Graph neural networks and fuzzy models offer effective and practical methods for solving various tasks at the large-scale graph level. Large-scale graph embedding based on deep methods and fuzzy models is categorized into fusion and integration. Feature extraction and graph structure at the local and global levels are based on augmented graph fusion. In fusion-based graph embedding, the fuzzy model is used as an activation function based on an aggregated process. In some cases, the fusion of graph neural network methods with fuzzy systems has been successful. However, no effective methods have been developed for integrating fuzzy models with deep methods. Two main issues are associated with this integration: (1) computational complexity due to the exponential increase in fuzzy rules with the number of features, and (2) the complexity of the solution space due to the combination of fuzzy regression rules between inputs and outputs. Additionally, modeling at the large-scale graph level using linear regression and graph neural networks is not sufficient. Therefore, this paper proposes a feature and structure combination method at the local and global levels using a combination of fuzzy modeling and graph transformers, an integrated deep learning technique called Fuzzy Graph Transformer (FuzzyGT). We conducted experiments on deep learning graph datasets to compare with the proposed model. Our method achieved the best results compared to other advanced models

Traditional logistic regression is plugged with degenerates and violent behavior in High-dimensional classification, because of the problem of non-invertible matrices in estimating model parameters. In this paper, to overcome the High-dimensionality of data, we introduce two new algorithms. First, we improve the efficiency of finite population Bayesian bootstrapping logistic regression classifier by using the rule of majority vote. Second, using simple random sampling without replacement to select a smaller number of covariates rather than the sample size and applying traditional logistic regression, we introduce the other new algorithm for High-dimensional binary classi cation. We compare the proposed algorithms with the regularized logistic regression models and two other classification algorithms, i. e., naive Bayes and K-nearest neighbors using both simulated and real data.

Background: Chronic kidney disease (CKD), characterized by progressive loss of renal function, is becoming a growing problem in the general population. New analytical technologies such as “ omics”-based approaches, including metabolomics, provide a useful platform for biomarker discovery and improvement of CKD management. In metabolomics studies, not only prediction accuracy is attractive, but also variable importance is critical because the identified biomarkers reveal pathogenic metabolic processes underlying the progression of chronic kidney disease. We aimed to use k-important neighbors (KIN), for the analysis of a High dimensional metabolomics dataset to classify patients into mild or advanced progression of CKD. Methods: Urine samples were collected from CKD patients (n=73). The patients were classified based on metabolite biomarkers into the two groups: mild CKD (glomerular filtration rate (GFR)> 60 mL/min per 1· 73 m2) and advanced CKD (GFR<60 mL/min per 1· 73 m2). Accordingly, 48 and 25 patients were in mild (class 1) and advanced (class 2) groups respectively. Recently, KIN was proposed as a novel approach to High dimensional binary classification settings. Through employing a hybrid dissimilarity measure in KIN, it is possible to incorporate information of variables and distances simultaneously. Results: The proposed KIN not only selected a few number of biomarkers, it also reached a Higher accuracy compared to traditional k-nearest neighbors (61. 2% versus 60. 4%) and random forest (61. 2% versus 58. 5%) which are currently known as the best classifieres. Conclusion: Real metabolomics dataset demonstrate the superiority of proposed KIN versus KNN in terms of both classification accuracy and variable importance.

In this note we describe some recent advances in the area of maximal function inequalities. We also study the behaviour of the centered Hardy- Littlewood maximal operator associated to certain families of doubling, radial decreasing measures, and acting on radial functions. In fact, we precisely determine when the weak type (1, 1) bounds are uniform in the dimension.