A Study on Flexible Bayes Classifier Using K-Nearest Neighbor Density Estimator

Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models

Most studies in wind integration ignore either the temporal or spatial correlation of the power data, which decreases the accuracy of the results. The objective of this paper is to model and verify the temporal correlation of wind power data using Copula and nonparametric kernel density estimation (KDE). A model for reconstructing wind power time series is proposed based on Copula theory. This model preserves the time correlation characteristics of the original wind power sequence as much as possible, which facilitates the subsequent research on the uncertainty of evolution over time. Then, based on the nonparametric KDE and maximum likelihood estimation algorithm, by selecting appropriate correlation coefficients, a time correlation model of Gaussian Copula is established and applied to the actual dataset of a wind farm in GEFCOM2014. Finally, the boxwhisker plot and the autocorrelation function are used to verify the uncertainty characteristics of the reconstructed sequence, and the accuracy of the fit is further proved by the root mean square error in both short-term and long-term case studies. From the comparison with original time series data, as well as the numerical results, the effectiveness of the proposed method is illustrated.

To evaluate the impact of the randomness and correlation of photovoltaic (PV) and load on AC/DC systems with a multiport current flow controller (M-CFC), this paper proposes a probabilistic optimal power flow calculation for AC/DC systems based on a nonparametric kernel density estimation. First, according to the M-CFC model, the DC power flow calculation method with M-CFC was deduced, and its influence on line loss was analyzed. Second, a nonparametric kernel density estimation with an adaptive bandwidth was used to accurately describe the probability distribution of the PV and load, and correlation samples of the PV and load were obtained by the mixed copula function. Then an optimization model that considers system loss and static security was established, and a fast nondominated sorting genetic algorithm based on the elite strategy (NSGA-II) was used to calculate the multi-objective probability optimal power flow of the AC/DC system. Finally, a case study was performed on the modified IEEE39 bus system using measured PV and load data. We verified the nonparametric kernel density estimation with an adaptive bandwidth can better adapt to random component uncertainty, and M-CFC can improve the static security of the system.

Estimators for derivatives associated with a density function can be useful in identifying its modes and inflection points. In addition, these estimators play an important role in plug-in methods associated with bandwidth selection in nonparametric kernel density estimation. In this paper, we extend the nonparametric class of density estimators proposed by Mynbaev and Martins-Filho (2010) to the estimation of m-order density derivatives. Contrary to some existing derivative estimators, the estimators in our proposed class have a full asymptotic characterization, including uniform consistency and asymptotic normality. An expression for the bandwidth that minimizes an asymptotic approximation for the estimators’ integrated squared error is provided. A Monte Carlo study sheds light on the finite sample performance of our estimators and contrasts it with that of density derivative estimators based on the classical Rosenblatt–Parzen approach.

Interval-grouped data are defined, in general, when the event of interest cannot be directly observed and it is only known to have been occurred within an interval. In this framework, a nonparametric kernel density estimator is proposed and studied. The approach is based on the classical Parzen–Rosenblatt estimator and on the generalisation of the binned kernel density estimator. The asymptotic bias and variance of the proposed estimator are derived under usual assumptions, and the effect of using non-equally spaced grouped data is analysed. Additionally, a plug-in bandwidth selector is proposed. Through a comprehensive simulation study, the behaviour of both the estimator and the plug-in bandwidth selector considering different scenarios of data grouping is shown. An application to real data confirms the simulation results, revealing the good performance of the estimator whenever data are not heavily grouped.

Naive Bayesian classifier (NBC) is a simple and effective classification model. However, the fact that the assumption of independence is often violated in reality makes it perform poorly on some datasets. In our pre-research, we attempt to improve the NBC model based on the strategy of the fuzzy feature selection. The main idea of the improvement strategy is to adjust the features' contribution to classification through the feature important factor (FIF) which describes the importance of the features. This strategy overcomes deficiencies caused by the assumption of independence. Based on the pre-research, we optimize the strategy of fuzzy feature selection with the establishment of the dual NBC model in order to improve the NBC model more. Through the experimental analysis on the UCI datasets, the strategy of the fuzzy feature selection on the dual NBC model is proved effective.

Fault detection in non-stationary processes is a timely research topic in industrial process monitoring. The core objective of this research is to tackle anomaly detection in non-stationary industrial processes with manipulated set-point changes and uncertainties in the prior knowledge about the statistical nature of the measurements. In this research, the fault detection problem is investigated from an unsupervised perspective and a modified PCA approach is proposed. This method utilizes the base-line loading matrices and an upper bound to be determined for the variation range of time-series to relax the assumption on stationary characteristics. Hence, the mean used for normalizing the time-series are adaptively updated (using soft-calculation) without any need for a high-complexity recalibration procedure as needed in other existing adaptive/recursive PCA methods. Moreover, the first- and second-order error indices are introduced to monitor the statistical behaviour of process measurements. To develop a more reliable system condition indicator, an overall health index is given based on the proposed features using a non-parametric kernel density estimator (KDE). The proposed approach does not require a heavy online calculation in comparison with the existing adaptive solutions and it can successfully detect faults from healthy measurements’ mean changes. Finally, an alarm generator algorithm is presented which generates two alarm types, caution and actual fault for processes operators, utilizing the proposed overall health index. The effectiveness of the modified PCA approach is validated by both numerical examples and industrial case studies.

Handwritten signature identification is a process that determines an individual’s true identity by analyzing their signature. This is an important task in various applications such as financial transactions, legal document verification, and biometric systems. Various techniques have been developed for signature identification, including feature-based methods and machine learning-based methods. However, verifying handwritten signatures in digital transactions and remote document authentication is still challenging. The inherent variety in people’s signatures, which may occur due to factors such as mood, exhaustion, or even the writing tool used, contributes to the problem. Furthermore, the proliferation of sophisticated forgery methods, such as freehand mimicking and sophisticated picture manipulation, necessitates the development of reliable and precise tools for identifying authentic signatures from fake ones.The present paper suggests a method for identifying signatures based on integrating static (off-line) handwritten signature data. This is done by fusing three types of signature features: Linear Discriminant Analysis (LDA) as appearance-based features, Fast Fourier Transform (FFT) as frequency-features, and Gray-Level Co-occurrence Matrix (GLCM) as texture-features. Then, these fused features are inputted into four types of machine learning algorithms: Naive Bayes, K-Nearest Neighbor, Decision Tree, and AdaBoost classifiers, to identify each person and to find the most robust algorithm in terms of accuracy and precision and recall. For experiments, we have used two famous datasets: SigComp2011 and CEDAR. After training datasets, the highest accuracy achieved was 100% on the CEDAR dataset and 94.43% on the SigComp2011 dataset using a Naive Bayes classifier. Index Terms— Fast Fourier Transform, Gray-Level Co-occurrence Matrix, Handwritten Signature, Linear Discriminant Analysis, Machine Learning.

This paper presents the methodology to detect and identify the type of fault that occurs in the shunt compensated static synchronous compensator (STATCOM) transmission line using a combination of Discrete Wavelet Transform (DWT) and Naive Bayes (NB) classifiers. To study this, the network model is designed using Matlab/Simulink. Different types of faults, such as Line to Ground (LG), Line to Line (LL), Double Line to Ground (LLG) and the three-phase (LLLG) fault, are applied at disparate zones of the system, with and without STATCOM, considering the effect of varying fault resistance. The three-phase fault current waveforms obtained are decomposed into several levels using Daubechies (db) mother wavelet of db4 to extract the features, such as the standard deviation (SD) and energy values. Then, the extracted features are used to train the classifiers, such as Multi-Layer Perceptron Neural Network (MLP), Bayes and the Naive Bayes (NB) classifier to classify the type of fault that occurs in the system. The results obtained reveal that the proposed NB classifier outperforms in terms of accuracy rate, misclassification rate, kappa statistics, mean absolute error (MAE), root mean square error (RMSE), percentage relative absolute error (% RAE) and percentage root relative square error (% RRSE) than both MLP and the Bayes classifier.

Classification is a basic topic in data mining and pattern recognition. Following advances in computer science, a lot of new methods have been proposed in recent years, such as artificial neural networks, decision trees, fuzzy set and Bayesian Networks, etc. As a probabilistic network, Bayesian Networks is a powerful tool for handling uncertainty in data mining and many other domains. Naïve Bayes Classifier (NBC) is a simple and effective classification method, which is built on the assumption of conditional independence between the class attributes. This topology structure can not describe the inherent relation among the features. In this paper, we apply Bayesian Networks Augmented Naïve Bayes (BAN) for the texture classification of aerial images, which relaxes the independent assumption in NBC. A new method for learning the networks topology structure based on training samples is adopted in this paper. Comparison experiments show higher accuracy of BAN classifier than NBC. The results also show the potential applicability of the proposed method.

Probability theory is the framework for making decision under uncertainty. In classification, Bayes' rule is used to calculate the probabilities of the classes and it is a big issue how to classify raw data rationally to minimize expected risk. Bayesian theory can roughly be boiled down to one principle: to see the future, one must look at the past. Naive Bayes classifier is one of the mostly used practical Bayesian learning methods. K-nearest neighbor is a supervised learning algorithm where the result of new instance query is classified based on majority of k-nearest neighbor category. The classifiers do not use any model to fit and only based on memory/training data. In this paper, after reviewing Bayesian theory, the naive Bayes classifier and k-nearest neighbor classifier is implemented and applied to a dataset "credit card approval" application. Eventually the performance of these two classifiers is observed on this application in terms of the correct classification and misclassification and how the performance of k-nearest neighbor classifier can be improved by varying the value of k.

Many databases store data in relational format, with different types of entities and information about links between the entities. Link-based classification is the problem of predicting the class label of a target entity given information about features of the entity and about features of the related entities. A natural approach to link-based classification is to upgrade standard classification methods from the propositional, single-table testing. In this paper we propose a new classification rule for upgrading naive Bayes classifiers (NBC). Previous work on relational NBC has achieved the best results with link independency assumption which says that the probability of each link to an object is independent from the other links to the object. We formalize our method by breaking it into two parts: (1) the independent influence assumption: that the influence of one path from the target object to a related entity is independent of another. We consider object-path independency and (2) the independent feature assumption of NBC: that features of the target entity and a related entity are probabilistically independent given a target class label. We derive a new relational NBC rule that places more weight on the target entity features than formulations of the link independency assumption. The new NBC rule yields higher accuracies on three benchmark datasets-Mutagenesis, MovieLens, and Cora-with average improvements ranging from 2% to 10%.

The joint probability modelling of storm surges and rainfall events is the main task in assessing compound flood risk in low-lying coastal areas. These extreme or non-extreme events may not be dangerous if considered individually but can intensify flooding impact if they occur simultaneously or successively. Recently, the copula approach has been widely accepted in compound flooding but is often limited to parametric or semiparametric distribution settings in a limited number of cases. However, both parametric and semiparametric approaches assume the prior distribution type for univariate marginals and copula joint density. In that case, there is a high risk of misspecification if the underlying assumption is violated. In addition, both approaches suffer from a lack of flexibility. This study uses bivariate copula density in the nonparametric distribution setting. The joint copula structure is approximated nonparametrically by employing the Bernstein copula estimator and Beta kernel copula density, and their performances are also compared. The proposed model is tested with 46 years of rainfall and storm surge observations collected on Canada's west coast. The marginal distribution of the selected flood variables is modelled using nonparametric kernel density estimation (KDE). Based on the different model compatibility tests, the Bernstein copula with normal KDE margins defined the joint dependence structure well. The selected nonparametric copula model is further employed to estimate joint and conditional return periods. It is found that flood hazard characteristics occurrence simultaneously is less frequent in AND-joint cases than in OR-joint cases. Also, the derived model is further used to estimate failure probability (FP) statistics to assess the variation of bivariate hydrologic risk during the project lifetime. It is found that FP statistics could be underestimated when neglecting the compound effect of storm surge and rainfall in the coastal flood risk.

With the development of China’s economy, the contradiction between energy, economy and ecological environment is becoming more and more prominent. However, the spatial and temporal evolution of the contradiction system of energy, economy and environment all over China is rarely focused on. This study assesses the provincial coordinated degree of the economy-energy-environment system over the period of 2001–2020 and analyzes their spatial and temporal evolution using principal component analysis (PCA), a coordination degree model, non-parametric Kernel Density Estimation (KDE), and spatial correlation analysis approaches. Results show that provincial coordination degrees from 2001 to 2020 vary between ‘barely balanced’ and ‘superiorly balanced’ with an overall improvement. However, the gap between high and low regional coordination has widen, while middle-level provinces gradually increase and are distributed more evenly. Limited spatial correlation of provincial coordination exists and the clustering level slightly increases over 2001–2020. Additionally, some less-developed regions, which are still staying at the ‘intermediately balanced’ state in 2020, call for attention.

Understanding the risks associated with the likelihood of extreme events and their respective consequences for the stability of hydraulic infrastructures is essential for flood forecasting and engineering design purposes. Accordingly, a hydrological methodology for providing reliable estimates of extreme discharge flows approaching hydraulic infrastructures was developed. It is composed of a preliminary assessment of missing data, quality and reliability for statistically assessing the frequency of flood flows, allied to parametric and non-parametric methods. Model and parameter uncertainties are accounted for by the introduced and proposed modified model averaging (modified MM) approach in the extreme hydrological event's prediction. An assessment of the parametric methods accuracy was performed by using the non-parametric Kernel Density Estimate (KDE) as a benchmark model. For demonstration and validity purposes, this methodology was applied to estimate the design floods approaching the case study ‘new Hintze Ribeiro bridge’, located in the Douro river, one of the three main rivers in Portugal, and having one of Europe's largest river flood flows. Given the obtained results, the modified MM is considered a better estimation method.