A new method for varying adaptive bandwidth selection

Designing tests able to effectively detect changes in the stationarity of a process generating data is a challenging problem, in particular when the process is unknown, and the only information available has to be extracted from a set of observations. This work proposes a novel approach for detecting changes in a process generating data whose distribution is unknown. Peculiarity of the approach is the use of the Intersection of Confidence Intervals (ICI) rule to monitor the process evolution. A change detection test derived from this approach is also presented. Experimental results show that the proposed test outperforms state-of-the art solutions, both in terms of efficiency and effectiveness, in particular when a reduced test configuration set is available.

Time-varying covariance is an important metric to measure the statistical dependence between non-stationary biological processes. Time-varying covariance is conventionally estimated from short-time data segments within a window having a certain bandwidth, but it is difficult to choose an appropriate bandwidth to estimate covariance with different degrees of non-stationarity. This paper introduces a local polynomial regression (LPR) method to estimate time-varying covariance and performs an asymptotic analysis of the LPR covariance estimator to show that both the estimation bias and variance are functions of the bandwidth and there exists an optimal bandwidth to minimize the mean square error (MSE) locally. A data-driven variable bandwidth selection method, namely the intersection of confidence intervals (ICI), is adopted in LPR for adaptively determining the local optimal bandwidth that minimizes the MSE. Experimental results on simulated signals show that the LPR-ICI method can achieve robust and reliable performance in estimating time-varying covariance with different degrees of variations and under different noise scenarios, making it a powerful tool to study the dynamic relationship between non-stationary biomedical signals. Further, we apply the LPR-ICI method to estimate time-varying covariance of functional magnetic resonance imaging (fMRI) signals in a visual task for the inference of dynamic functional brain connectivity. The results show that the LPR-ICI method can effectively capture the transient connectivity patterns from fMRI.

Healthcare professionals prescribe foot orthoses (FOs) for treatment and prevention of lower limb injuries, but previous reviews of the effectiveness of FOs have been inconclusive. We have therefore performed a review emphasizing the magnitude of treatment effects to evaluate the clinical effectiveness of FOs in the treatment and prevention of lower limb injuries.Qualifying studies were mainly controlled trials, but some uncontrolled clinical trials of patients with chronic injuries were analysed separately. Injuries included plantar fasciitis, tibial stress fractures and patellofemoral pain syndrome; these were included because of the large treatment costs for these frequent injuries in New Zealand. Outcomes were pain, comfort, function and injury status. Continuous measures were expressed as standardized differences using baseline between-subject standard deviations, and magnitudes were inferred from the intersection of 90% confidence intervals with thresholds of a modified Cohen scale. Effects based on frequencies were expressed as hazard ratios and their magnitudes were inferred from intersection of confidence intervals with a novel scale of thresholds.The effects of FOs for treatment of pain or injury prevention were mostly trivial. FOs were not effective in treating or preventing patellofemoral pain syndrome. Some studies showed moderate effects for treatment of plantar fasciitis. Only a few studies showed moderate or large beneficial effects of FOs in preventing injuries.Customized semi-rigid FOs have moderate to large beneficial effects in treating and preventing plantar fasciitis and posterior tibial stress fractures, and small to moderate effects in treating patellofemoral pain syndrome. Given the limited randomized controlled trials or clinical controlled trials available for the injuries of interest, it may be that more or less benefit can be derived from the use of FOs, but many studies did not provide enough information for the standardized effect sizes to be calculated. Further research with randomized controlled trials is needed to establish the clinical utility of a variety of FOs for the treatment and prevention of various lower limb injuries.

The problem of reconstructing a signal waveform when the observed realizations are corrupted by intensive noise and random shifts is considered in this paper. Several ways of performing bispectrum filtering are proposed and investigated. First, it is shown that the signal reconstruction is more efficient if one applies smoothing to the recovered real and imaginary parts of the Fourier spectrum separately instead of filtering the magnitude and phase spectra recovered from a bispectrum estimate. Second, several nonadaptive filters are studied, and it is demonstrated that the proper choice of the filter type and its parameters is critical. Some adaptive filtering techniques based on the Z-parameter and on local polynomial approximation (LPA)-intersection of confidence intervals (ICI) are discussed. The performances of nonadaptive and adaptive filtering techniques in the bispectrum-based signal reconstruction are studied using the mean-squared error as the criterion. It is shown that the use of LPA-ICI and other adaptive filters provides improvement of signal reconstruction in comparison to the conventional bispectrum method and the combined bispectrum filtering methods proposed earlier for nonadaptive filters. The benefits achieved are mainly observed for low (smaller than unity) signal-to-noise ratios.

Image gradient, as a preprocessing step is an essential tool in image processing in many research areas such as edge detection, segmentation, smoothing, inpainting, etc. In the present paper, we develop a new gradient by integrated the quaternion framework with LPA-ICI (local polynomial approximation – the intersection of confidence intervals) based on anisotropic gradient concepts for the color image processing applications. Computer simulations on the Berkeley Segmentation Dataset show that the new quaternion anisotropic gradient exhibits fewer color artifacts compared to state-of-the-art techniques including well-knowledge gradient operators.

SummaryDemosaicing and denoising are the most significant steps in the imaging process for both images and videos. The correlation noise corrupts the image quality, such that an accurate interpretation of the image is avoided. Thus, demosaicing is utilized to restructure the full‐color image from imperfect color samples. In this article, cat shuffled shepherd optimization‐based local polynomial approximation and intersection of confidence intervals (Cat SSO‐based LPA‐ICI) approach is developed for video demosaicing. The LPA‐ICI model is employed for frame demosaicing in which the second‐order polynomial interpolation filter coefficients are produced using the devised optimization algorithm, named cat SSO technique. Similarly, generative adversarial network classifier is also applied for frame demosaicing. In addition, initialization and flow estimation is performed for the demosaicing process. Besides, spatio temporal demosaicing model is utilized in order to get a noise‐free sequence. However, the developed cat SSO technique is newly devised by the incorporation of the shuffled shepherd optimization algorithm and cat swarm optimization technique. The created video demosaicing model outperformed with peak signal‐to‐noise ratio, root mean square error, and second derivative‐like measure of enhancement values of 56.85 dB, 0.46, and 60.62, respectively.

Kernel density estimation (KDE) is a widely used method in geography to study concentration of point pattern data. Geographical networks are 1.5 dimensional spaces with specific characteristics, analyzing events occurring on networks (accidents on roads, leakages of pipes, species along rivers, etc.). In the last decade, they required the extension of spatial KDE. Several versions of Network KDE (NKDE) have been proposed, each with their particular advantages and disadvantages, and are now used on a regular basis. However, scant attention has been given to the temporal extension of NKDE (TNKDE). In practice, when the studied events happen at specific time points and are constrained on a network, the methodologies used by geographers tend to overlook either the network or the temporal dimension. Here we propose a TNKDE based on the recent development of NKDE and the product of kernels. We also adapt classical methods of KDE (Diggle's correction, Abramson's adaptive bandwidth and bandwidth selection by leave‐one‐out maximum likelihood). We also illustrate the method with Montreal road crashes involving a pedestrian between 2016 and 2019.

An improved mean shift segmentation method featuring adaptive parameter selection is presented in this paper. We associate the bandwidths and weight for each point in a spatial-range feature space with boundary information in an image plane. Varying weight and bandwidth for each pixel are assigned according to a boundary map, which is obtained by learning multiple edge cues. We consider two groups of edge cues and two regressing modules, approach the cue combination as a supervised learning problem from the ground truth data (manually sketched boundary maps). From our preliminary results, the provided method can combine the top-down information got from regression models with the mean shift process and constrain over-clustering of pixels belonging different land objects.

We propose a short-time polynomial regression (STPR) for time-varying signal analysis. The advantage of using polynomials is that the notion of a spectrum is not needed and the signals can be analyzed in the time domain over short durations. In the presence of noise, such modeling becomes important, because the polynomial approximation performs smoothing leading to noise suppression. The problem of optimal smoothing depends on the duration over which a fixed-order polynomial regression is performed. Considering the STPR of a noisy signal, we derive the optimal smoothing window by minimizing the mean-square error (MSE). For a fixed polynomial order, the smoothing window duration depends on the rate of signal variation, which, in turn, depends on its derivatives. Since the derivatives are not available a priori, exact optimization is not feasible. However, approximate optimization can be achieved using only the variance expressions and the intersection-of-confidence-intervals (ICI) technique. The ICI technique is based on a consistency measure across confidence intervals corresponding to different window lengths. An approximate asymptotic analysis to determine the optimal confidence interval width shows that the asymptotic expressions are the same irrespective of whether one starts with a uniform sampling grid or a nonuniform one. Simulation results on sinusoids, chirps, and electrocardiogram (ECG) signals, and comparisons with standard wavelet denoising techniques, show that the proposed method is robust particularly in the low signal-to-noise ratio regime.

Signals in HF radio channels are suffered from the effect of delay spread, time-varying interference and additive Gaussian noise. The performances of two differential modulation methods FDDD and TDDD for OFDM system are analyzed in this paper. By analysis and simulations, the relationship of the subcarrier bandwidth and BER is demonstrated, which shows that the selection of optimal subcarrier bandwidth contributes largely to the performance of HF communications.

In an environment of shared radio spectrum, multiple systems may interfere with each other and cause significant impacts on system coexistence. In this paper we propose an adaptive subband selection technique based on orthogonal frequency division multiplexing (OFDM) to avoid interference for better system coexistence when multiple systems are operating in the same unlicensed industrial, scientific and medical (ISM) bands. Under the assumption that the interference power level and the interfered frequency bands are identified at the receiver, interference thresholds, determined over both Gaussian and multipath fading channels, are applied to adaptively select the transmission subbands so that interference is avoided and the system coexistence issues are relaxed. To verify the effectiveness of the proposed adaptive subband selection method, the system bit error rates (BERs) under different interference levels are simulated and compared.

Nadaraya-Watson kernel regression estimator (NWKRE) is a typical kernel regression estimator which is a kernel-based and non-parametric regression method to estimate the conditional expectation of a random variable and the non-linear mapping from input to output. For NWKRE, the selection of bandwidth, i.e., smoothing parameter h, plays a very important role in the fitting performance. In order to enhance the performance of NWKRE, an adaptive Nadaraya-Watson kernel regression estimator is proposed, ANWKRE for short. There are two main strategies to determine the adaptive or local bandwidth factor λ: geometric mean and arithmetic mean based determination methods, respectively. In this paper, we firstly investigate the mathematical properties of geometric mean and arithmetic mean in the framework of regression analysis. Then, some experimental comparisons are conducted to demonstrate our theoretical results. The experimental results find that the arithmetic mean based ANWKRE can obtain a smoother regression estimation for unknown function.

Particle-based transport models are widely used for simulating the movement of pollutants in environmental systems. Unlike grid-based methods, particles naturally address advective transport without numerical dispersion. However, these models require concentration reconstruction from the discrete particle information. This is computationally demanding in multidimensional problems, posing a challenge for field-scale models requiring frequent reconstruction. Grid Projected Kernel Density Estimation (GPKDE) is a cell-averaged reconstruction with improvements in computational performance compared to classical KDE. Currently, no programs implementing this method are readily integrated into particle simulators, compatible with three-dimensional domains, and particles with unequal weights. This article introduces a Fortran code for general-purpose GPKDE, with modular functionalities facilitating the integration into external software. The program implements locally adaptive kernel bandwidth selection and alternatives for the reconstruction from particles with non-uniform weights. The code is parallelized with the OpenMP library. Numerical test cases demonstrate the program’s applicability and scalability of the parallel implementation.

Diabetes mellitus poses a growing global health concern, particularly in low- and middle-income countries where early detection remains limited, demanding classification models that balance accuracy, interpretability, and adaptability to heterogeneous clinical data. This study proposes and evaluates the Adaptive Kernel Probability Model (AKPM), a novel nonparametric probabilistic classifier designed to enhance diabetes prediction by performing localized kernel density estimation with adaptive bandwidth selection via k-nearest neighbors. Implemented and tested on the Pima Indians Diabetes Dataset, AKPM outperformed conventional classifiers—Naïve Bayes and Gaussian Mixture Models (GMM)—across all evaluation metrics, achieving 87.5% accuracy, 83.3% precision, 76.9% recall, and an F1-score of 80.0% for the diabetic class, alongside 89.3% precision and 92.6% recall for the normal class. These results surpassed GMM (83.0% accuracy, 71.6% F1-score) and Naïve Bayes (80.0% accuracy, 66.6% F1-score), confirming AKPM’s superior capability to detect diabetic cases while minimizing false negatives. Offering transparent posterior inference and a modular design, AKPM emerges as a reliable and interpretable solution for clinical decision support systems and real-world healthcare applications.

The results of a study noise filtering in temperature time series measuring channels using basic frequency filtering algorithms are presented. The study was carried out from the perspective of high frequency random noise suppression. Temperature time series filtering was compared using sliding window procedures with adaptive bandwidth selection, median sliding window, and Baxter-King band-pass approximation. Experimental comparative analysis of filtering efficiency was carried out using the statistical programming language R and open libraries with sliding regression methods. The recorders of surface atmosphere parameters were ultrasonic meteorological stations located at the test site of IMKES SB RAS.