Many real-world data are considered as graphs, such as computer networks, social networks and protein-protein interaction networks. Graph embedding methods are powerful tools for representing large graphs in various domains. A graph embedding method projects the components of a graph, such as its nodes or edges, into a vector space with a lower dimensionality than the adjacency matrix of the graph, and aims to preserve the characteristics of the graph. The generated embedding vectors have been utilized in various graph mining applications such as node classification, link prediction and anomaly detection. Despite the wide success of the graph embedding methods, little study has been done to facilitate a better understanding of the graph embeddings. In this paper, inspired by advancements in interpreting word embeddings, we propose two interpretability measures to quantify the interpretability of graph embeddings by leveraging useful network centrality properties and perform comparisons of different graph embedding methods. Using these scores, we can provide insights into the representational power of graph embedding methods.

Scientists' publication impacts ranking is an important topic in scientometrics which is performed based on various proposed criteria. One of the well-known indicators is h-index which evaluates researchers achievements based on number of citations. The h-index has utilized in many research data sources because of its appropriate properties, but similar to other assessment indicators, it has own disadvantages. hindex cannot give a fair comparison between junior and senior researches. There are two reasons for this unfair comparison: (1) h-index depends on the research period of scholars and (2) the number of received citations can be increased by time, even if researcher doesn't publish new papers, the h-index increases. Consequently, in addition to h-index, the number of the years of academic research (called the research period) is preferable to be considered as an independent indicator, which makes us able to have a more fair evaluation. So these two objectives, maximizing h-index and minimizing research period, can be considered as a multi-criteria comparison task to assess researchers. In this paper, we propose a strategy based on Pareto dominance ranking which uses dominance concept to obtain an order for researchers. In order to complete ranking between scientists in the same rank, a multi-criteria decision making measure called VIKOR is utilized. Therefore, a total ranking measure (P-V index) is obtained using Perto front concept and VIKOR measure. The proposed method is applied on 235 researchers who are conducting research on Evolutionary Computation (EC) topic. The h-index value and the research period of scholars are collected via Google Scholar service. P-V index obtains 26 Pareto ranks for all researchers and places six EC scientists on the first Pareto front.

In recent years, discovering relationships among entities and their features in a dataset has been received a great attention in data analytics. This study aims to reveal the relationships among entities in a dataset according to a specific sequence of features which are guided according to the accuracy of the hierarchical clustering made up by the features. In this paper, a new metric, called Discriminating Features based Cohesion (DFC) factor, is defined as pair-wise stickiness measure among entities which indicates their degree of attachment (i.e., cohesive force). In this direction, a new framework is proposed; which utilizes an evolutionary algorithm (i.e., DE) for the optimal discriminating feature selection and also a hierarchical clustering method for computing DFC factors. DE algorithm is employed to identify features which their clustering hierarchical tree has the maximum accuracy, then the intermediate and final DFC factors' matrices are computed by using a hierarchical clustering of the most discriminating features. The intermediate and final DFC factors' matrices have been utilized to discovery the knowledge among Dataset Entities including answering crucial data mining queries which cannot be answered by using a standalone clustering method. In order to conduct a case study, a real-world dataset is utilized; which contains 17 entities (i.e., countries) presented by corresponding 24 continuous features. The DE algorithm finds the most discriminating features in each step, which are eliminated for the next step to calculate a matrix of DFC factors. In the final step, the proposed method ranks the entities in terms of their DFC factor and features based on their elimination order (i.e., discrimination power).

Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream applications such as link prediction and anomaly detection, it is essential for such networks to be transferred into a low dimensional space. Recently, network embedding, a technique that converts a large graph into a low-dimensional representation, has become increasingly popular due to its strength in preserving the structure of a network. Efficient dynamic network embedding, however, has not yet been fully explored. In this paper, we present a dynamic network embedding method that integrates the history of nodes over time into the current state of nodes. The key contribution of our work is 1) generating dynamic network embedding by combining both dynamic and static node information 2) tracking history of neighbors of nodes using LSTM 3) significantly decreasing the time and memory by training an autoencoder LSTM model using temporal walks rather than adjacency matrices of graphs which are the common practice. We evaluate our method in multiple applications such as anomaly detection, link prediction and node classification in datasets from various domains.

Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evolving patterns in a large dynamic network. In this paper, we propose a dynamic embedding method, dynnode2vec, based on the well-known graph embedding method node2vec. Node2vec is a random walk based embedding method for static networks. Applying static network embedding in dynamic settings has two crucial problems: 1) Generating random walks for every time step is time consuming 2) Embedding vector spaces in each timestamp are different. In order to tackle these challenges, dynnode2vec uses evolving random walks and initializes the current graph embedding with previous embedding vectors. We demonstrate the advantages of the proposed dynamic network embedding by conducting empirical evaluations on several large dynamic network datasets.

In the recent years, Large-Scale Global Optimization (LSGO) algorithms attempt to solve real-world problems efficiently. The imbalance in the contribution of variables and the interaction among variables pose major challenges for LSGO algorithms. This paper proposes mapping schemes based on the interaction among variables and the imbalance in the contribution of variables. The proposed mapping schemes present the different relations between the constructed class of variables according to the interaction feature and the constructed class of variables according to the imbalance feature. Covering a wide range of real-world problems is considered in the mapping schemes; therefore it can provide some insights to design LSGO benchmark suites. By developing LSGO benchmark suites with the ability of representing many-real world problems, researchers will be motivated to realize the success or failure level of LSGO algorithms for tackling various types of LSGO problems. Also, a preliminary set of experiments is conducted to present the importance of considered features in each scheme.

Differential Evolution (DE) is a simple powerful evolutionary algorithm for solving global continuous optimization problems. The especial characteristic of DE algorithm is calculating a weighted difference vector of two random candidate solutions in the population to generate the new promising candidate solutions. A major operation of the DE algorithm is the mutation which can affect its performance. The main goal of this study is investigating the influence of ordering vectors on various mutation schemes. We design some Monte-Carlo based simulations to analyze several mutation schemes by calculating the probability of closeness of a new trial solutions to a random optimal solution. These simulations indicate that mutation schemes can enhance the performance of the DE algorithm which they consider right ordering of the vectors in their mutation operators. Also, we introduce a new mutation scheme which considers in ordering vectors in the mutation scheme. We benchmark the modified DE algorithm with the ordered mutation scheme (DE/order) on CEC-2014 test functions with three dimensions 30, 50, and 100. Simulation results confirm that DE/order obtains a promising performance on the majority of the test functions on all mentioned dimensions.

Cooperative Coevolution (CC) framework has become a powerful approach to solve large-scale global optimization problems effectively. Although a number of significant modifications of CC algorithms have been introduced in recent years, the theoretical studies of population initialization strategies in the CC framework are quite limited so far. The population initialization strategies can help a population-based algorithm to start with better candidate solutions for achieving better results. In this paper, we propose a CC algorithm with population initialization strategies based on the center region to improve its performance. Three population initialization strategies, namely, center-based normal distribution sampling, central golden region, and hybrid random-center normal distribution sampling are utilized in the CC framework. These population initialization strategies attempt to generate points around center-point with different schemes. The performance of the proposed algorithm is evaluated on CEC-2013 LSGO benchmark functions. Simulation results confirm that the proposed algorithm obtains a promising performance on the majority of the nonseparable high dimension benchmark functions.

Cooperative Co-evolutionary algorithms are effective approaches to solve large-scale optimization problems. The crucial challenge in these methods is the design of a decomposition method which is able to detect interactions among variables. In this paper, we proposed a decomposition method based on High Dimensional Model Representation (HDMR) which extracts separable and nonseparable subcomponents for Cooperative Co-evolutionary algorithms. The entire decomposition procedure is conducted before applying the optimization. The experimental results for D=1000 on twenty CEC-2010 benchmark functions show that the proposed method is promisingly efficient to solve large-scale optimization problems. The proposed approach is compared with two other methods and discussed in details.