An intuitionistic fuzzy kernel ridge regression classifier for binary classification

Graph Embedded Intuitionistic Fuzzy Random Vector Functional Link Neural Network for Class Imbalance Learning

The domain of machine learning is confronted with a crucial research area known as class imbalance (CI) learning, which presents considerable hurdles in the precise classification of minority classes. This issue can result in biased models where the majority class takes precedence in the training process, leading to the underrepresentation of the minority class. The random vector functional link (RVFL) network is a widely used and effective learning model for classification due to its good generalization performance and efficiency. However, it suffers when dealing with imbalanced datasets. To overcome this limitation, we propose a novel graph-embedded intuitionistic fuzzy RVFL for CI learning (GE-IFRVFL-CIL) model incorporating a weighting mechanism to handle imbalanced datasets. The proposed GE-IFRVFL-CIL model offers a plethora of benefits: 1) leveraging graph embedding (GE) to preserve the inherent topological structure of the datasets; 2) employing intuitionistic fuzzy (IF) theory to handle uncertainty and imprecision in the data; and 3) the most important, it tackles CI learning. The amalgamation of a weighting scheme, GE, and IF sets leads to the superior performance of the proposed models on KEEL benchmark imbalanced datasets with and without Gaussian noise. Furthermore, we implemented the proposed GE-IFRVFL-CIL on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and achieved promising results, demonstrating the model's effectiveness in real-world applications. The proposed GE-IFRVFL-CIL model offers a promising solution to address the CI issue, mitigates the detrimental effect of noise and outliers, and preserves the inherent geometrical structures of the dataset.

Ordinal Regression With Pinball Loss

Ordinal regression (OR) aims to solve multiclass classification problems with ordinal classes. Support vector OR (SVOR) is a typical OR algorithm and has been extensively used in OR problems. In this article, based on the characteristics of OR problems, we propose a novel pinball loss function and present an SVOR method with pinball loss (pin-SVOR). Pin-SVOR is fundamentally different from traditional SVOR with hinge loss. Traditional SVOR employs the hinge loss function, and the classifier is determined by only a few data points near the class boundary, called support vectors, which may lead to a noise sensitive and re-sampling unstable classifier. Distinctively, pin-SVOR employs the pinball loss function. It attaches an extra penalty to correctly classified data that lies inside the class, such that all the training data is involved in deciding the classifier. The data near the middle of each class has a small penalty, and that near the class boundary has a large penalty. Thus, the training data tend to lie near the middle of each class instead of on the class boundary, which leads to scatter minimization in the middle of each class and noise insensitivity. The experimental results show that pin-SVOR has better classification performance than state-of-the-art OR methods.

A distance-based kernel for classification via Support Vector Machines

Support Vector Machines (SVMs) are a type of supervised machine learning algorithm widely used for classification tasks. In contrast to traditional methods that split the data into separate training and testing sets, here we propose an innovative approach where subsets of the original data are randomly selected to train the model multiple times. This iterative training process aims to identify a representative data subset, leading to improved inferences about the population. Additionally, we introduce a novel distance-based kernel specifically designed for binary-type features based on a similarity matrix that efficiently handles both binary and multi-class classification problems. Computational experiments on publicly available datasets of varying sizes demonstrate that our proposed method significantly outperforms existing approaches in terms of classification accuracy. Furthermore, the distance-based kernel achieves superior performance compared to other well-known kernels from the literature and those used in previous studies on the same datasets. These findings validate the effectiveness of our proposed classification method and distance-based kernel for SVMs. By leveraging random subset selection and a unique kernel design, we achieve notable improvements in classification accuracy. These results have significant implications for diverse classification problems in Machine Learning and data analysis.

Evaluation modeling of highway collapse hazard based on rough set and support vector machine

The prediction of possibility and risk classification of collapse is an important issue in the process of highway construction in mountain area. Based on the principle of rough set and support vector machine, a landslide hazard prediction model was established. First of all, according to field investigation, an evaluation index system and a sample set of evaluation index data were established, the rough set decision table was constructed by preprocessing the original data based on the function classification of standard evaluation index, and then, the influence indexes of the collapse activity were reduced by rough set theory, and the main 9 indexes affecting the collapse activity as the key discriminant factors of support vector machine model, namely slope shape of slope, aspect of slope, slope of slope, height of slope, exposed structural face, stratum lithology, relationship between weakness face and free face, vegetation cover rate and weathering degree of rock were extracted. Then, taking the data of 13 post earthquake collapses in Yingxiu-Wolong highway of Hanchuan County measured by the authors in the field as training samples, the optimal model parameters were analyzed and calculated. When the penalty parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C$$\end{document}C is 8 and the kernel parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}σ is 0.5, the correct rate of cross-validation is 100%, and the model is optimal. At last, 4 other landslide data were tested, the discriminant results of the test sample data were compared with the results obtained by uncertainty measure and distance discriminant analysis. The results show that the discriminant results of the test sample data by RS-SVM were consistent with the results obtained by uncertainty measure and distance discriminant analysis, the accurate rate is 100%. The collapse hazard analysis model based on rough set and support vector machine can reduce the computation while ensuring the accuracy of evaluation, and better solve the small sample and nonlinear problems, can provide certain a good idea for collapse hazard evaluation in the future.

An empirical evaluation of sampling methods for the classification of imbalanced data

In numerous classification problems, class distribution is not balanced. For example, positive examples are rare in the fields of disease diagnosis and credit card fraud detection. General machine learning methods are known to be suboptimal for such imbalanced classification. One popular solution is to balance training data by oversampling the underrepresented (or undersampling the overrepresented) classes before applying machine learning algorithms. However, despite its popularity, the effectiveness of sampling has not been rigorously and comprehensively evaluated. This study assessed combinations of seven sampling methods and eight machine learning classifiers (56 varieties in total) using 31 datasets with varying degrees of imbalance. We used the areas under the precision-recall curve (AUPRC) and receiver operating characteristics curve (AUROC) as the performance measures. The AUPRC is known to be more informative for imbalanced classification than the AUROC. We observed that sampling significantly changed the performance of the classifier (paired t-tests P < 0.05) only for few cases (12.2% in AUPRC and 10.0% in AUROC). Surprisingly, sampling was more likely to reduce rather than improve the classification performance. Moreover, the adverse effects of sampling were more pronounced in AUPRC than in AUROC. Among the sampling methods, undersampling performed worse than others. Also, sampling was more effective for improving linear classifiers. Most importantly, we did not need sampling to obtain the optimal classifier for most of the 31 datasets. In addition, we found two interesting examples in which sampling significantly reduced AUPRC while significantly improving AUROC (paired t-tests P < 0.05). In conclusion, the applicability of sampling is limited because it could be ineffective or even harmful. Furthermore, the choice of the performance measure is crucial for decision making. Our results provide valuable insights into the effect and characteristics of sampling for imbalanced classification.

Group decision making method with hesitant fuzzy preference relations based on additive consistency and consensus

To address the situation where the multi-criteria decision making (MCDM) has problems with hesitant fuzzy preference relations (HFPRs), this paper develops a group decision making method considering the additive consistency and consensus simultaneously. First, a new normalized method for HFPRs is developed to address the situation where the evaluation information has different number of elements. Second, for improving the unacceptable consistent HFPRs, an algorithm is designed to derive acceptable consistent HFPRs. The main characteristic of the design algorithm is that the values that need to be revised are identified first, and then design the local adjustment process. Third, an algorithm is developed to obtain a group of normalized HFPRs (NHFPRs), considering the additive consistency of HFPRs. Fourth, for improving the individual consistency and group consensus simultaneously, an algorithm is designed to obtain a group of HFPRs with acceptable consistency and consensus. Finally, the method of determining the decision makers’ weights and a procedure for MCDM problems with HFPRs are given. An illustrative example in conjunction with comparative analysis is used to demonstrate the proposed method which is feasible and efficient for practical MCDM problems.