taking account of the differences of effect extent and intensity for roads of different levels.Summarized at town scale,the population burden and the annual rural economic income of unit road service capacity were used as the surrogates of social and economic demands for road service.This method was applied to the road network of the Three Parallel River Region,the northwestern Yunnan Province,China to evaluate the development of road network in this region.In results,the total road length of this region in 2005 was 3.70×104km,and the length ratio between national,provincial,county and rural roads was 1∶2∶8∶47.From 1989 to 2005,the regional road service capacity increased by 13.1%,of which the contributions from the national,provincial,county and rural roads were 11.1%,19.4%,22.6%,and 67.8%,respectively,revealing the effect of′All Village Accessible′policy of road development in the mountainous regions in the last decade.The spatial patterns of population burden and economic requirement of unit road service suggested that the areas farther away from the national and provincial roads have higher road development priority(RDP).Based on the modified KDE model and the framework of RDP evaluation,this study provided a useful approach for developing an optimal plan of road development at regional scale.

STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE:EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY

In this paper we study a fractional stochastic heat equation on Rd （d 〉 1） with additive noise /t u（t, x） = Dα/δ u（t, x）＋ b（u（t, x） ） ＋ WH （t, x） where D α/δ is a nonlocal fractional differential operator and W H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d = 1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.

African Lion Population Estimates in Tanzania’s Ruaha National Park

Tanzania is considered a country with the largest number of African lions (Panthera leo). However, the continued absence of ecological population estimates and understanding of the associated factors influencing lion distribution hinders the development of conservation planning. This is particularly true in the Ruaha-Rungwa landscape, where it was estimated that more than 10% of the global lion population currently resides. By using a call-back survey method, we aimed to provide population estimates (population size and density) of African lions in the Ruaha National Park, between wet (March 2019) and dry (October 2019) seasons. We also assessed the key factors that influenced the distribution of the observed lions towards call-back stations. Ferreira & Funston’s (2010) formula was used to calculate population size and in turn used to estimate density in the sampled area, while the Generalized Linear Model (GLMM) with zero-inflated Poisson error distribution was used to determine factors that influence the distribution of the observed lions to call-back stations. The population size we calculated for the sampled area of 3137.2 km2 revealed 286 lions (95% CI, 236 - 335) during the wet season, and 196 lions (95% CI, 192 - 200) during the dry season. The density of lions was 9.1/100 km2 during the wet season, and 6.3/100 km2 during the dry season. Distance to water source had a significant negative effect on the distribution of the observed lions to the call-back stations, while habitat had a marginal effect. Our findings show that, although lion population estimates were larger during the wet season than the dry season, the season had no effect on the distribution of the observed lions to call-back stations. We suggest that the proximity to water sources is important in study design. Further, we suggest that density and population size are useful indices in identifying conservation area priorities and lion coexistence strategies.

Smart Parking Management System “MOTAH”

With a surge in the university’s student and staff population, parking problems and congestion have rapidly intensified. The recent inclusion of women drivers, particularly during official working hours, has exacerbated these challenges. This pressing issue underscores the critical necessity for a structured approach to managing university entries and overseeing parking at the gates. The proposed smart parking management system aims to address these concerns by introducing a design concept that restricts unauthorized access and provides exclusive parking privileges to authorized users. Through image processing, the system identifies available parking spaces, relaying real-time information to users via a mobile application. This comprehensive solution also generates detailed reports (daily, weekly, and monthly), aiding university safety authorities in future gate management decisions.

Multivariate Statistical Process Monitoring of an Industrial Polypropylene Catalyzer Reactor with Component Analysis and Kernel Density Estimation

Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.

Video Scene Invariant Crowd Density Estimation Using Geographic Information Systems

Crowd density is an important factor of crowd stability.Previous crowd density estimation methods are highly dependent on the specific video scene.This paper presented a video scene invariant crowd density estimation method using Geographic Information Systems(GIS) to monitor crowd size for large areas.The proposed method mapped crowd images to GIS.Then we can estimate crowd density for each camera in GIS using an estimation model obtained by one camera.Test results show that one model obtained by one camera in GIS can be adaptively applied to other cameras in outdoor video scenes.A real-time monitoring system for crowd size in large areas based on scene invariant model has been successfully used in 'Jiangsu Qinhuai Lantern Festival,2012'.It can provide early warning information and scientific basis for safety and security decision making.

Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation

In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.

Deep density estimation via invertible block-triangular mapping

In this work,we develop an invertible transport map,called KRnet,for density estimation by coupling the Knothe–Rosenblatt(KR)rearrangement and the flow-based generative model,which generalizes the real-valued non-volume preserving(real NVP)model(arX-iv:1605.08803v3).The triangular structure of the KR rearrangement breaks the symmetry of the real NVP in terms of the exchange of information between dimensions,which not only accelerates the training process but also improves the accuracy significantly.We have also introduced several new layers into the generative model to improve both robustness and effectiveness,including a reformulated affine coupling layer,a rotation layer and a component-wise nonlinear invertible layer.The KRnet can be used for both density estimation and sample generation especially when the dimensionality is relatively high.Numerical experiments have been presented to demonstrate the performance of KRnet.

Kernel density estimation and marginalized-particle based probability hypothesis density filter for multi-target tracking

In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis density filter algorithm based on marginalized particle and kernel density estimation is proposed, which utilizes the idea of marginalized particle filter to enhance the estimating performance of the PHD. The state variables are decomposed into linear and non-linear parts. The particle filter is adopted to predict and estimate the nonlinear states of multi-target after dimensionality reduction, while the Kalman filter is applied to estimate the linear parts under linear Gaussian condition. Embedding the information of the linear states into the estimated nonlinear states helps to reduce the estimating variance and improve the accuracy of target number estimation. The meanshift kernel density estimation, being of the inherent nature of searching peak value via an adaptive gradient ascent iteration, is introduced to cluster particles and extract target states, which is independent of the target number and can converge to the local peak position of the PHD distribution while avoiding the errors due to the inaccuracy in modeling and parameters estimation. Experiments show that the proposed algorithm can obtain higher tracking accuracy when using fewer sampling particles and is of lower computational complexity compared with the PF-PHD.

AN EFFECTIVE IMAGE RETRIEVAL METHOD BASED ON KERNEL DENSITY ESTIMATION OF COLLAGE ERROR AND MOMENT INVARIANTS

In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time.