Gaussian Kernel Density Research Articles

Dynamic Spatiotemporal Causality Analysis for Network Traffic Flow Based on Transfer Entropy and Sliding Window Approach

With the rapid development of sensor and communication technologies, a large amount of spatiotemporal traffic data has been accumulated, presenting the characteristics of big data. The potential information and regularity of traffic state evolution can be extracted from the huge traffic flow time series data and applied to intelligent transportation systems. This study proposes a dynamic spatiotemporal causality modeling approach to analyze traffic causal relationships for the large-scale road network. Transfer entropy algorithm is utilized to detect the spatiotemporal causality of network traffic states based on the extensive traffic time series data, which could measure the amount and direction of information transmission. A combination of Gaussian kernel density estimation and sliding window approach is proposed to calculate the transfer entropy and construct dynamic spatiotemporal causality graphs based on the causality significance test. The indexes of affected coefficient, influence coefficient, input degree, and output degree are defined to evaluate the causal interaction of traffic states among different road segments and identify the critical roads and potential bottlenecks of the existing road network. Experimental results based on real-world traffic sensor data indicate that the structures of traffic causality graphs are time-varying; the traffic cause-effect interaction among different road segments during the peak time is more significant than that during the nonpeak time; and the critical road segments can be identified, which are mainly located at the intersections of arterial roads, undertaking the convergence and dispersion of large traffic flows.

Enhancing Time Series Predictors with Generalized Extreme Value Loss

Time series prediction has wide applications in many safety-critical scenarios. According to previous studies, time series of recorded events usually contain a non-trivial proportion of extreme events, featured with extremely large/small values and may have huge societal consequences if overlooked by a predictive model (i.e., predictor). Despite its significance in time series, we however observe the conventional square loss in time series prediction would ignore the modeling of extreme events. Specifically, we prove the square loss as a learning objective of the predictor behaves equivalently as a Gaussian kernel density estimator (KDE) on the recorded events, which is light-tailed itself and unable to model the ground-truth event distribution, usually heavy-tailed due to the existence of extreme events. Considering the benefits of forecasting extreme events, we propose a unified loss form called Generalized Extreme Value Loss (GEVL), which bridges the misalignment between the tail parts of the estimation and the ground-truth via transformations on either the observed events or the estimator. Following the proposed framework, we present three heavy-tailed kernels and derive the corresponding GEVLs which show different levels of trade-off between modeling effectiveness and computational resources.Comprehensive experiments validate our novel loss form substantially enhances representative time series predictors in modeling extreme events.

Health assessment of wind turbine based on laplacian eigenmaps

ABSTRACT With the increasing complexity of wind turbines, the current situation of high failure rates and high maintenance costs has attracted the attention of wind power operators. The research on the health status monitoring of wind turbines is of great significance to the development of the wind power industry. In this study, a novel method for evaluating the health status of wind turbines is proposed. The method fully considers the characteristics of wind turbine health status with high-dimensional nonlinearity. Firstly, the Gaussian kernel density estimation Local Outlier Factor (GLOF) is used to clean the data. Secondly, feature parameters are extracted by Partial Least Squares (PLS). Finally, the dimension reduction method based on Laplacian Eigenmaps (LE) is used to map the processed wind turbine data, and the standard deviation of horizontal and vertical scales is used as the health condition evaluation model to evaluate the performance of the wind turbine. It was validated in a large onshore wind turbine dataset which collected three years of Supervisory Control And Data Acquisition (SCADA) system data. The results show that this method can stably monitor the health degradation of wind turbines and provide a theoretical basis for the staff to arrange the maintenance time of wind turbines reasonably.

Location‐based social network recommendations with computational intelligence‐based similarity computation and user check‐in behavior

AbstractLocation recommending frameworks plays a very significant role in suggesting the users with new places to visit especially when users are visiting unfamiliar areas. Most of the existing recommender systems do not consider the fact that different users have different behavior while checking in. Some approaches do not consider the essential factors while providing recommendations. These systems lack adaptability and hence they provide poor recommendations. An adaptive approach to provide users with a personalized recommendation has been proposed in this paper. We have considered three features namely, user activeness feature, user similarity feature, and the spatial feature. In addition to this, we have also considered the location popularity for a given timeslot. We have divided the users into inactive and active based on the degree of activeness on social networks using fuzzy c‐means clustering. We have provided two strategies based on the activeness of the user. A two‐dimensional Gaussian kernel density estimation strategy is used for the active user. A one‐dimensional power‐law function strategy is used for inactive users. Moreover, we have integrated the time‐based popularity of the location and probability estimation based on the similarity between the users. To evaluate the proposed model, we have used a large‐scale Foursquare dataset.

Data‐driven modeling for fatigue loads of large‐scale wind turbines under active power regulation

AbstractAdvanced control methods for coordinatively optimizing active power dispatch and fatigue load distribution of wind turbines (WTs) in mountain wind farms, require the fatigue load modeling that has not been fully studied. This study proposes a data‐driven modeling method for fatigue loads of large‐scale WT under active power regulation. Firstly, load simulations based on Monte Carlo approach are conducted to overcome the uncertainty of fatigue load caused by turbulent wind. Subsequently, the target components of WT are selected according to the fatigue load dataset distribution at various power setpoints and the sensitivity to active power. Specifically, the Jarque–Bera statistic is used to evaluate the distribution characteristics of datasets; the single‐value processing determines the valid value through the maximum probability of the Gaussian kernel density distribution of the dataset; the Morris screening is employed to select the valid value with high sensitivity to active power regulation. Afterwards, arbitrary polynomial chaos expansion and support vector regression are performed to establish the data model of fatigue loads, respectively. Finally, the proposed method is applied into a 1.5‐MW commercial WT model designed by the manufacturer through the Bladed software. The obtained data‐driven model establishes a basis of simultaneously optimizing active power dispatch and fatigue load distribution, making it possible to reduce energy cost in mountain wind farms.

Probabilistic Load Forecasting for Building Energy Models.

In the current energy context of intelligent buildings and smart grids, the use of load forecasting to predict future building energy performance is becoming increasingly relevant. The prediction accuracy is directly influenced by input uncertainties such as the weather forecast, and its impact must be considered. Traditional load forecasting provides a single expected value for the predicted load and cannot properly incorporate the effect of these uncertainties. This research presents a methodology that calculates the probabilistic load forecast while accounting for the inherent uncertainty in forecast weather data. In the recent years, the probabilistic load forecasting approach has increased in importance in the literature but it is mostly focused on black-box models which do not allow performance evaluation of specific components of envelope, HVAC systems, etc. This research fills this gap using a white-box model, a building energy model (BEM) developed in EnergyPlus, to provide the probabilistic load forecast. Through a Gaussian kernel density estimation (KDE), the procedure converts the point load forecast provided by the BEM into a probabilistic load forecast based on historical data, which is provided by the building’s indoor and outdoor monitoring system. An hourly map of the uncertainty of the load forecast due to the weather forecast is generated with different prediction intervals. The map provides an overview of different prediction intervals for each hour, along with the probability that the load forecast error is less than a certain value. This map can then be applied to the forecast load that is provided by the BEM by applying the prediction intervals with their associated probabilities to its outputs. The methodology was implemented and evaluated in a real school building in Denmark. The results show that the percentage of the real values that are covered by the prediction intervals for the testing month is greater than the confidence level (80%), even when a small amount of data are used for the creation of the uncertainty map; therefore, the proposed method is appropriate for predicting the probabilistic expected error in load forecasting due to the use of weather forecast data.

A distributed density estimation algorithm and its application to naive Bayes classification

We consider the problem of learning a density function from observations of an unknown underlying model in a distributed setting, where the observations are partitioned into different sites. Applying commonly used density estimation methods such as Gaussian Mixture Model (GMM) or Kernel Density Estimation (KDE) to distributed data leads to an extensive amount of communication. A familiar approach to address this issue is to sample a small subset of data and collect them into a central node to run the density estimation algorithms on them. In this paper, we follow an alternative to the sub-sampling approach by proposing the nested Log-Poly model. This model provides an accurate density estimation from a small sized statistic of the entire data. In distributed settings, it transfers the small sized statistics from the client nodes to a central node. The estimation process is then run in the central node. The proposed model can be used in different learning tasks such as classification in supervised learning and clustering in unsupervised learning. However, the properties of nested Log-Poly make it a suitable model for one-dimensional density estimations in the distributed settings. This makes Log-Poly a good choice for naive Bayes classifier, where one-dimensional density estimation is required for every feature conditioned on the class label. We provide a theoretical analysis of the efficiency of our model in estimating a wide range of probability density functions. Our experiments show that nested Log-Poly outperforms the state of the art density estimators on several synthetic datasets. We compare the accuracy and the communication load of naive Bayes classifier using nested Log-Poly and other related density estimators on several real datasets. The experimental outcomes depict that nested Log-Poly has less communication load, while maintaining a competitive classification accuracy compared to similar methods that use the entire data. Moreover, we present a comprehensive comparison between nested Log-Poly and validated KDE with sub-sampling, in terms of the number of communicated variables and the number of bytes transferred between the clients and the central node. Nested Log-Poly provides comparable accuracy with the validated KDE with sub-sampling, while communicating fewer variables. However, our method needs to compute and transmit the variables with a high precision in order to accurately capture the details of the underlying distributions.

Using Improved Conditional Generative Adversarial Networks to Detect Social Bots on Twitter

The detection and removal of malicious social bots in social networks has become an area of interest in industry and academia. The widely used bot detection method based on machine learning leads to an imbalance in the number of samples in different categories. Classifier bias leads to a low detection rate of minority samples. Therefore, we propose an improved conditional generative adversarial network (improved CGAN) to extend imbalanced data sets before applying training classifiers to improve the detection accuracy of social bots. To generate an auxiliary condition, we propose a modified clustering algorithm, namely, the Gaussian kernel density peak clustering algorithm (GKDPCA), which avoids the generation of data-augmentation noise and eliminates imbalances between and within social bot class distributions. Furthermore, we improve the CGAN convergence judgment condition by introducing the Wasserstein distance with a gradient penalty, which addresses the model collapse and gradient disappearance in the traditional CGAN. Three common oversampling algorithms are compared in experiments. The effects of the imbalance degree and the expansion ratio of the original data on oversampling are studied, and the improved CGAN performs better than the others. Experimental results comparing with three common oversampling algorithms show that the improved CGAN achieves the higher evaluation scores in terms of F1-score, G-mean and AUC.

A Fast Method for Estimating the Number of Clusters Based on Score and the Minimum Distance of the Center Point

Clustering is widely used as an unsupervised learning algorithm. However, it is often necessary to manually enter the number of clusters, and the number of clusters has a great impact on the clustering effect. At present, researchers propose some algorithms to determine the number of clusters, but the results are not very good for determining the number of clusters of data sets with complex and scattered shapes. To solve these problems, this paper proposes using the Gaussian Kernel density estimation function to determine the maximum number of clusters, use the change of center point score to get the candidate set of center points, and further use the change of the minimum distance between center points to get the number of clusters. The experiment shows the validity and practicability of the proposed algorithm.

Super-Resolution Doppler Velocity Estimation by Kernel-Based Range–$\tau$ Point Conversions for UWB Short-Range Radars

Lower band ultrawideband (UWB) Doppler radar is promising for through-wall imaging, e.g., human body detection in rescue scenarios. The inherent problem with pulse-Doppler radar is the tradeoff between the Doppler velocity resolution and the resulting temporal resolution that makes it difficult to conduct real-time target tracking, because the separation of micro-Doppler velocities of the human body requires a higher Doppler velocity resolution. This problem is particularly severe for lower band UWB radar systems, which are required to attain a sufficient penetration depth in concrete material in the through-the-wall imaging scenario. Because UWB signals generally have large fractional bandwidths, the reflected pulse is located over a range gate along the slow-time direction; this is well known as the range walk problem. As a promising solution to this problem, this article newly introduces a technique for a super-resolution Doppler velocity estimation algorithm based on Gaussian kernel density estimation, which converts observed range– $\tau $ points to Doppler-associated ranges. In addition, this approach makes an important contribution for super-resolution range extraction with a compressed sensing (CS) filter, which is combined with the range-point migration (RPM) method for human body imaging associated with micro-Doppler components. 2-D or 3-D numerical simulations, including human body imaging scenario, demonstrate that the proposed method allows both accurate Doppler velocity estimation and human body imaging, which can be updated at the pulse-repetition interval.

Weighted-averaging-based classification of laser-induced breakdown spectroscopy measurements using most informative spectral lines

In this study, efficient spectral line selection and weighted-averaging-based processing schemes are proposed for the classification of laser-induced breakdown spectroscopy (LIBS) measurements. For fast on-line classification, a set of representative spectral lines are selected and processed relying on the information metric, instead of the time consuming full spectrum based analysis. The most informative spectral line sets are investigated by the joint mutual information estimation (MIE) evaluated with the Gaussian kernel density, where dominant intensity peaks associated with the concentrated components are not necessarily most valuable for classification. In order to further distinguish the characteristic patterns of the LIBS measured spectrum, two-dimensional spectral images are synthesized through column-wise concatenation of the peaks along with their neighbors. For fast classification while preserving the effect of distinctive peak patterns, column-wise Gaussian weighted averaging is applied to the synthesized images, yielding a favorable trade-off between classification performance and computational complexity. To explore the applicability of the proposed schemes, two applications of alloy classification and skin cancer detection are investigated with the multi-class and binary support vector machines classifiers, respectively. The MIE measures associated with selected spectral lines in both applications show a strong correlation to the actual classification or detection accuracy, which enables to find out meaningful combinations of spectral lines. In addition, the peak patterns of the selected lines and their Gaussian weighted averaging with neighbors of the selected peaks efficiently distinguish different classes of LIBS measured spectrum.

Estimating load spectra probability distributions of train bogie frames by the diffusion-based kernel density method

The load spectra of a train bogie frame are used for bogie frame design, simulated fatigue testing and reliability evaluation and fatigue life prediction, however, modelling the bogie load spectrum is one of the most challenging tasks in this field. In this paper, diffusion-based kernel density estimation (DKDE) is used to obtain the load spectra distributions of train bogie frames. A full-scale B-type subway motor bogie and a full-scale high-speed EMU trailer bogie are analysed. DKDE, Gaussian kernel density estimation (GKDE) and parametric estimation are used to fit the distributions of the loads. Goodness-of-fit tests suggest that the distributions obtained by DKDE are close to the actual distributions. Fatigue damage are calculated to evaluate the distributions estimated by DKDE and GKDE. From the distributions obtained by DKDE, reasonable maximum load values and reasonable extrapolated load spectra are deduced.

Dynamic driving and counterfactual decomposition of the influencing factors of household energy consumption among provinces in China

Based on the panel data of 30 provinces in China from 2006 to 2016, the Gaussian kernel density estimation was initially used to describe the characteristics of the inter-provincial differences in household energy consumption (HEC), a dynamic panel data model was established secondly to study the main factors affecting HEC, and finally the counterfactual decomposition method was used to calculate the contribution of each factor to the inter-provincial differences in HEC. The research results are shown as follows: First, the inter-provincial HEC in China shows a phenomenon of agglomeration and growth, and the HEC level of different regions presents difference and imbalance. Second, the logarithms of consumption habits, total population and residents' income have significant effects on the logarithm of HEC, the influence coefficients are 0.191, 0.073 and 0.745, respectively; HEC not only has significant inertia characteristics, but also has certain population size effect and wealth effect. Third, the logarithms of technological progress, urbanization and household energy price have significant effects on the logarithm of HEC, the influence coefficients are 0.864, 0.195 and −0.346, respectively; the HEC saved by technological transformation is not sufficient to offset the increase in HEC demand, urbanization can improve HEC significantly, but the household energy price significantly inhibits HEC. Finally, from the perspective of contribution, the total population, residents' income and urbanization contribute a lot to the inter-provincial differences, totaling 73.02%. The possible innovations of this paper are as follows: First, the contribution of the influencing factors to the difference of inter-provincial HEC is studied, which is rarely seen in the previous literature. Second, compared with traditional decomposition method, counterfactual decomposition method is more convenient for economic interpretation. Third, the divergent conclusions of scholars are pointed out in this paper, and the actual impact of influencing factors on HEC are clarified.

Adaptive DBSCAN Algorithm Based on Sample Density Gradient

DBSCAN is a classic and commonly applied density-based clustering algorithm, but its clustering accuracy depends on the choice of two input parameters. This paper presents a new algorithm for adaptative parameter determination in DBSCAN. The assumption of this new algorithm is that regions with larger sample density gradient usually corresponds to the edge areas of clusters. The main idea is to generate some pre-clusters and determine the values of parameters by their statistics information. We first randomly pick pairs of points in the sample space to form circles, which are called “disks”. Then we estimate the density information of a disk by random sampling, and define the criteria of disk quality to select disks with larger sample density gradient. Finally, we obtain the suitable parameters of DBSCAN in terms of the distributions of radius and points number of these extracted disks by Gaussian kernel density estimation. Experimental results show that the new algorithm improves the accuracy of DBSCAN and performs better than classic algorithms like k-means and Birch in some cases.

An improved partitioning algorithm based on FCM algorithm for extended target tracking in PHD filter

Extended target Gaussian mixture probability hypothesis density (ET-GM-PHD) filter is a promising approach for multi-extended target tracking problem. Correct partitions of measurements are significant to the GM-PHD filter. In order to partition the measurement sets accurately and rapidly, an improved Fuzzy C-Means (FCM) approach is proposed. The proposed approach consists of two stages. Firstly, elliptical gating and Gaussian kernel density analysis technique are used to remove the clutter. Secondly, an improved FCM approach which takes the full merits of the prior information of targets is implemented. The predictive state of targets is utilized in the FCM initialization. And the shape of targets is considered in the iteration of FCM. Both real data and simulated data are performed in this work. Experimentation infers that the proposed method outperforms the others on both effectiveness and computation, especially when multiple closely targets are involved.

Adaptive visual target tracking algorithm based on classified-patch kernel particle filter

We propose a high-performance visual target tracking (VTT) algorithm based on classified-patch kernel particle filter (CKPF). Novel features of this VTT algorithm include sparse representations of the target template using the label-consistent K-singular value decomposition (LC-KSVD) algorithm; Gaussian kernel density particle filter to facilitate candidate template generation and likelihood matching score evaluation; and an occlusion detection method using sparse coefficient histogram (ASCH). Experimental results validate superior performance of the proposed tracking algorithm over state-of-the-art visual target tracking algorithms in scenarios that include occlusion, background clutter, illumination change, target rotation, and scale changes.

Nonparametric Method for Modeling Clustering Phenomena in Emergency Calls Under Spatial-Temporal Self-Exciting Point Processes

In this paper, a nonparametric spatial-temporal self-exciting point process is proposed to model clustering features in emergency calls. Gaussian kernel density functions are considered. The expectation-maximization algorithm is adopted for estimating the model. A simulation study is designed to carefully examine the performance of the proposed nonparametric method. The spatial-temporal patterns of the emergency calls in Montgomery County of Pennsylvania are studied using the proposed nonparametric model. The results demonstrate that the proposed nonparametric model captures the clustering phenomena present in the emergency calls from Montgomery County very well. Further, the proposed parameter estimation method results in robust and precise estimates.

3D Surface Matching by a Voxel-Based Buffer-Weighted Binary Descriptor

3D surface matching by local feature descriptors is a fundamental task in 3D object registration, recognition, and retrieval. In view of 2D projected descriptors’ information compression and 3D directly voxelized descriptors’ sensitivity to density variation and boundary, this paper first proposes a voxel-based buffer-weighted binary descriptor, named VBBD. After local surfaces of detected keypoints are voxelized, each voxel’s buffer region is established, and the buffer-weighted Gaussian kernel density is calculated. If the current voxel’s buffer-weighted density is larger than its local surface’s average density, the voxel is labeled 1, otherwise, it is 0. The proposed descriptor has several merits: 1) direct acquisition of 3D information without projection, the neighbor information is less compressed. 2) voxels are labeled and binarized according to the buffer-weighted density, which improves the robustness to boundary effect, noise and density variation. Based on the VBBD, a global optimal surface matching method based on a Kuhn_Munkres (KM) algorithm is adopted. The strategy has several advantages: 1) by calculating the descriptors of large-scaled surfaces which are down sampled, the number of the point cloud is reduced, and meanwhile, large-scaled information is obtained; and 2) KM algorithm is adopted to find matching pairs to achieve final maximum weight sum of all matching pairs, which can efficiently avoid local optimum. The experimental results show that, compared with other state-of-the-art descriptors, the VBBD has better descriptiveness and robustness, and the surface matching strategy by the VBBD can achieve both high recall and precision.

Study on probability distribution of electrified railway traction loads based on kernel density estimator via diffusion

The probabilistic modeling for traction load is one of the most basic and challenging work in the field of electrified railway. The improved diffusion-based kernel density estimator (DKDE) is used for the first time to establish the probability distribution of traction loads. Based on the diffusion partial differential equation of finite domain, DKDE can be obtained by discrete and inverse discrete cosine transform. The DKDE effectively accounts for both the optimal bandwidth selection and boundary correction. Based on the measured data (feeder currents and re/active power), four goodness-of-fit tests are applied to test the estimated probability distribution of traction loads. Compared with the parametric estimation models and Gaussian kernel density estimator (GKDE) respectively, the results show that this probability distribution of traction loads by DKDE is more accurate and suitable. Moreover, this DKDE has strong applicability and versatility for the random variation of different traction loads.

Saliency Preprocessing Locality-Constrained Linear Coding for Remote Sensing Scene Classification

Locality-constrained Linear Coding (LLC) shows superior image classification performance due to its underlying properties of local smooth sparsity and good construction. It encodes the visual features in remote sensing images and realizes the process of modeling human visual perception of an image through a computer. However, it ignores the consideration of saliency preprocessing in the human visual system. Saliency detection preprocessing can effectively enhance a computer’s perception of remote sensing images. To better implement the task of remote sensing image scene classification, this paper proposes a new approach by combining saliency detection preprocessing and LLC. This saliency detection preprocessing approach is realized using spatial pyramid Gaussian kernel density estimation. Experiments show that the proposed method achieved a better performance for remote sensing scene classification tasks.