Kernel Probability Density Estimation Research Articles

Recognition method for biomimetic camouflage communication signal imitating cetacean click in underwater multipath channels

Focusing on the need of biomimetic camouflage communication signal recognition in underwater multipath channels, we propose a recognition method for biomimetic camouflage click communication train (BCCCT) based on time delay difference (TDD) coding in multipath channels. For the problem of multipath interference, we perform multipath determination on the received signal by autocorrelation, filter relevant peak points, determine the time delays between multipaths, and remove the multipath interference signals according to the determined time delays. A click extraction method based on the double sliding window is proposed, which locates the boundary of click by signal envelope. By analyzing the distribution characteristics of the time interval of adjacent clicks (TIAC) of BCCCT and real click train (RCT), we model the TIACs based on Gaussian kernel probability density estimation (PDE), and recognize the BCCCTs by the Convolutional Neural Networks (CNN), which takes the PDE curve as the system input. The numerical simulations and a lake experiment are carried out to measure the effectiveness of the recognition method proposed under different signal-to-noise ratios (SNR), coding parameters, and channels. The recognition accuracy can achieve 80 % at 0 dB in the constructed channels. Moreover, in the real underwater communication environment, the recognition accuracy can achieve 95 %.

Recognition method for underwater imitation whistle communication signals by slope distribution

Underwater bionic covert communication has been extensively studied. However, there are little researches on bionic communication signals recognition. We propose a recognition method for bionic binary orthogonal keying modulated signals (BBOKMSs) coded by time frequency (TF) contour. The BBOKMSs realize the covert communication by mimicking the real dolphin whistles with a series of segmented chirp rate modulated signals. We first put forward a TF contours extraction method by the dynamic adaptive threshold calculated by the cross sampling. Next, the slope of TF curve is modeled based on Gaussian kernel probability density estimation (PDE) for the slope distribution. Based on the characteristics of BBOKMSs, the characteristic parameters of PDE curve are calculated and used to recognize the BBOKMSs by support vector machine (SVM). Finally, the numerical simulations are carried out to measure the effectiveness of the recognition method proposed under different SNRs, coding parameters, and channels in this paper. It is shown that when the modulation slope is higher than 20 kHz/s and the code length is longer than 20 ms, the recognition accuracy can reach more than 90% at a SNR of −5 dB in the constructed underwater aquatic channel.

Optimization of the Kernel Probability Density Estimation of a Two-Dimensional Random Variable with Independent Components

Optimization of the Kernel Probability Density Estimation of a Two-Dimensional Random Variable with Independent Components

Analysis of the ratio of the mean square deviations of the kernel probability density estimation in the conditions of independent and dependent random variables

The influence on the approximation properties of a nonparametric probability density estimate of Rosenblatt-Parzen type of the information on the dependence of random variables is determined. The ratio of the asymptotic expressions of the mean square deviations of independent and dependent random variables is obtained. This relation for a two-dimensional random variable is considered as a quantitative assessment of the influence of information about their dependence on the approximation properties of the kernel probability density estimate. The established ratio is determined by the kind of probability density and the volumes of the initial statistical data that are used in estimating the probability densities of dependent and independent random variables. The general results obtained are considered in detail for two-dimensional linearly dependent random variables with normal distribution laws. The functional dependence of the ratio of the mean square deviations of the independent and dependent two-dimensional random variables on the correlation coefficient is determined. The dependence of the considered ratio on the volume of statistical data is analyzed. A method for estimating the functional of the second derivatives of two-dimensional random variables with normal distribution laws is developed. The results obtained are the basis for the development of modifications of “fast” procedures for optimizing kernel estimates of probability densities in conditions of large samples.

Optimization of the kernel probability density estimation of a twodimensional random variable with independent components

Optimization of the kernel probability density estimation of a twodimensional random variable with independent components

Estimation of a nonlinear functional from the probability density when optimizing nonparametric decision functions

A method for estimating the nonlinear functional of the probability density of a two-dimensional random variable is proposed. It is relevant when implementing procedures for fast bandwidths selection in the problem of optimization of kernel probability density estimates. The solution of this problem allows to significantly improve the computational efficiency of nonparametric decision rules. The basis of the proposed approach is the analysis of the formula for the optimal bandwidth of the kernel probability density estimation. In this case, the bandwidth of kernel functions is represented as the product of an indeterminate parameter and the average square deviations of random variables. The main component of an undefined parameter is a nonlinear functional of the probability density. The considered functional is determined by the type of probability density and does not depend on the density parameters. For a family of two-dimensional lognormal laws of distribution of independent random variables, the approximation errors of the considered nonlinear functional from the probability density are determined. The possibility of applying the proposed methodology when evaluating nonlinear functionals of probability densities that differ from the lognormal distribution laws is investigated. An analysis is made of the effect of the resulting approximation errors on the root-mean-square criteria for restoring a non-parametric estimate of the probability density of a two-dimensional random variable.

Dependencies Between Histogram Parameters and the Kernel Estimate of the Probability Density of a Multidimensional Random Variable

The dependencies between the sampling intervals of the domain of values of a multidimensional random variable and the blur coefficients of the kernel probability density estimate are determined. The results of an analysis of the asymptotic properties of a multidimensional nonparametric estimate of the probability density of the Rosenblatt–Parzen type and its modifications are investigated. Modification of the kernel probability density estimate is a smoothed multi-dimensional histogram. The formulas for calculating the optimal parameters of the kernel function blur coefficients and the lengths of the sampling intervals of the values of the components of a multidimensional random variable are analyzed. Blur coefficients are presented as the products of an indefinite parameter and the mean square deviations of random components. An indefinite parameter and the number of sampling intervals of multidimensional random variables are found from the condition of minimum mean square deviations of the considered probability density estimates. Based on the results obtained, the relationships between the blur coefficient parameters and the discretization procedure of the range of values of a multidimensional random variable are established. The discovered patterns are characterized by a set of constants. The constants under consideration are represented by the ratio of nonlinear functionals of the probability density and their second derivatives with respect to each random component. The values of the constants are characterized by the type of probability density and are independent of their parameters. From computational experimental data, we establish the relationships between the constants and the product of the counterexcess coefficients with the components of a multidimensional random variable. The results obtained make it possible to quickly determine the lengths of sampling intervals of the values of the components of a multidimensional random variable from the kernel function blur coefficients of a nonparametric probability density estimate.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Selection of the Blur Coefficient for Probability Density Kernel Estimates Under Conditions of Large Samples

A fast algorithm is proposed for choosing the blur factors of kernel functions of a non-parametric probability density estimate under conditions of large-scale statistical data. It is shown that the basis of the algorithm is the result of a study of the asymptotic properties of a new kernel probability density estimate. The properties of the developed algorithm are analyzed and the method of its application is formulated.

RETRACTED ARTICLE: Motion video tracking technology in sports training based on Mean-Shift algorithm

Mean-Shift is known for its real time and robustness in visual tracking. This is a very good algorithm. In recent years, the algorithm has developed rapidly and has great development prospects. This paper studies Mean-Shift theory and target tracking theory and analyses its advantages in video tracking. By combining the three-frame difference method, nearest neighbour method, and the direction parameter of the target, the Mean-Shift theory based on kernel probability density estimation is studied in the video application in moving target recognition and tracking in sequence images. First, use the prediction method to initially locate the target’s position, and then use the Mean-Shift algorithm to perform iterative calculation to determine the true position of the target. Experiments show that the Mean-Shift algorithm avoids global search, and the improved algorithm introduces the number of iterations, reduces the computational complexity of the algorithm, reduces the time consumption, and ensures the real-time tracking of the algorithm.

Fast Algorithm for Choosing Blur Coefficients in Multidimensional Kernel Probability Density Estimates

A method is proposed for quickly choosing the blur coefficients of kernel functions in a non-parametric estimate of a multidimensional probability density of Rosenblatt–Parzen type. The technique is based on the analysis of the asymptotic properties of a multidimensional probability density estimate. The properties of the fast algorithm for choosing the blur coefficients of a kernel probability density estimate are investigated.

A Generic-Driven Wrapper Embedded With Feature-Type-Aware Hybrid Bayesian Classifier for Breast Cancer Classification

Breast cancer is one of the most common cancers diagnosed in women. For preventive diagnosis, feature selection is an essential step to construct the breast cancer classifier. The features of a real breast cancer dataset are usually composed of discrete and continuous ones. Also, the Area Under the Curve (AUC) of the receiver operating characteristic receives more attention in such a medical field. The existing research work is insufficient to take into account both the hybrid trait of the features and the specific classification objective. We have proposed a wrapper method, i.e., a integrated framework in which Bayesian classifiers are embedded for the feature selection of breast cancer datasets. To deal with both the discrete features and the continuous features, we adopt the naive approach for the discrete features but the kernel probability density estimation for the continuous ones, respectively, which leads to feature-type-aware hybrid Bayesian classifiers. All the classifiers are fed with different feature subsets and evaluated by their AUC metrics as the fitness indexes. Thus, with the genetic algorithm, we can obtain a near optimal feature subset, which yields a good AUC metric with its corresponding classifiers. Moreover, the one-class F-score is used to help enhance the convergence of the algorithm. Experiments are done both with the continuous Wisconsin diagnostic breast cancer dataset and the real breast cancer dataset for Chinese women. The results prove that the proposed wrapper is feasible, accurate and efficient, compared with the related genetic algorithm based approaches.

Outlier analyses of the Protein Data Bank archive using a probability-density-ranking approach

Outlier analyses are central to scientific data assessments. Conventional outlier identification methods do not work effectively for Protein Data Bank (PDB) data, which are characterized by heavy skewness and the presence of bounds and/or long tails. We have developed a data-driven nonparametric method to identify outliers in PDB data based on kernel probability density estimation. Unlike conventional outlier analyses based on location and scale, Probability Density Ranking can be used for robust assessments of distance from other observations. Analyzing PDB data from the vantage points of probability and frequency enables proper outlier identification, which is important for quality control during deposition-validation-biocuration of new three-dimensional structure data. Ranking of Probability Density also permits use of Most Probable Range as a robust measure of data dispersion that is more compact than Interquartile Range. The Probability-Density-Ranking approach can be employed to analyze outliers and data-spread on any large data set with continuous distribution.

Blind Signal Separation with Kernel Probability Density Estimation Based on MMI Criterion Optimized by Conjugate Gradient

Blind Signal Separation with Kernel Probability Density Estimation Based on MMI Criterion Optimized by Conjugate Gradient

On some convergence properties of the subspace constrained mean shift

Subspace constrained mean shift (SCMS) is a non-parametric, iterative algorithm that has recently been proposed to find principal curves and surfaces based on a new definition involving the gradient and Hessian of a kernel probability density estimate. Although simulation results using synthetic and real data have demonstrated the usefulness of the SCMS algorithm, a rigorous study of its convergence is still missing. This paper aims to take initial steps in this direction by showing that the SCMS algorithm inherits some important convergence properties of the mean shift (MS) algorithm. In particular, the monotonicity and convergence of the density estimate values along the sequence of output values of the algorithm is shown. Also, it is shown that the distance between consecutive points of the output sequence converges to zero, as does the projection of the gradient vector onto the subspace spanned by the D−d eigenvectors corresponding to the D-d largest eigenvalues of the local inverse covariance matrix. These last two properties provide theoretical guarantees for stopping criteria. By modifying the projection step, three variations of the SCMS algorithm are proposed and the running times and performance of the resulting algorithms are compared.

Comparison of statistical downscaling techniques for multisite daily rainfall conditioned on atmospheric variables for the Sydney region

Predictions of rainfall spatial and temporal variability (including climate change effects) on a catchment basis are urgently required by water resource planners within Australia. Large spatial scale predictions of (typically 300 to 500 km grids) global scale climate scenarios output by General Circulation Models (GCMs) are inadequate for such use as they do not capture the large degree of spatial variability over smaller distances, which is inherent in rainfall. Multisite daily rainfall - a common requirement within many hydrological models - is a required input for modelling complex multi-catchment systems, as small scale spatial variability due to factors such as topography has a large bearing on how much rainfall falls in a given area. Statistical downscaling is a technique that can produce such fine spatial scale rainfall pattern predictions conditional on the larger scale climate scenarios output by a GCM. The GLIMCLIM (Generalised Linear Model for daily Climate time series) software package (Chandler, 2002) has been used to analyse and simulate spatial daily rainfall given natural climate variability influences in the UK, and further to predict the influence of various future climate scenarios on regional rainfall by downscaling larger spatial scale GCM simulations. This paper describes the comparison of this method to the non-parametric, non-homogeneous hidden Markov model - kernel probability density estimation (NNHMM-KDE) downscaling technique of Mehrotra & Sharma (2006), a method which has found application in Australia previously.

An information theoretic approach for improving data driven prediction of protein model quality

We present the results of an information theory-based approach to select an optimal subset of features for the prediction of protein model quality. The optimal subset of features was calculated by means of a backward selection procedure. The performances of a probabilistic classifier modeled by means of a Kernel Probability Density Estimation method (KPDE) were compared with those of a feed-forward Artificial Neural Network (ANN) and a Support Vector Machine (SVM).

Smoothed multi-variate histogrammed PDEs, and [formula omitted] optimisation

With increasing requirements from particle physics for effective multi-variate discrimination techniques, a number of alternative probability density estimate (PDE) methods have appeared in recent years. These relatively advanced methods attempt to form effective PDEs in the presence of low statistics where a simple histogramming method does not perform well. In this paper a multi-variate histogrammed PDE method is presented. The method incorporates a simple Laplace smoothing procedure and χ 2 -triggered optimisation that results in the automatic selection of near-optimal binning and greatly improved PDE performance at low statistics. The performance of the smoothed histogrammed PDE is compared to a theoretically ideal PDE, and to results from a kernel PDE and a neural network.

Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: A review

Frequency analysis is a technique of fitting a probability distribution to a series of observations for defining the probabilities of future occurrences of some events of interest, e.g., an estimate of a flood magnitude corresponding to a chosen risk of failure. The use of this technique has played an important role in engineering practice. The assumptions of independence and stationarity are necessary conditions to proceed with such analyses. However, in the context of climate change, it is possible that these assumptions would no longer hold and the results of conventional frequency analysis would become doubtful. Under such circumstances, it is important that recourse be made to other suitable approaches which incorporate non-independence and non-stationarity of hydro-meteorological extremes. In paper, a brief review of the current approaches to these issues is presented. Approaches that remove the effect of serial dependence to obtain independent observations are presented and the ones that involve kernel or wavelet-based probability density estimation are only discussed for frequency analysis of dependent observations. For frequency analysis of non-stationary observations, the reviewed approaches include the extremal, r-largest, peaks-over-threshold, time-varying moments, pooled flood frequency analysis, local likelihood and quantile regression. Synthesis of the reviewed approaches is presented, issues related to establishing non-stationary behavior are discussed and future challenges in frequency analysis of hydro-meteorological extremes are discussed as well. Extensions to some of the reviewed approaches and new avenues of research have been identified for further development and improvement. It is also concluded that, to be most useful, non-stationarity considerations be incorporated into new risk assessment frameworks.

On central and non-central limit theorems in density estimation for sequences of long-range dependence

This paper studies the asymptotic properties of the kernel probability density estimate of stationary sequences which are observed through some non-linear instantaneous filter applied to long-range dependent Gaussian sequences. It is shown that the limiting distribution of the kernel estimator can be, in quite contrast to the case of short-range dependence, Gaussian or non-Gaussian depending on the choice of the bandwidth sequences. In particular, if the bandwidth h( N) for sample of size N is selected to converge to zero fast enough, the usual √ Nh( N) rate asymptotic normality still holds.