The Advances of the Research for Random Recursive Sets(Ⅰ)

We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;

Efficiency-Controllable Random Walks on a Class of Recursive Scale-Free Trees with a Deep Trap

Controls, especially effficiency controls on dynamical processes, have become major challenges in many complex systems. We study an important dynamical process, random walk, due to its wide range of applications for modeling the transporting or searching process. For lack of control methods for random walks in various structures, a control technique is presented for a class of weighted treelike scale-free networks with a deep trap at a hub node. The weighted networks are obtained from original models by introducing a weight parameter. We compute analytically the mean first passage time （MFPT） as an indicator for quantitatively measurinM the et^ciency of the random walk process. The results show that the MFPT increases exponentially with the network size, and the exponent varies with the weight parameter. The MFPT, therefore, can be controlled by the weight parameter to behave superlinearly, linearly, or sublinearly with the system size. This work provides further useful insights into controllinM eftlciency in scale-free complex networks.

An Intrusion Detection System for SDN Using Machine Learning

Software Defined Networking(SDN)has emerged as a promising and exciting option for the future growth of the internet.SDN has increased the flexibility and transparency of the managed,centralized,and controlled network.On the other hand,these advantages create a more vulnerable environment with substantial risks,culminating in network difficulties,system paralysis,online banking frauds,and robberies.These issues have a significant detrimental impact on organizations,enterprises,and even economies.Accuracy,high performance,and real-time systems are necessary to achieve this goal.Using a SDN to extend intelligent machine learning methodologies in an Intrusion Detection System(IDS)has stimulated the interest of numerous research investigators over the last decade.In this paper,a novel HFS-LGBM IDS is proposed for SDN.First,the Hybrid Feature Selection algorithm consisting of two phases is applied to reduce the data dimension and to obtain an optimal feature subset.In thefirst phase,the Correlation based Feature Selection(CFS)algorithm is used to obtain the feature subset.The optimal feature set is obtained by applying the Random Forest Recursive Feature Elimination(RF-RFE)in the second phase.A LightGBM algorithm is then used to detect and classify different types of attacks.The experimental results based on NSL-KDD dataset show that the proposed system produces outstanding results compared to the existing methods in terms of accuracy,precision,recall and f-measure.

Identification of differential gene expression for microarray data using recursive random forest

Background The major difficulty in the research of DNA microarray data is the large number of genes compared with the relatively small number of samples as well as the complex data structure. Random forest has received much attention recently; its primary characteristic is that it can form a classification model from the data with high dimensionality. However, optimal results can not be obtained for gene selection since it is still affected by undifferentiated genes. We proposed recursive random forest analysis and applied it to gene selection. Methods Recursive random forest, which is an improvement of random forest, obtains optimal differentiated genes after step by step dropping of genes which, according to a certain algorithm, have no effects on classification. The method has the advantage of random forest and provides a gene importance scale as well. The value of the area under the curve （AUC） of the receiver operating characteristic （ROC） curve, which synthesizes the information of sensitivity and specificity, is adopted as the key standard for evaluating the performance of this method. The focus of the paper is to validate the effectiveness of gene selection using recursive random forest through the analysis of five microarray datasets; colon, prostate, leukemia, breast and skin data. Results Five microarray datasets were analyzed and better classification results have been attained using only a few genes after gene selection. The biological information of the selected genes from breast and skin data was confirmed according to the National Center for Biotechnology Information （NCBI）. The results prove that the genes associated with diseases can be effectively retained by recursive random forest. Conclusions Recursive random forest can be effectively applied to microarray data analysis and gene selection. The retained genes in the optimal model provide important information for clinical diagnoses and research of the biological mechanism of diseases.