Deterministic convergence analysis via smoothing group Lasso regularization and adaptive momentum for Sigma-Pi-Sigma neural network

A recurrent sigma pi sigma neural network

In this paper, a novel recurrent sigma‒sigma neural network (RSPSNN) that contains the same advantages as the higher-order and recurrent neural networks is proposed. The batch gradient algorithm is used to train the RSPSNN to search for the optimal weights based on the minimal mean squared error (MSE). To substantiate the unique equilibrium state of the RSPSNN, the characteristic of stability convergence is proven, which is one of the most significant indices for reflecting the effectiveness and overcoming the instability problem in the training of this network. Finally, to establish a more precise evaluation of its validity, five empirical experiments are used. The RSPSNN is successfully applied to the function approximation problem, prediction problem, parity problem, classification problem, and image simulation, which verifies its effectiveness and practicability.

Identification of water pollution sources and analysis of pollution trigger conditions in Jiuqu River, Luxian County, China

Against the backdrop of ecological conservation and high-quality development in the Yangtze River Basin, there is an increasing demand for enhanced water pollution prevention and control in small watersheds. To delve deeper into the intricate relationship between pollutants and environmental features, as well as explore the key factors triggering pollution and their corresponding warning thresholds, this study was conducted along the Jiuqu River, a strategically managed unit in the upstream region of the Yangtze River, between 2022 and 2023. A total of seven monitoring sites were established, from which 161 valid water samples were collected. The k-nearest neighbors mutual information (KNN-MI) technique indicated that water temperature (WT) and relative humidity (RH) were the main environmental factors. The principal component analysis (PCA) of ten water quality parameters and three environmental factors unveiled the distinguishing characteristics of the primary pollution sources. Consequently, the pollution sources were categorized as treated wastewater > groundwater runoff > phytoplankton growth > abstersion wastewater > agricultural drainage. Furthermore, the regression decision tree (RDT) algorithm was used to explore the combined effects between pollutants and environmental factors, and to provide visual decision-making process and quantitative results for understanding the triggering mechanism of organic pollution in Jiuqu River. It conclusively identifies total phosphorus (TP) as the predominant triggering parameter with the threshold of 0.138 mg/L. The study is helpful to deal with potential water pollution problems preventatively and shows the interpretability and predictive performance of the RDT algorithm in water pollution prevention.

A New Oversampling Method Based on the Classification Contribution Degree

Data imbalance is a thorny issue in machine learning. SMOTE is a famous oversampling method of imbalanced learning. However, it has some disadvantages such as sample overlapping, noise interference, and blindness of neighbor selection. In order to address these problems, we present a new oversampling method, OS-CCD, based on a new concept, the classification contribution degree. The classification contribution degree determines the number of synthetic samples generated by SMOTE for each positive sample. OS-CCD follows the spatial distribution characteristics of original samples on the class boundary, as well as avoids oversampling from noisy points. Experiments on twelve benchmark datasets demonstrate that OS-CCD outperforms six classical oversampling methods in terms of accuracy, F1-score, AUC, and ROC.