Data classification with a relaxed model of variable kernel density estimation

A simple and effective object recognition scheme is to represent and march images on the basis of color histograms. To obtain robustness against varying imaging circumstances (e.g. a change in illumination, object pose, and viewpoint), color histograms are constructed from color invariants. However in general, color invariants are negatively affected by sensor noise due to the instabilities of these color invariant transforms at many RGB values. To suppress the effect of noise blow-up for unstable color invariant values, in this paper color invariant histograms are computed using variable kernel density estimators. To apply variable kernel density estimation in a principled way, models are proposed for the propagation of sensor noise through color invariants. As a result the associated uncertainty is known for each color invariant value. The associated uncertainty is used to derive the parameterization of the variable kernel density estimator during histogram construction. It is empirically verified that the proposed method compares favorably to traditional color histograms for object recognition.

Short-term wind speed forecasting is essential for enhancing the efficiency and dependability of wind renewable energy installations. Although often used, conventional point predictions generated by machine learning techniques frequently fail to accurately capture the natural uncertainty associated with wind speed variation. Modeling this type of uncertainty is crucial for providing credible information as the level of uncertainty increases. Prediction intervals (PIs) offer a probabilistic framework for quantifying forecast uncertainty. This paper presents a hybrid forecasting methodology that combines support vector regression (SVR) with adaptive kernel density estimation (AKDE) to estimate wind speed prediction intervals over various short-term horizons (10, 30, 60, and 120 minutes). In contrast to standard kernel density estimation (KDE), which employs a uniform bandwidth and may overlook local data attributes, the adaptive KDE approach adjusts the bandwidth in accordance with the local distribution of forecast errors, thereby facilitating more precise and locally tuned uncertainty quantification. The efficacy of the proposed SVR-AKDE model is evaluated against conventional KDE-based interval estimation. Outcomes are assessed by recognized PI quality indicators, including prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW), and coverage width-based criterion (CWC). Simulation findings confirm the efficacy of our approach and demonstrate that the SVR-AKDE-based PI forecasting consistently provides enhanced coverage and narrower widths compared to traditional KDE. This approach provides a comprehensive solution for short-term wind speed forecasting with quantifiable uncertainty, therefore enhancing its application in operational wind energy control.

Radio source counts provide a fundamental census of cosmic radio emission, yet their estimation is usually based on coarse histograms that suffer from bin-choice bias, boundary effects, and survey incompleteness. We apply and rigorously evaluate kernel density estimation (KDE) as a nonparametric alternative to the conventional binned method for estimating differential radio source counts. Using simulated flux-limited samples derived from an input luminosity function model, we compare the performance of standard KDE, adaptive KDE, and traditional binning methods. Our results show that KDE-based approaches yield more accurate and stable estimates, particularly in the high-flux regime where data are sparse and conventional methods struggle. We also apply the adaptive KDE method to real observational data from the LOFAR Two-Metre Sky Survey Deep Fields. Our analysis robustly confirms the pronounced “drop and bump” feature at sub-mJy flux densities, but also reveals that a secondary, modest bump seen in the binned data at ∼10 mJy is likely a binning artifact. We also demonstrate the flexibility of KDE in addressing observational incompleteness through weighted estimation, which applies weights continuously at the level of individual sources rather than averaging them in discrete bins. These strengths make KDE a powerful tool for source-count analyses in current and future radio surveys and, more broadly, in analogous studies at other wavelengths. All computations in this study are implemented with AstroKDE , a Python package we have developed for astronomical applications.

Nowadays IoT and big data technologies make it easy to collect a huge amount of precise data about geospatial mobility. This abundant data improves mobility systems' study and optimization by allowing the application of data-driven approaches to gather accurate mobility models. In this paper, we evaluate techniques based on the optimization of Kernel Density Estimation (KDE) for modelling and generalizing the observed spatial data. We show how traditional KDE models fail to generalize the information obtained from mobility datasets, if not properly tuned. This mostly comes from the heterogeneity of the data, which changes over time (e.g., day and night) and space (e.g., dense or suburban areas). These issues call for fine grained parameter tuning, which we solve by automatically finding the optimal parameters for classical and variable KDE (V-KDE) approaches. We extensively compare the models' errors in capturing the mobility patterns using car sharing data. Our results show how optimized KDE and V-KDE models can better capture mobility patterns than traditional KDE approaches, both in 2D (i.e., origin or destination only) or 4D (i.e., representing origin-destination matrices) scenarios. We offer our tool available as open-source as a python module.

Reliability analysis techniques combining with various surrogate models have attracted increasing attention because of their accuracy and great efficiency. However, they primarily focus on the structures with continuous response, while very rare researches on the reliability analysis for structures with discontinuous response are carried out. Furthermore, existing adaptive reliability analysis methods based on importance sampling (IS) still have some intractable defects when dealing with small failure probability, and there is no related research on reliability analysis for structures involving discontinuous response and small failure probability. Therefore, this paper proposes a novel reliability analysis method called AGPC-IS for such structures, which combines adaptive Gaussian process classification (GPC) and adaptive-kernel-density-estimation-based IS. In AGPC-IS, an efficient adaptive strategy for design of experiments (DoE), taking into consideration the classification uncertainty, the sampling uniformity and the regional classification accuracy improvement, is developed with the purpose of improving the accuracy of Gaussian process classifier. The adaptive kernel density estimation is introduced for constructing the quasi-optimal density function of IS. In addition, a novel and more precise stopping criterion is also developed from the perspective of the stability of failure probability estimation.The efficiency, superiority and practicability of AGPC-IS are verified by three examples

For engineering, there are two major challenges in reliability analysis. First, to ensure the accuracy of simulation results, mechanical products are usually defined implicitly by complex numerical models that require time-consuming. Second, the mechanical products are fortunately designed with a large safety margin, which leads to a low failure probability. This paper proposes an efficient and high-precision adaptive active learning algorithm based on the Kriging surrogate model to deal with the problems with low failure probability and time-consuming numerical models. In order to solve the problem with multiple failure regions, the adaptive kernel-density estimation is introduced and improved. Meanwhile, a new criterion for selecting points based on the current Kriging model is proposed to improve the computational efficiency. The criterion for choosing the best sampling points considers not only the probability of misjudging the sign of the response value at a point by the Kriging model but also the distribution information at that point. In order to prevent the distance between the selected training points from too close, the correlation between training points is limited to avoid information redundancy and improve the computation efficiency of the algorithm. Finally, the efficiency and accuracy of the proposed method are verified compared with other algorithms through two academic examples and one engineering application.

We study kernel density estimator from the ranked set samples (RSS). In the kernel density estimator, the selection of the bandwidth gives strong influence on the resulting estimate. In this article, we consider several different choices of the bandwidth and compare their asymptotic mean integrated square errors (MISE). We also propose a plug-in estimator of the bandwidth to minimize the asymptotic MISE. We numerically compare the MISE of the proposed kernel estimator (having the plug-in bandwidth estimator) to its simple random sampling counterpart. We further propose two estimators for a symmetric distribution, and show that they outperform in MISE all other estimators not considering symmetry. We finally apply the methods in this article to analyzing the tree height data from Platt et al. (1988) and Chen et al. (2003).

This paper presents a novel method for designing an adaptive control system using radial basis function neural network. The method is capable of dealing with nonlinear stochastic systems in strict-feedback form with any unknown dynamics. The proposed neural network allows the method not only to approximate any unknown dynamic of stochastic nonlinear systems, but also to compensate actuator nonlinearity. By employing dynamic surface control method, a common problem that intrinsically exists in the back-stepping design, called “explosion of complexity”, is resolved. The proposed method is applied to the control systems comprising various types of the actuator nonlinearities such as Prandtl–Ishlinskii (PI) hysteresis, and dead-zone nonlinearity. The performance of the proposed method is compared to two different baseline methods: a direct form of backstepping method, and an adaptation of the proposed method, named APIC-DSC, in which the neural network is not contributed in compensating the actuator nonlinearity. It is observed that the proposed method improves the failure-free tracking performance in terms of the Integrated Mean Square Error (IMSE) by 25%/11% as compared to the backstepping/APIC-DSC method. This depression in IMSE is further improved by 76%/38% and 32%/49%, when it comes with the actuator nonlinearity of PI hysteresis and dead-zone, respectively. The proposed method also demands shorter adaptation period compared with the baseline methods.

The analysis of survival functions is concerned with knowing how long humans will survive, This means studying and analyzing the time from the beginning of the disease to the end point of death. For example, the survival function of patients with heart attacks was studied and analyzed at Al Manathira General Hospital. The Weibull distribution was used to match the real data. The scale parameter & survival function have been estimated for Weibull distribution with have two parameters, this distribution was used in two cases, prior data unconflict & prior data conflict. A regular Bayes method & robust Bayes were used for estimation. We used inverse gamma distribution as a prior where it is a conjugate prior for Weibull distribution. Two simulation experiments have been used; the first experiment used was prior data unconflict where the regular Bayes method is the best for estimating the scale & survival function by using the integrated mean square error (IMSE) as a criterion for comparing. The second experiment is in the case of prior data conflict. The results showed that the robust Bayes method is the best for estimation of the scale parameter & survival function by using (IMSE).

The existence of missing geomagnetic reversals has been proposed, with potential for new magnetostratigraphic age controls. We estimate geomagnetic reversal frequency from 0 to 155 Ma using adaptive‐bandwidth kernel density estimation (AKDE) to evaluate data sparseness and to assess how reversal frequency changes when recently identified geomagnetic reversals are incorporated into the geomagnetic polarity time scale (GPTS) data set. AKDE is a two‐stage procedure that uses an initial density estimator based on an initial (pilot) bandwidth. We found that the pilot bandwidth determined using cross‐validation is stable with respect to data set length. The AKDE results obtained based on the cross‐validated pilot bandwidth reveal four troughs after the Cretaceous Normal Superchron, spaced 13.5–15.0 Myr apart and corresponding to relatively long chrons (>0.8 Myr). One trough near 32 Ma becomes less distinct after the four recently identified reversals are added to the data set. This sensitivity suggests that troughs in the frequency curve may indicate missing geomagnetic reversals.

Density estimation is an important aspect of statistics. Statistical inference often requires the knowledge of observed data density. A common method of density estimation is the kernel density estimation (KDE). It is a nonparametric estimation approach which requires a kernel function and a window size (smoothing parameter H). It aids density estimation and pattern recognition. So, this work focuses on the use of a modified intersection of confidence intervals (MICIH) approach in estimating density. The Nigerian crime rate data reported to the Police as reported by the National Bureau of Statistics was used to demonstrate this new approach. This approach in the multivariate kernel density estimation is based on the data. The main way to improve density estimation is to obtain a reduced mean squared error (MSE), the errors for this approach was evaluated. Some improvements were seen. The aim is to achieve adaptive kernel density estimation. This was achieved under a sufficiently smoothing technique. This adaptive approach was based on the bandwidths selection. The quality of the estimates obtained of the MICIH approach when applied, showed some improvements over the existing methods. The MICIH approach has reduced mean squared error and relative faster rate of convergence compared to some other approaches. The approach of MICIH has reduced points of discontinuities in the graphical densities the datasets. This will help to correct points of discontinuities and display adaptive density. Keywords: approach, bandwidth, estimate, error, kernel density

To improve the efficiency of differential mobile robots (DWMR), improving their trajectory tracking capabilities is important. Especially in navigation problems with complex paths. This paper presents a new combination of Backstepping Controller (BSC) and Fractional Order Proportional-IntegralDerivative (FOPID) controller for DWMR. The improved Grey Wolf Optimization (GWO) strategy combines GWO with the Slime Molding Algorithm (SMA) to determine the parameters of FOPID. The designed controller addresses the nonlinearities, ensuring system stability and accurate trajectory tracking. The cost function used for the optimization process is a combination of Integral Absolute Error (IAE) and Integral Mean Square Error (ISE) to minimize the state deviation and enhance the response capability. The results are demonstrated through simulations on MATLAB-Simulink with different trajectory scenarios and compared with state-of-the-art optimization techniques such as PSO or GWO. The results show that the controller helps to improve the trajectory tracking ability, the cost function and the position error are improved compared to other optimization techniques.

A bandwidth selection method that combines the concept of least-squares cross-validation and the plug-in approach is being introduced in connection with kernel density estimation. A simulation study reveals that this hybrid methodology outperforms some commonly used bandwidth selection rules. It is shown that the proposed approach can also be readily employed in the context of variable kernel density estimation. We conclude with two illustrative examples.

There is a lot of indoor air pollution, especially from cigarette smoke, wall paint, air fresheners and gas. With this situation, the room uses Air Box WP6003 air quality detection device by transmitting information about air quality through visualization index. This study aims to improve prediction accuracy with fuzzy time series methods processed through 2 naïve and moving average models using forecast transformers and without transformers. The level of prediction accuracy is calculated through several metrics, namely Mean Absolute Percentage Error (MAPE), Sum of Squares Error (SSE), Mean Square Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). These results can be calculated between the actual value and the predicted value. The data used is 204584 data from 4 parameters including Temperature, TVOC, HCHO and CO2. The test results with the difference from the forecast transformer and without transformer are comparable. Temperature value obtained using naïve with transformer from RMSE of 0.158866 and naïve without transformer of 0.782397, data using moving average with transformer obtained by 0.147546 and moving average without transformer of 0.772570. This can be explained by the error analysis that was tried, where the error rate continued to increase so that the experimental results continued to be far from the actual number. From the test results it can be concluded that the accuracy of air quality prediction using naïve forecast transformer is pretty accurate.

Summary We consider dynamic discrete choice models with heterogeneity in both the levels parameter and the state dependence parameter. We first present an empirical analysis that motivates the theoretical analysis which follows. The theoretical analysis considers a simple two-state, first-order Markov chain model without covariates in which both transition probabilities are heterogeneous. Using such a model we are able to derive exact small sample results for bias and mean squared error (MSE). We discuss the maximum likelihood approach and derive two novel estimators. The first is a bias corrected version of the Maximum Likelihood Estimator (MLE) although the second, which we term MIMSE, minimizes the integrated mean square error. The MIMSE estimator is always well defined, has a closed-form expression and inherits the desirable large sample properties of the MLE. Our main finding is that in almost all short panel contexts the MIMSE significantly outperforms the other two estimators in terms of MSE. A final section extends the MIMSE estimator to allow for exogenous covariates.