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Publisher Summary This chapter discusses the process of object classification with the very useful maximum-likelihood method. One straightforward and quite powerful approach is the use of the Bayes maximum-likelihood classifier. It generates second-order surfaces that partition the color space into disjoint regions, one for each object type (i.e., for each color of pixel). Assuming Gaussian distributions for the clusters of points in color space, the Bayes classifier maximizes the probability that each pixel will be assigned correctly. The first step is to train the classifier to recognize the three types of pixels. This requires a training set containing pixels that are known to fall in the background, inside normal cells, and inside abnormal cells. It is the statistics of these training set pixels that constitute the knowledge the classifier has about the problem. Estimating these statistics is the process of classifier training.

Given the increased risks of water scarcity and the presence of polluting agents in water resources, this paper aims at the development and presentation of a computational tool capable of assessing water quality based on digital processing techniques applied to satellite images. Initially, a database was created for Brazilian regions, consisting of hydrographic basins' satellite images associated with the Water Quality Index (WQI), according to the criteria established by the National Water Agency (ANA). Hitherto, the database consisted of 85 images, 61 were used in the training stage and 24 in the testing stage. In both stages, the images were subjected to thresholding using Otsu's Method, binarization, linear expansion on saturation, application of a Laplacian filter, extraction of characteristics by using co-occurrence matrices and classification by the Bayes Discriminant. Such techniques were also implemented on a computational platform in the MATLAB® environment, responsible for the interface between the system and users. The proposed system presented an approximate 70% success rate regarding the classification of WQIs, which can be improved as more information is made available to improve the databases. HIGHLIGHTS Application of satellite images and processing techniques to assess water quality.; Assessment of water quality in hydrographic basins without on-site measurements.; Application of Otsu's method, linear expansion by saturation and Laplacian filter.; Water features extraction and classification by co-occurrence matrices and Bayesian Linear Discriminant Analysis Classifier.

Accurately predicting the height of water flowing fractured zone is of great significance to coal mine safety mining. In recent years, most mines in China have entered deep mining. Aiming at the problem that it is difficult to accurately predict the height of water flowing fractured zone under the condition of large mining depth, the mining depth, height mining, inclined length of working face and coefficient of hard rock lithology ratio are selected as the main influencing factors of the height of water flowing fractured zone. The relationship between various factors and the height of water flowing fractured zone is analyzed by SPSS software. Based on the data mining tool Weka platform, Bayesian classifier, artificial neural network and support vector machine model are used to mine and analyze the measured data of water flowing fractured zone, and the detailed accuracy, confusion matrix and node error rate are compared. The results show that, the accuracy rate of instance classification of the three models is greater than 60%. The accuracy of the artificial neural network model is the highest and the node error rate is the lowest. In general, the training effect of the artificial neural network model is the best. By predicting engineering examples, the prediction accuracy of the model reaches 80%, and a good prediction effect is obtained. The height prediction system of water flowing fractured zone is developed based on VB language, which can provide a reference for the prediction of the height failure grade of water flowing fractured zone.

Monitoring of the forests with the help of remote sensing of the Earth systems is actual on the present stage of people development. Existing systems of research do not allow to use geographic information databases and don't include the spectrum of exploration that are presented in our work. The aim of this article is to develop the method of identification of tree species composition of forests on the basis of geographic information database in the integration with correlation analysis. It will give the possibility to find the most negative things that influence on the condition of forest ecosystems and neutralize them at the first stage of their influence. Satellite images that are received from the satellites Landsat 5 and 8 are used to make the database. Tree species composition of Mozhariv forest during 20 years is analyzed as an example in this article. Classification of tree species composition of forests using space images is made on the basis of Bayes classifier. There is a special geographic information database for further data processing and identification of tree species composition is developed. Forest is analyzed on the number of trees in each species during continuous time measures (in 2000, 2010 and 2020) in this article. Results of the work are presented with the help of graphics. Correlation analysis, which helps to make the analysis of tightness of connections between changes trees in number and different forest criteria, is made to identify tree species composition of forest. Developed method together with well-known methods of monitoring of forests help us to make effective application for analysis of tree species composition of forest changes and to make better existing information systems including different quality demands. Peculiarity of developed information system is in using of the data processing module as a part of geographic information system and implementing correlation analysis with identification of factors that influence each other. It helps to increase quality in management and monitoring of forest resources. Geographic information becomes available for users., На сучасному етапі розвитку суспільства актуальним є моніторинг лісових насаджень за допомогою дистанційного зондування Землі (ДЗЗ). Існуючі системи дослідження змін рослинності неефективно використовують геоінформаційної бази даних (ГБД) та не охоплюють спектр спостережень, розглянутих у даній роботі. Метою статті є розробка методу визначення породного складу лісових насаджень на основі геоінформаційної бази даних в інтеграції з кореляційним аналізом. Це дасть можливість виявляти найбільш негативні чинники, що впливають на стан лісових екосистем та нейтралізувати їх на початковій стадії впливу. Для створення бази даних використовуються космічні знімки, отримані від супутників Landsat 5 та 8. В якості прикладу проаналізовано лісовий покрив Можарівського лісництва за останні 20 років. Класифікація породного складу лісових насаджень за космічними знімками виконується на основі класифікатора Байєса. В роботі створена спеціалізована геоінформаційна база даних для подальшої обробки даних та встановлення породного складу. В роботі проаналізовано лісовий покрив за кількістю дерев по кожній породі окремо протягом тривалих часових рядів (2000, 2010 та 2020 роки). Результати досліджень мають графічне відображення. Для аналізу лісового покриву також проведено кореляційний аналіз, який визначає щільність взаємозв’язків між зміною кількості деревних насаджень та різними лісовими показниками. Розроблений метод разом з відомими методами моніторингу лісів дозволяють створити ефективне програмне забезпечення для аналізу зміни лісових насаджень та удосконалити існуючі інформаційні системи з урахуванням різних вимог до якості. Особливістю створюваної інформаційної системи є використання модуля обробки даних в складі геоінформаційної системи та проведення кореляційного аналізу з встановленням залежності факторів. Це сприяє підвищенню якості управління та моніторингу лісових ресурсів, доступності геоінформації для користувачів.

The problem of classification of an observation into von Mises-Fisher populations is considered when the concentration parameters and the mean directions are unknown. For two von Mises-Fisher distr...

In order to reduce the high dimensional feature space in the text classification, feature selection plays a significant role. The dimension reduction of feature space reduces the computation cost and improves the text classification system accuracy. Hence, the identification of an optimal combination of features is an essential task in text classification. In this paper, the proposed work introduces a novel hybrid feature selection method based on binary poor and rich optimization algorithm (HBPRO) to obtain the appropriate subset of optimal features. The optimal feature subset which is selected by our proposed work is evaluated using Nave Bayes classifier with two popular benchmark text corpus datasets. The experimental results confirm that the proposed feature selection scheme (HBPRO) produces higher accuracy with a reduced number of features when compared with other feature selection techniques.

Providing early predictions of academic performance is necessary for identifying at-risk students and subsequently providing them with timely intervention for critical factors affecting their academic performance. Although e-book systems are often used to provide students with teaching/learning materials in university courses, seldom has research made the early prediction based on their online reading behaviours by implementing machine learning classifiers. This study explored to what extent university students’ academic achievement can be predicted, based on their reading behaviours in an e-book supported course, using the classifiers. It further investigated which of the features extracted from the reading logs influence the predictions. The participants were 100 first-year undergraduates enrolled in a compulsory course at a university in Taiwan. The results suggest that logistic regression supports vector classification, decision trees, and random forests, and neural networks achieved moderate prediction performance with accuracy, precision, and recall metrics. The Bayes classifier identified almost all at-risk students. Additionally, student online reading behaviours affecting the prediction models included: turning pages, going back to previous pages and jumping to other pages, adding/deleting markers, and editing/removing memos. These behaviours were significantly positively correlated to academic achievement and should be encouraged during courses supported by e-books. Implications for practice or policy: For identifying at-risk students, educators could prioritise using Gaussian naïve Bayes in an e-book supported course, as it shows almost perfect recall performance. Assessors could give priority to logistic regression and neural networks in this context because they have stable achievement prediction performance with different evaluation metrics. The prediction models are strongly affected by student online reading behaviours, in particular by locating/returning to relevant pages and modifying markers.

Sentiment analysis is an important research topic and is currently being developed. Sentiment analysis is carried out to see the opinion or tendency of a person's opinion on a problem or object, whether it tends to have a negative or positive view. The main purpose of this research is to find out public sentiment towards the Full Day school policy comments from the Facebook Page of the Ministry of Education and Culture of the Republic of Indonesia and to determine the performance of the Na-ïve Bayes Classifier Algorithm. The results of this study indicate that the public's negative sentiment towards the Full Day School policy is higher than positive or neutral sentiment. The highest accuracy value is the Naïve Bayes Classifier algorithm with the trigram feature selection of the 300 data training model with a value of 80%. This simulation has proven that the larger the training data and the selection of features used in the NBC Algorithm affect the accuracy of the results. Meanwhile, the simulation results from 10 test data with 5 different NBC and Lexicon algorithms also show that the Full Day School Policy proposed by the Indonesian Minister of Education and Culture has a higher negative sentiment than positive or neutral by most Facebook users who express opinions through comments. The highest accuracy value is the Naïve Bayes Classifier algorithm with the trigram feature selection of the 300 data training model with a value of 80%. This simulation has proven that the larger the training data and the selection of features used in the NBC Algorithm affect the accuracy of the results. Meanwhile, the simulation results from 10 test data with 5 different NBC and Lexicon algorithms also show that the Full Day School Policy proposed by the Indonesian Minister of Education and Culture has a higher negative sentiment than positive or neutral by most users. Facebook that expresses opinions through comments. The highest accuracy value is the Naïve Bayes Classifier algorithm with the tri-gram feature selection of the 300 data training model with a value of 80%. This simulation has proven that the larger the training data and the selection of features used in the NBC Algorithm affect the accuracy results.

Lampung province has development activity orienting on source potential in the agricultural sector mainly food crops. Yield estimation of food crops is one of the things crucial problems in the agricultural sector, because of the farmers' lack of knowledge about the bountiful harvest, and climate change big impact on the yield of food crops. Then it was needed to be developed modeling to prediction system of food crops by data mining, with Naïve Bayes Classifier (NBC) which expected will give information and can use by the farmer and industrial food crops. On classification, progress attributes that use there is the temperature (°C), humidity (%), rainfall (mm), photoperiodicity (hour), and production result (ton) as a class attribute. The data of research that getting there are climate data and yield of food crops by data from the Central Bureau of Statistics (BPS) and the Meteorology, Climatology and Geophysics Agency (BMKG) from 2010 to 2017 at Lampung Province. Data of food crops used in this research there are paddy, maize, and soybean. The research results about the average accuracy of modeling that development using the 10-fold cross-validation method, that had an accuracy value of 72.78% and Root Mean Square Error (RMSE) there is 0.438.

We propose a new nonparametric procedure to solve the problem of classifying objects represented by $d$-dimensional vectors into $K \geq 2$ groups. The newly proposed classifier was inspired by the $k$ nearest neighbour (kNN) method. It is based on the idea of a depth-based distributional neighbourhood and is called $k$ nearest depth neighbours (kNDN) classifier. The kNDN classifier has several desirable properties: in contrast to the classical kNN, it can utilize global properties of the considered distributions (symmetry). In contrast to the maximal depth classifier and related classifiers, it does not have problems with classification when the considered distributions differ in dispersion or have unequal priors. The kNDN classifier is compared to several depth-based classifiers as well as the classical kNN method in a simulation study. According to the average misclassification rates, it is comparable to the best current depth-based classifiers.

To study the application of wearable devices in the sixth generation (6G) Internet of things (IoT) communication environment, a human behaviour recognition method of wearable devices is designed by using artificial intelligence technology. First, the information in IoT is analyzed and processed by using data mining technology, and the classifier model is determined though experiments. Second, a human behaviour recognition model is designed by using artificial neural network (ANN), and the learning of neural network parameters is conducted by back propagation algorithm to improve the ability of behaviour recognition. Finally, the classifier and the human behaviour recognition model based on ANN are tested. The experimental results indicate that the classification accuracy of compound Bayes classification is the highest, so the compound Bayes classifier can be used as the data mining technology of wearable devices in IoT. When the number of neuron nodes in the hidden layer is 11, the recognition accuracy of human behaviour is more than 75%. In addition, compared with other algorithms, the overall recognition effect is better. Thus, the designed recognition model can be used for the recognition of human behaviour and it provides a reference for the study of the application of wearable devices in the environment of IoT.

Opinion mining has gained much attention in the recent years due to the rapid growth of social media. It is a task of analyzing customer reviews to make decisions by classifying the reviews into positive or negative. These text reviews have high dimensions that lead to the curse of dimensionality. To handle this high dimension of text data, improved gain ratio is proposed to select the features with the highest ranking. Naїve Bayes classifier with kernel density function is used to evaluate the feature set. The Naїve Bayes classifier with Kernel density estimation is a nonparametric classifier that computes the probability density function based on the kernel estimator. This classifier produces higher accuracy in various benchmarking datasets.

In the field of software development, the main problem is to recognize the security-oriented issues within the reported bugs due to its inacceptable rate to provide the satisfied reliability on customer and software dataset. The objective is to propose a novel machine learning approach for multiclass supervised classification named Bug Severity classification to overcome these challenges with the use of supervised Artificial Neural Network and stacking based Navies Bayes classifier. This proposed approach directly examines the latent and highly descriptive features. Primarily, using the natural language programming approaches bug report text is preprocessed. After then, N gram is employed for extracting features by overcoming data sparsity problems. Further, the supervised Artificial Neural Network extracts the salient feature patterns of the corresponding severity classes. Finally, the stacking-based Navies Bayes classifier is employed for classifying multiple bug severity classes.

Recent studies of imbalanced data classification have shown that the imbalance ratio (IR) is not the only cause of performance loss in a classifier, as other data factors, such as small disjuncts, noise, and overlapping, can also make the problem difficult. The relationship between the IR and other data factors has been demonstrated, but to the best of our knowledge, there is no measurement of the extent to which class imbalance influences the classification performance of imbalanced data. In addition, it is also unknown which data factor serves as the main barrier for classification in a data set. In this article, we focus on the Bayes optimal classifier and examine the influence of class imbalance from a theoretical perspective. We propose an instance measure called the Individual Bayes Imbalance Impact Index (IBI3) and a data measure called the Bayes Imbalance Impact Index (BI3). IBI3 and BI3 reflect the extent of influence using only the imbalance factor, in terms of each minority class sample and the whole data set, respectively. Therefore, IBI3 can be used as an instance complexity measure of imbalance and BI3 as a criterion to demonstrate the degree to which imbalance deteriorates the classification of a data set. We can, therefore, use BI3 to access whether it is worth using imbalance recovery methods, such as sampling or cost-sensitive methods, to recover the performance loss of a classifier. The experiments show that IBI3 is highly consistent with the increase of the prediction score obtained by the imbalance recovery methods and that BI3 is highly consistent with the improvement in the F1 score obtained by the imbalance recovery methods on both synthetic and real benchmark data sets.

Sentiment analysis aims to automatically detect the underlying attitudes that users express. For the documents with complex unstructured data, such as reviews, emojis and surveys, it is usually hard to precisely identify the real emotion. Thus, it becomes urgent, yet challenging, to develop a technique that can process and make use of the unstructured information. In this article, we consider sentiment classification for those unstructured features extracted from texts. We propose a regularization-based framework to pursue better classification performance by (1) introducing polarity shifters assembled with sentiment words to create novel bigram features and (2) simultaneously constructing a constraint graph to encode the relative polarity among unstructured features to improve the parameter estimation procedure. Under these settings, our approach can uncover the intrinsic semantic information from the unstructured text data. Theoretically, we justify its underlying equivalent connection with the standard Bayes classifier, which is ideally optimal when the sample distribution is known. Moreover, we show that our new method yields better generalization ability due to the reduced solution search space and the appealing asymptotic consistency. The superior performance from real data experiments demonstrates the robustness and effectiveness of the proposed method.

The Bayes classifier is often used because it is simple, and the maximum posterior probability (MPP) criterion it uses is equivalent to the least error rate criterion. However, it has issues in the following circumstances: (i) if information instead of correctness is more important, we should use the maximum likelihood criterion or maximum information criterion, which can reduce the rate of failure to report small probability events. (ii) For unseen instance classifications, the previously optimised classifier cannot be properly used when the probability distribution of true classes is changed. (iii) When classes’ feature distributions instead of transition probability functions (TPFs) are stable, it is improper to train the TPF, such as the logistic function, with parameters. (iv) For multi-label classifications, it is difficult to optimise a group of TPFs with parameters that the Bayes classifier needs. This study addresses these issues by comparing the MPP criterion with the maximum likelihood criterion and maximum mutual information (MMI) criterion. It suggests using the MMI criterion for most unseen instance classifications. It presents a new iterative algorithm, the channel matching (CM) algorithm, for the MMI classification. It uses two examples to show the advantages of the CM algorithm: fast and reliable.

Parametric and nonparametric pattern recognition have been studied for almost a century based on a Bayesian paradigm, which is, in turn, founded on the principles of Bayes theorem. It is well known that the accuracy of the Bayes classifier cannot be exceeded. Typically, this reduces to comparing the testing sample to mean or median of the respective distributions. Recently, Oommen and his co-authors have presented a pioneering and non-intuitive paradigm, namely that of achieving the classification by comparing the testing sample with another descriptor, which could also be quite distant from the mean. This paradigm has been termed as being “anti-Bayesian,” and it essentially uses the quantiles of the distributions to achieve the pattern recognition. Such classifiers attain the optimal Bayesian accuracy for symmetric distributions even though they operate with a non-intuitive philosophy. While this paradigm has been applied in a number of domains (briefly explained in the body of this paper), its application for nonparametric domains has been limited. This paper explains, in detail, how such quantile-based classification can be extended to the nonparametric world, using both traditional and kernel-based strategies. The paper analyzes the methodology of such nonparametric schemes and their robustness. From a fundamental perspective, the paper utilizes the so-called large sample theory to derive strong asymptotic results that pertain to the equivalence between the parametric and nonparametric schemes for large samples. Apart from the new theoretical results, the paper also presents experimental results demonstrating their power. These results pertain to artificial data sets and also involve a real-life breast cancer data set obtained from the University Hospital Centre of Coimbra. The experimental results clearly confirm the power of the proposed “anti-Bayesian” procedure, especially when approached from a nonparametric perspective.

The Bayes classifier depends on the conditional densities and the prior probabilities. Among many density functions, the Gaussian density has received more attention mainly motivated by its analytical tractability. The parameters of the Bayes classifier for the Gaussian distribution data are generally unknown, and approximations are calculated for the mean vector $${\hat{{\varvec{\mu }}}}$$ and the covariance matrix $${\hat{\varSigma }}$$ . When a pattern is inserted in the training set of the class $$\omega _i$$ , the values of the parameters $$\hat{{\varvec{\mu }}}_{{\varvec{i}}}$$ and $${\hat{\varSigma }}_{i}$$ change by an amount given by $$\varDelta \hat{{\varvec{\mu }}}_{{\varvec{i}}}$$ and $$\varDelta {\hat{\varSigma }}_i$$ , respectively. The insertion of one pattern can cause a perturbation, so we claim that this perturbation can be used for supervised classification purposes. Based on this assumption, we propose a supervised classifier called Perturbation-based Classifier PerC that assigns the class of the query pattern as the one that presents the smallest perturbation among all the classes after the insertion of this query pattern in the classes. The rationale is that the addition of a pattern that belongs to one specific class should not alter much the distribution of that class. PerC only uses the perturbations ( $$\varDelta \hat{{\varvec{\mu }}}_{{\varvec{i}}}$$ and $$\varDelta {\hat{\varSigma }}_i$$ ) to evaluate the class of a query pattern; so, it is a parameter-free classifier. The proposed method was assessed on 21 datasets from the UCI Machine Learning Repository, and its results were compared with classifiers from the literature. Results have shown that PerC obtains very competitive recognition rates.

PURPOSE: This feasibility and validation study addresses the potential use of magnetic resonance imaging (MRI) texture analysis of the pancreas in patients with chronic pancreatitis (CP).METHODS: Extraction of 851 MRI texture features from diffusion weighted imaging (DWI) of the pancreas was performed in 77 CP patients and 22 healthy controls. Features were reduced to classify patients into subgroups, and a Bayes classifier was trained using a tenfold cross-validation forward selection procedure. The classifier was optimized to obtain the best average m-fold accuracy, sensitivity, specificity, and positive predictive value. Classifiers were: presence of disease (CP vs. healthy controls), etiological risk factors (alcoholic vs. nonalcoholic etiology of CP and tobacco use vs. no tobacco use), and complications to CP (presumed pancreatogenic diabetes vs. no diabetes and pancreatic exocrine insufficiency vs. normal pancreatic function).RESULTS: The best classification performance was obtained for the disease classifier selecting only five of the original features with 98% accuracy, 97% sensitivity, 100% specificity, and 100% positive predictive value. The risk factor classifiers obtained good performance using 9 (alcohol: 88% accuracy) and 10 features (tobacco: 86% accuracy). The two complication classifiers obtained similar accuracies with only 4 (diabetes: 83% accuracy) and 3 features (exocrine pancreatic function: 82% accuracy).CONCLUSION: Pancreatic texture analysis demonstrated to be feasible in patients with CP and discriminate clinically relevant subgroups based on etiological risk factors and complications. In future studies, the method may provide useful information on disease progression (monitoring) and detection of biomarkers characterizing early-stage CP.