Gaussian Kernel Density Estimation Research Articles

The environment of QSO triplets at 1 ≲ z ≲ 1.5

ABSTRACT We present an analysis of the environment of six QSO triplets at 1 ≲ z ≲ 1.5 by analysing multiband (r, i, z, or g, r, i) images obtained with Megacam at the CFHT telescope, aiming to investigate whether they are associated or not with galaxy protoclusters. This was done by using photometric redshifts trained using the high-accuracy photometric redshifts of the COSMOS2015 catalogue. To improve the quality of our photometric redshift estimation, we included in our analysis near-infrared photometry (3.6 and 4.5$\, \mu$m) from the unWISE survey available for our fields and the COSMOS survey. This approach allowed us to obtain good photometric redshifts with dispersion, as measured with the robust σNMAD statistics (which scales as (1 + z)−1), of ∼0.04 for our six fields. Our analysis setup was reproduced on lightcones constructed from the Millennium Simulation data and the latest version of the L-GALAXIES semi-analytic model to verify the protocluster detectability in such conditions. The density field in a redshift slab containing each triplet was then analysed with a Gaussian kernel density estimator. We did not find any significant evidence of the triplets inhabiting dense structures, such as a massive galaxy cluster or protocluster.

A proposed data acquisition system and algorithm for signal processing of moving-coil geophone\u2019s output

The study of different types of vibrational and seismic movements is important for exploration in strata monitoring, machine health monitoring, earthquake detection, etc. In order to study these vibrational movements, it needs to be acquired first for analysis. Data acquisition using the seismic sensors is a challenging task. This paper presents a data acquisition system developed to acquire seismic signals from a moving-coil geophone. The paper also discusses a signal interpretation algorithm that is devised to perform automatic detection of a seismic event occurrence by separating through the waveform and non-waveform components in the sensor’s output using Gaussian naive Bayes classifier and Kernel density estimation technique. The proposed method is effective in the identification of a useful signal and identification of its nature of origin. Accuracy of the algorithm was 99% for the waveform classification. Sensitivity of the data acquisition system for the seismic sensors was 1.589 µm s–1. Further, the developed data acquisition system and the algorithm can be used in mines for seismological studies aimed at separating the vibration signal generated due to explosion and the one caused due to Earth’s tectonic and seismic activities.

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.

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.

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.

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.

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.

An adaptive point-of-interest recommendation method for location-based social networks based on user activity and spatial features

Point-of-interest (POI) recommendations can help users effectively explore new locations according to their preferences, which is an important research aspect for location-based social networks (LBSNs). However, most existing POI recommendation methods lack adaptability when making recommendations for users with different preferences, which causes unsatisfactory recommendation results. To this end, in this paper, we propose an adaptive POI recommendation method by combining user activity and spatial features, which can operate adaptively according to user activity. First, we extract three-dimensional user activity, time-based POI popularity and distance features using a probabilistic statistical analysis method from historical check-in datasets on LBSNs. Second, we devise a user activity clustering algorithm that is based on fuzzy c-means and compute POI popularity by applying smoothing technology to adjacent continuous time slots. Finally, we propose an adaptive recommendation scheme, which includes a two-dimensional Gaussian kernel density estimation algorithm and a one-dimensional power-law function algorithm with POI popularity according to user activity. Extensive experiments on Foursquare and Gowalla datasets show that the proposed method outperforms the baseline methods in terms of both precision and recall.

New probabilistic price forecasting models: Application to the Iberian electricity market

This article presents original Probabilistic Price Forecasting Models, for day-ahead hourly price forecasts in electricity markets, based on a Nadaraya–Watson Kernel Density Estimator approach. A Gaussian Kernel Density Estimator function is used for each input variable, which allows to calculate the parameters of the probability density function (PDF) of a Beta distribution for the hourly price variable. Thus, valuable information is obtained from PDFs such as point forecasts, variance values, quantiles, probabilities of prices, and time series representations of forecast uncertainty. A Reliability Indicator is also introduced to give a measure of “reliability” of forecasts. The Probabilistic Price Forecasting Models were satisfactorily applied to the real-world case study of the Iberian Electricity Market. Input variables of these models include recent prices, power demands and power generations in the previous day, power demands in the previous week, forecasts of demand, wind power generation and weather for the day-ahead, and chronological data. The best model, corresponding to the best combination of input variables that achieves the lowest MAE, obtains one of the highest Reliability Indicator values. A systematic analysis of MAE values of the Probabilistic Price Forecasting Models for different combinations of input variables showed that as more types of input variables were considered in these models, MAE values improved and Reliability Indicator values usually increased.

Short-term power load probability density forecasting based on Yeo-Johnson transformation quantile regression and Gaussian kernel function

Penetration of renewable resources into power systems, such as wind and solar power, has significantly grown the complexity and level of uncertainty in both power generation and demand sides, which are highly desirable to exploit more advanced methods to address the uncertainties. The probability density forecasting method using quantile regression can describe probability distributions of future power load. However, existing quantile regression probability density forecasting methods may encounter embarrassing cross phenomenon, affecting the effectiveness of probability density forecasting. To avoid the crossing issue, this study proposes a probability density forecasting method based on Yeo-Johnson transformation quantile regression using Gaussian kernel function. Gaussian kernel density estimation using a rule of thumb bandwidth is innovatively hybridized with Yeo-Johnson transformation quantile regression for short-term power load probability density forecasting. The evaluation metrics for forecasting errors and prediction interval are adopted to carry out a comprehensive study on load uncertainty handling. One-hourly historical load data of August 2014 in summer and December 2014 in winter from Ottawa, Canada are used to evaluate the performance of proposed model. The results show that the proposed method not only efficiently avoids the quantile crossing problem but also obtains smooth probability density curves and more accurate forecasting results.

Geographical heterogeneity and inequality of access to improved drinking water supply and sanitation in Nepal

BackgroundPer United Nations’ Sustainable Development Goals, Nepal is aspiring to achieve universal and equitable access to safe and affordable drinking water and provide access to adequate and equitable sanitation for all by 2030. For these goals to be accomplished, it is important to understand the country’s geographical heterogeneity and inequality of access to its drinking-water supply and sanitation (WSS) so that resource allocation and disease control can be optimized. We aimed 1) to estimate spatial heterogeneity of access to improved WSS among the overall Nepalese population at a high resolution; 2) to explore inequality within and between relevant Nepalese administrative levels; and 3) to identify the specific administrative areas in greatest need of policy attention.MethodsWe extracted cluster-sample data on the use of the water supply and sanitation that included 10,826 surveyed households from the 2011 Nepal Demographic and Health Survey, then used a Gaussian kernel density estimation with adaptive bandwidths to estimate the distribution of access to improved WSS conditions over a grid at 1 × 1 km. The Gini coefficient was calculated for the measurement of inequality in the distribution of improved WSS; the Theil L measure and Theil T index were applied to account for the decomposition of inequality.Results57% of Nepalese had access to improved sanitation (range: 18.1% in Mahottari to 100% in Kathmandu) and 92% to drinking-water (range: 41.7% in Doti to 100% in Bara). The most unequal districts in Gini coefficient among improved sanitation were Saptari, Sindhuli, Banke, Bajura and Achham (range: 0.276 to 0.316); and Sankhuwasabha, Arghakhanchi, Gulmi, Bhojpur, Kathmandu (range: 0.110 to 0.137) among improved drinking-water. Both the Theil L and Theil T showed that within-province inequality was substantially greater than between-province inequality; while within-district inequality was less than between-district inequality. The inequality of several districts was higher than what is calculated by regression of the Gini coefficient and our estimates.ConclusionsThis study showed considerable geographical heterogeneity and inequality not evidenced in previous national statistics. Our findings may be useful in prioritizing resources to reduce inequality and expand the coverage of improved water supply and sanitation in Nepal.

Homogeneity quantification of nanoparticles dispersion in composite materials

As the quantitative evaluation of dispersion of nanoparticles are crucial for the research of nanocomposites, including ceramic, metal, and polymer nanocomposites, we proposed two quantifiable tools for the evaluation of dispersion in the nanocomposites by using machine‐learning algorithms, that is the coefficient of variation of K‐nearest neighboring distances (CVKD value) and the information entropy derived from the probability density function. In total 230 different type of dispersion morphologies of nanocomposites were investigated by using K‐nearest neighboring algorithms, Gaussian mixture model, expectation maximization, and Kernel density estimation algorithms. The smaller values of CVKD or information entropy represented much more homogeneous dispersion of nanoparticles. It might be expected the information exhibited in the present study could assist in the rational design and fabrication of superior nanocomposites. POLYM. COMPOS., 40:1000–1005, 2019. © 2018 Society of Plastics Engineers