Community detection has become an important research topic in machine learning due to the proliferation of network data. However, most existing methods have been developed based on only exploiting the topology structures of the network, which can result in missing the advantage of using the nodes' attribute information. As a result, it is expected that much valuable information that could be used to improve the quality of discovered communities will be ignored. To solve this limitation, we propose a novel Augment Graph Regularization Nonnegative Matrix Factorization for Attributed Networks (AGNMF-AN) method, which is simple yet effective. Firstly, Augment Attributed Graph (AAG) is applied to combine both the topological structure and attributed nodes of the network. Secondly, we introduced an effective framework to update the affinity matrix, in which the affinity matrix's weight in each iteration is modified adaptively instead of using a fixed affinity matrix in the classical graph regularization-based nonnegative matrix factorization methods. Thirdly, the $l_{2,1}$ -norm is utilized to reduce the effect of random noise and outliers in the quality of structure community. Experimental results show that our method performs unexpectedly well in comparison to existing state-of-the-art methods in attributed networks.

Existence of debris structures inevitably ascends the rate of scour process around bridge piers and flow area not only lead into remarkable deviation of flow but also increase the velocity around bridge piers. A myriad of experimental and field studies to understand effective parameters on the scour depth with debris effects were conducted. To reach permissible values of the scour depth for the practical uses, relationships extracted in previous investigations suffer from lack of generalization for experimental data ranges. In this way, neuro-fuzzy group method of data handling (NF-GMDH)-based self-organized models is applied to evaluate the pier scour depth. In this study, NF-GMDH network is implemented using evolutionary algorithms listed particle swarm optimization (PSO), gravitational search algorithm (GSA), and genetic algorithm (GA). In all, 243 experimental datasets including a wide range of input and output parameters to develop the proposed models were compiled from various literature. The efficiency of NF-GMDH networks for training and testing stages was perused. NF-GMDH-PSO model provided the scour depth with more precise predictions (root mean squared error (RMSE) = 0.388 and scatter index (SI) = 0.343) in comparison with NF-GMDH-GA (RMSE = 0.402 and SI = 0.361) and NF-GMDH-GSA (RMSE = 0.456 and SI = 0.407) networks. In addition, blockage ratio (ΔA) was taken into account as the most sumptuous parameter with utmost level of effectiveness using the sensitivity analysis.

In this research, group method of data handling (GMDH) as a one of the self-organized approaches is utilized to predict three-dimensional free span expansion rates around pipeline due to waves. The GMDH network is developed using gene-expression programming (GEP) algorithm. In this way, GEP was performed in each neuron of GMDH instead of polynomial quadratic neuron. Effective parameters on the three-dimensional scour rates include sediment size, pipeline geometry, and wave characteristics upstream of pipeline. Four-dimensionless parameters are considered as input variables by means of dimensional analysis technique. Furthermore, scour rates along the pipeline, vertical scour rate, and additionally scour rates in the left and right of pipeline are determined as output parameters. Results of the proposed GMDH-GEP models for the training stages and testing ones are evaluated using various statistical indices. Performances of the GMDH-GEP models are compared with artificial neural network (ANN), GEP, GMDH, and traditional equations-based regression models. Moreover, sensitivity analysis and parametric study are conducted to perceive influences of different input parameters on the three-dimensional scour rates.

Subspace distance is an invaluable tool exploited in a wide range of feature selection methods. The power of subspace distance is that it can identify a representative subspace, including a group of features that can efficiently approximate the space of original features. On the other hand, employing intrinsic statistical information of data can play a significant role in a feature selection process. Nevertheless, most of the existing feature selection methods founded on the subspace distance are limited in properly fulfilling this objective. To pursue this void, we propose a framework that takes a subspace distance into account which is called "Variance-Covariance subspace distance". The approach gains advantages from the correlation of information included in the features of data, thus determines all the feature subsets whose corresponding Variance-Covariance matrix has the minimum norm property. Consequently, a novel, yet efficient unsupervised feature selection framework is introduced based on the Variance-Covariance distance to handle both the dimensionality reduction and subspace learning tasks. The proposed framework has the ability to exclude those features that have the least variance from the original feature set. Moreover, an efficient update algorithm is provided along with its associated convergence analysis to solve the optimization side of the proposed approach. An extensive number of experiments on nine benchmark datasets are also conducted to assess the performance of our method from which the results demonstrate its superiority over a variety of state-of-the-art unsupervised feature selection methods. The source code is available at https://github.com/SaeedKarami/VCSDFS.