Kernel Density Estimation Approach Research Articles

Cross Attention Transformers for Multi-modal Unsupervised Whole-Body PET Anomaly Detection.

Cancers can have highly heterogeneous uptake patterns best visualised in positron emission tomography. These patterns are essential to detect, diagnose, stage and predict the evolution of cancer. Due to this heterogeneity, a general-purpose cancer detection model can be built using unsupervised learning anomaly detection models; these models learn a healthy representation of tissue and detect cancer by predicting deviations from healthy appearances. This task alone requires models capable of accurately learning long-range interactions between organs, imaging patterns, and other abstract features with high levels of expressivity. Such characteristics are suitably satisfied by transformers, and have been shown to generate state-of-the-art results in unsupervised anomaly detection by training on healthy data. This work expands upon such approaches by introducing multi-modal conditioning of the transformer via cross-attention, i.e. supplying anatomical reference information from paired CT images to aid the PET anomaly detection task. Using 83 whole-body PET/CT samples containing various cancer types, we show that our anomaly detection method is robust and capable of achieving accurate cancer localisation results even in cases where healthy training data is unavailable. Furthermore, the proposed model uncertainty, in conjunction with a kernel density estimation approach, is shown to provide a statistically robust alternative to residual-based anomaly maps. Overall, a superior performance is demonstrated against leading alternatives, drawing attention to the potential of these approaches.

Kantorovich Distance Based Fault Detection Scheme for Non-Linear Processes

Fault detection is necessary for safe operation in modern process plants. The kernel principal component analysis (KPCA) technique has been widely utilized for monitoring non-linear processes because it enhances dimension reduction and fault detection in non-linear space. In this paper, an improved non-linear fault detection strategy based on Kantorovich distance (KD) and kernel principal component analysis is proposed. The KD statistic is based on the optimal mass transport theory where the distance between two distributions is computed with respect to a cost function. The addressed fault detection problem models the data using the KPCA framework and utilizes the ability of the KD statistical indicator to detect faults. The detection stage involves comparing the residuals of training fault-free data and testing faulty data using the KD statistic. Additionally, the reference threshold for the KD statistic is computed using the kernel density estimation (KDE) approach as compared to the previously utilized three-sigma rule approach. The detection performance is illustrated with the help of three benchmark case studies: a continuous stirred tank reactor (CSTR) process, Tennessee Eastman (TE) process and an experimental distillation column process. The performance analysis suggests the superiority of the KPCA-KD fault detection scheme in monitoring various sensor faults. Moreover, comparison with traditional statistical indicators of PCA and KPCA schemes shows that the proposed scheme enhances fault detection and achieves an improved detection rate in monitoring different categories of faults.

Role of geographic risk factors and social determinants of health in COVID-19 epidemiology: Longitudinal geospatial analysis in a midwest rural region.

Studies examining the role of geographic factors in coronavirus disease-2019 (COVID-19) epidemiology among rural populations are lacking. Our study is a population-based longitudinal study based on rural residents in four southeast Minnesota counties from March through October 2020. We used a kernel density estimation approach to identify hotspots for COVID-19 cases. Temporal trends of cases and testing were examined by generating a series of hotspot maps during the study period. Household/individual-level socioeconomic status (SES) was measured using the HOUSES index and examined for association between identified hotspots and SES. During the study period, 24,243 of 90,975 residents (26.6%) were tested for COVID-19 at least once; 1498 (6.2%) of these tested positive. Compared to other rural residents, hotspot residents were overall younger (median age: 40.5 vs 43.2), more likely to be minorities (10.7% vs 9.7%), and of higher SES (lowest HOUSES [SES] quadrant: 14.6% vs 18.7%). Hotspots accounted for 30.1% of cases (14.5% of population) for rural cities and 60.8% of cases (27.1% of population) for townships. Lower SES and minority households were primarily affected early in the pandemic and higher SES and non-minority households affected later. In rural areas of these four counties in Minnesota, geographic factors (hotspots) play a significant role in the overall burden of COVID-19 with associated racial/ethnic and SES disparities, of which pattern differed by the timing of the pandemic (earlier in pandemic vs later). The study results could more precisely guide community outreach efforts (e.g., public health education, testing/tracing, and vaccine roll out) to those residing in hotspots.

6G Multisource-Information-Fusion-Based Indoor Positioning via Gaussian Kernel Density Estimation

With the in-depth development of the Internet of Things (IoT) and the constant discussion of 6G visions, the future development of indoor location-based services (LBSs) in the 6G-enabled IoT is attracting people’s attention. In fact, due to the continuous updating of network techniques, the complexity of the indoor environment and the number of connected wireless access points (APs) will increase dramatically, which leads to the diversity of the received signal strength (RSS) on the performance of signal propagation distance estimation, resulting in low positioning accuracy and poor robustness. In response to this problem, this article proposes a multisource information fusion-based indoor positioning approach via Gaussian kernel density estimation. First, the heuristic distribution model is used to establish the mathematical relationship between the RSS from different Wi-Fi APs and the signal propagation distance, and then the Gaussian kernel density estimation approach is applied to estimate the signal propagation distance distribution. Second, the normalized signal propagation distance distribution is set as the basic probability assignment in the Dempster–Shafer (D–S) evidence theory, and then the multisource RSS information is fused according to D–S evidence synthesis rules. Meanwhile, the trust function synthesized by the D–S evidence theory is used to select matching reference points (RPs). Finally, the fuzzy decision algorithm is used to select the ideal matching RPs from the matching RPs for the positioning. Experimental results show that the proposed approach has higher positioning accuracy and stronger positioning robustness compared to existing ones.

A new method for predicting the extreme dynamic responses of wave energy converters

The copula-based environmental contour approach in the existing literature is only ‘partially’ non-parametric. Theoretically, the derived environmental contours from this ‘non-parametric’ copula-based approach will still be somewhat rigid. Optimally, the environmental contours for a specific ocean site should be developed based on a joint model of the environmental variables and the joint model should be directly estimated by a two-dimensional non-parametric approach. In this study, the use of a bivariate kernel density estimation approach for generating environmental contours is proposed. The advantages of the proposed new method were validated using two calculation examples based on measured wave data at two offshore locations. It was found, in a wave energy converter (WEC) application example, that the design value will increase by 23.4% if the proposed method is used in comparison to using the technique based on the non-parametric Gumbel copula environmental contour method. It was also concluded that the design value will increase by 15.98% if the proposed method is used in comparison to using the technique based on the non-parametric Clayton copula environmental contour method. The calculation results in this paper clearly demonstrate that the proposed new method can be used to effectively forecast the extreme dynamic responses of WECs.

Identifying convergence in nitrogen oxides emissions from motor vehicles in China: A spatial panel data approach

Motor vehicles have become an important source of nitrogen oxides (NOx) emissions in China. It is critical to identify the development trend of NOx emissions from motor vehicles (NOV). This study revealed the spatial distribution changes of NOV during 2006–2015. Moreover, we emphasized the verification of the convergence in cross-province NOV per capita (NOVPC) and NOV per vehicle (NOVPV), and we applied a kernel density estimation approach and a dynamic spatial convergence model to examine σ and β convergence, respectively. The results showed that the total NOV and NOV proportion both presented significantly increasing trends. In addition, provincial NOV, NOVPC, and NOVPV were found to be positively spatially autocorrelated. The kernel density estimates showed that NOVPC diverged from 2009 to 2012 and converged after 2012, while NOVPV showed a convergence trend during the entire sample period. The spatial β convergence model results confirmed both absolute and conditional β convergence in provincial NOVPC and NOVPV. Furthermore, the speed of absolute convergence was lower than that of conditional convergence. Lastly, increases in vehicles per capita and traffic pressure were responsible for the growth in NOVPC and NOVPV, although the growth of NOVPC was also attributed to rapid urbanization, while technological progress could play a decisive role in reducing NOVPV.

Automatic Construction of Indoor 3D Navigation Graph from Crowdsourcing Trajectories

Lacking indoor navigation graph has become a bottleneck in indoor applications and services. This paper presents a novel automated indoor navigation graph reconstruction approach from large-scale low-frequency indoor trajectories without any other data sources. The proposed approach includes three steps: trajectory simplification, 2D floor plan extraction and 3D navigation graph construction. First, we propose a ST-Join-Clustering algorithm to identify and simplify redundant stay points embedded in the indoor trajectories. Second, an indoor trajectory bitmap construction based on a self-adaptive Gaussian filter is developed, and we then propose a new improved thinning algorithm to extract 2D indoor floor plans. Finally, we present an improved CFSFDP algorithm with time constraints to identify the 3D topological connection points between two different floors. To illustrate the applicability of the proposed approach, we conducted a real-world case study using an indoor trajectory dataset of over 4000 indoor trajectories and 5 million location points. The case study results showed that the proposed approach improves the navigation network accuracy by 1.83% and the topological accuracy by 13.7% compared to the classical kernel density estimation approach.

Understanding collective human movement dynamics during large-scale events using big geosocial data analytics

Conventional approaches for modeling human mobility pattern often focus on human activity and movement dynamics in their regular daily lives and cannot capture changes in human movement dynamics in response to large-scale events. With the rapid advancement of information and communication technologies, many researchers have adopted alternative data sources (e.g., cell phone records, GPS trajectory data) from private data vendors to study human movement dynamics in response to large-scale natural or societal events. Big geosocial data such as georeferenced tweets are publicly available and dynamically evolving as real-world events are happening, making it more likely to capture the real-time sentiments and responses of populations. However, precisely-geolocated geosocial data is scarce and biased toward urban population centers. In this research, we developed a big geosocial data analytical framework for extracting human movement dynamics in response to large-scale events from publicly available georeferenced tweets. The framework includes a two-stage data collection module that collects data in a more targeted fashion in order to mitigate the data scarcity issue of georeferenced tweets; in addition, a variable bandwidth kernel density estimation(VB-KDE) approach was adopted to fuse georeference information at different spatial scales, further augmenting the signals of human movement dynamics contained in georeferenced tweets. To correct for the sampling bias of georeferenced tweets, we adjusted the number of tweets for different spatial units (e.g., county, state) by population. To demonstrate the performance of the proposed analytic framework, we chose an astronomical event that occurred nationwide across the United States, i.e., the 2017 Great American Eclipse, as an example event and studied the human movement dynamics in response to this event. However, this analytic framework can easily be applied to other types of large-scale events such as hurricanes or earthquakes.

Joint probability distribution of coastal winds and waves using a log-transformed kernel density estimation and mixed copula approach

The planning, designing, and risk assessment of coastal structures heavily rely on realistic statistical analyses of coastal winds and waves (CWW). In this study, we propose a novel bivariate joint probabilistic approach to describe the complex dependence and model the joint probability distribution (JPD) for CWW. A log-transformed kernel density estimation (KDE) is applied to fit the univariate marginal cumulative distribution (MCD) of the CWW measured at ShiDao station. As a connectivity function between the univariate MCD and JPD, a mixed copula is developed using a linear combination of Gumbel, Clayton, and Frank copula. The analytical results indicate that the optimum MCD for the ocean parameters can be effectively obtained using the log-transform KDE when compared with the Kernel-Pareto and GEV. Compared with five commonly used single copulas (i.e., Gaussian, t, Gumbel, Clayton, and Frank copula), the mixed copula is more suitable for describing the bivariate complex dependency structure between the ocean parameters and can yield more realistic JPD estimations. The return period and conditional probability calculated by the mixed copula were discussed and compared with the best fit single copula, which concluded that the log-transformed KDE and mixed copula approach can improve the precision of statistical analyses for CWW.

FR–KDE: A Hybrid Fuzzy Rule-Based Information Fusion Method with its Application in Biomedical Classification

Granular computing (GrC) is an essential tool to solve human real problem since the information granules is close to human perception schemes. In GrC, both classification accuracy and interpretability play significant roles. Fuzzy rule (FR) based classification systems are effective methods solving this problem. However, the accuracy of FR may be decreased when solving some complex application. In this paper, a novel model called FR–KDE integrating the FR and kernel density estimation (KDE) in the framework of Dempster–Shafer evidence theory is proposed to deal with the classification problem. By fusing the result of FR and KDE via the Dempster’s combination rule, it can reduce the uncertainty of FR and obtain better accuracy. To illustrate the effect of the FR–KDE approach, it is applied to the medical data classification problem. Experimentally, the results demonstrate that the FR–KDE method is effective in handling biomedical data classification problems.

Spatiotemporal persistence of bat roadkill hotspots in response to dynamics of habitat suitability and activity patterns

Wildlife roadkill hotspots are frequently used to identify priority locations for implementing mitigation measures. However, understanding the landscape-context and the spatial and temporal dynamics of these hotspots is challenging. Here, we investigate the factors that drive the spatiotemporal variation of bat mortality hotspots on roads along three years. We hypothesize that hotspot locations occur where bat activity is higher and that this activity is related to vegetation density and productivity, probably because this is associated with food availability. Statistically significant clusters of bat-vehicle collisions for each year were identified using the Kernel Density Estimation (KDE) approach. Additionally, we used a spatiotemporal analysis and generalized linear mixed models to evaluate the effect of local spatiotemporal variation of environmental indices and bat activity to predict the variation on roadkill hotspot locations and to asses hotspot strength over time. Between 2009 and 2011 we conducted daily surveys of bat casualties along a 51-km-long transect that incorporates different types of roads in southern Portugal. We found 509 casualties and we identified 86 statistically significant roadkill hotspots, which comprised 12% of the road network length and contained 61% of the casualties. Hotspots tended to be located in areas with higher accumulation of vegetation productivity along the three-year period, high bat activity and low temperature. Furthermore, we found that only 17% of the road network length was consistently classified as hotspots across all years; while 43% of hotspots vanished in consecutive years and 40% of new road segments were classified as hotspots. Thus, non-persistent hotspots were the most frequent category. Spatiotemporal changes in hotspot location are associated with decreasing vegetation production and increasing water stress on road surroundings. This supports our hypothesis that a decline on overall vegetation productivity and increase of roadside water deficit, and the presumed lower abundance of prey, have a significant effect on the decrease of bat roadkills. To our knowledge, this is the first study demonstrating that freely available remote sensing data can be a powerful tool to quantify bat roadkill risk and assess its spatiotemporal dynamics.

The Role of Options in Goals-Based Wealth Management

We develop a facile methodology using dynamic programming for goals-based wealth management over long horizons where rebalancing uses the standard securities and also derivative securities. A kernel density estimation approach is developed to accommodate any number of derivative assets, solving a high dimensional problem with fast computation. The approach easily accommodates skewed and fat-tailed distributions. Portfolio performance is much better with the use of options, especially for investors with aggressive goals.

Mapping global urban boundaries from the global artificial impervious area (GAIA) data

Urban boundaries, an essential property of cities, are widely used in many urban studies. However, extracting urban boundaries from satellite images is still a great challenge, especially at a global scale and a fine resolution. In this study, we developed an automatic delineation framework to generate a multi-temporal dataset of global urban boundaries (GUB) using 30 m global artificial impervious area (GAIA) data. First, we delineated an initial urban boundary by filling inner non-urban areas of each city. A kernel density estimation approach and cellular-automata based urban growth modeling were jointly used in this step. Second, we improved the initial urban boundaries around urban fringe areas, using a morphological approach by dilating and eroding the derived urban extent. We implemented this delineation on the Google Earth Engine platform and generated a 30 m resolution global urban boundary dataset in seven representative years (i.e. 1990, 1995, 2000, 2005, 2010, 2015, and 2018). Our extracted urban boundaries show a good agreement with results derived from nighttime light data and human interpretation, and they can well delineate the urban extent of cities when compared with high-resolution Google Earth images. The total area of 65 582 GUBs, each of which exceeds 1 km2, is 809 664 km2 in 2018. The impervious surface areas account for approximately 60% of the total. From 1990 to 2018, the proportion of impervious areas in delineated boundaries increased from 53% to 60%, suggesting a compact urban growth over the past decades. We found that the United States has the highest per capita urban area (i.e. more than 900 m2) among the top 10 most urbanized nations in 2018. This dataset provides a physical boundary of urban areas that can be used to study the impact of urbanization on food security, biodiversity, climate change, and urban health. The GUB dataset can be accessed from http://data.ess.tsinghua.edu.cn.

A novel environmental contour method for predicting long-term extreme wave conditions

Abstract This paper proposes a novel environmental contour line method based on measured ocean wave data for predicting the long-term extreme wave conditions. For implementing the proposed environmental contour line method, a bivariate kernel density estimation approach is used along with over-smoothed bandwidth selection. The environmental contours obtained using the proposed method have been compared with those obtained using the Gaussian copula (Nataf transformation) method and another parameterized model, and the effectiveness and superiority of the proposed method have been clearly substantiated. The research results in this paper demonstrate that the proposed method can be utilized as an effective tool for predicting the long-term extreme wave conditions.

On the Distribution Modeling of Heavy-Tailed Disk Failure Lifetime in Big Data Centers

It has become commonplace to observe frequent multiple disk failures in big data centers in which thousands of drives operate simultaneously. Disks are typically protected by replication or erasure coding to guarantee a predetermined reliability. However, in order to optimize data protection, real life disk failure trends need to be modeled appropriately. The classical approach to modeling is to estimate the probability density function of failures using nonparametric estimation techniques such as kernel density estimation (KDE). However, these techniques are suboptimal in the absence of the true underlying density function. Moreover, insufficient data may lead to overfitting. In this article, we propose to use a set of transformations to the collected failure data for almost perfect regression in the transform domain. Then, by inverse transformation, we analytically estimated the failure density through the efficient computation of moment generating functions, and hence, the density functions. Moreover, we developed a visualization platform to extract useful statistical information such as model-based mean time to failure. Our results indicate that for other heavy-tailed data, the complex Gaussian hypergeometric distribution and classical KDE approach can perform best if the overfitting problem can be avoided and the complexity burden is overtaken. On the other hand, we show that the failure distribution exhibits less complex Argus-like distribution after performing the Box-Cox transformation up to appropriate scaling and shifting operations.

Assessment of attenuation regressions for earthquake-triggered landslides in the Italian Apennines: insights from recent and historical events

We address the modeling of spatial distribution of coseismic landslides, based on an empirical approach applied to both recent and historical well-documented events. We analyze a dataset of 11 historical and recent normal faulting earthquakes in the Italian Central Apennines. Firstly, making use of a kernel density estimator approach, we calculated the regression between the extent of the maximum area affected by landslides (A; km2) and Mw, on the combined dataset of recent and historic earthquakes: Log A = (1.0397 Mw)–3.9288. Then, for recent earthquakes only, we analyzed the attenuation regression of landslide density (Dens; no. of landslides/km2) with distance from surface fault trace (Dfault; meters): Dens = 0.3661 × exp (− 5.053 Dfault). Historical events, still presenting systematically lower values of landslide densities, can be regressed on the same functional form resulting in a similar factor of attenuation with distance but with a different scaling factor. We thus argue that empirical regressions on historical earthquake-triggered landslides can be successfully exported elsewhere if a well-documented catalog is present and a calibration with several recent events can be done.

A Flexible Method for Estimating Luminosity Functions via Kernel Density Estimation

Abstract We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding the binning of LFs. One challenge in applying KDE to LFs is how to treat the boundary bias problem, as astronomical surveys usually obtain truncated samples predominantly due to the flux-density limits of surveys. We use two solutions, the transformation KDE method ( ) and the transformation–reflection KDE method ( ) to reduce the boundary bias. We develop a new likelihood cross-validation criterion for selecting optimal bandwidths, based on which the posterior probability distribution of the bandwidth and transformation parameters for and are derived within a Markov Chain Monte Carlo sampling procedure. The simulation result shows that and perform better than the traditional binning method, especially in the sparse data regime around the flux limit of a survey or at the bright end of the LF. To further improve the performance of our KDE methods, we develop the transformation–reflection adaptive KDE approach ( ). Monte Carlo simulations suggest that it has good stability and reliability in performance, and is around an order of magnitude more accurate than using the binning method. By applying our adaptive KDE method to a quasar sample, we find that it achieves estimates comparable to the rigorous determination in a previous work, while making far fewer assumptions about the LF. The KDE method we develop has the advantages of both parametric and nonparametric methods.

Analyzing traffic violation behavior at urban intersections: A spatio-temporal kernel density estimation approach using automated enforcement system data

The Automated Enforcement System (AES) has become the most important traffic enforcement system in China. In this study, a spatio-temporal kernel density estimation (STKDE) model, integrating spatio-temporal statistics and three-dimensional visualization techniques, was applied to reveal the spatial and temporal patterns of traffic violation behavior at urban intersections. The multivariate Gaussian kernel function was selected for space and time density estimation, as it has been shown to be a good arbitrary probability density function for continuous multivariate data. Because the STKDE model builds a space-time cube that adopts different colors of voxels to visualize the density of traffic violations, an optimal bandwidth selector that combines unconstrained pilot bandwidth matrices with a data-driven method was selected for achieving the best visualization result. The raw AES traffic violation data over 200 weekdays from 69 intersections in the city of Wujiang were empirically analyzed. The results show that the STKDE space-time cube made it easier to detect the spatio-temporal patterns of traffic violations than did the traditional hotspots map. An interesting finding was that traffic sign violations and traffic marking violations were primarily concentrated not in regular peak hours, but during the time period of 14:00-16:00, which indicates that these intersections were the most congested during this period. Primarily, the STKDE model identified seven patterns of spatio-temporal traffic violation hotspots and coldspots. These results are important because their prediction of temporal trends of traffic violations may help contribute toward the understanding and improvement of intersection safety problems.

A kernel density estimation approach of North Indian Ocean tropical cyclone formation and the association with convective available potential energy and equivalent potential temperature

Tropical cyclone (TC) is the one of the most devastating weather systems which causes enormous loss of life and property in the coastal regions of North Indian Ocean (NIO) rim countries. TC modelling can help decision-makers and inhabitants in shoreline zones to take necessary planning and actions in advance. To model TC activity, it is essential to know the factors that affect TC activities. The formation of tropical cyclones in the NIO basin is significantly modulated by Convective Available Potential Energy (CAPE) and Equivalent Potential Temperature (EPT). In this paper, a kernel density estimation approach (KDE) has been developed and evaluated to determine the extent of this modulation for the period 1979-2016. The distribution of genesis was defined by the KDE approach and validated by both classical and standard plug-in estimators. Results suggest a strong correlation of TC genesis densities with CAPE in the month of October-November (post-monsoon season) followed by the month of April-May (pre-monsoon season). Findings indicate the potential for predicting TC activities in the NIO well before the TC season.

Real-Time Event Classification in Power System With Renewables Using Kernel Density Estimation and Deep Neural Network

Real-time classification of events facilitates corrective control strategies, supervisory protection schemes, and on-line transient stability assessment of a power system. The synchrophasor-based event classification techniques face challenges like similar responses for different classes of events, i.e., inter-class similarity (ICS), applicability to limited classes of events, and moderate real-time performance for a large power system. In addition, the enhanced ICS effect of increased renewable penetration on events classification needs to be addressed. This paper proposes a kernel density estimation approach for accurate real-time classification of events in a power system with renewables using synchrophasor data. The proposed method uses a diffusion type kernel density estimator (DKDE) to characterize the shape of 3-D voltage and frequency distribution along time in terms of probability density functions (PDFs). That have distinct scale, shape, and orientation for different classes of events. Thereafter, a set of statistical features is derived from PDFs to train a multi-layered deep neural network for event classification. The proposed method is validated for renewables in IEEE-39 bus system and real transmission system of India grid using DIgSILENT/PowerFactory and also on a real phasor measurement unit data for India grid, where it showed better performance for ICS and renewable integration cases.