A novel granular approach for detecting dynamic online communities in social network

The great surge in the research of community discovery in complex network is going on due to its challenging aspects. Dynamicity and overlapping nature are among the common characteristics of these networks which are the main focus of this paper. In this research, we attempt to approximate the granular human-inspired viewpoints of the networks. This is especially helpful when making decisions with partial knowledge. In line with the principle of granular computing, in which precision is avoided, we define the micro- and macrogranules in two levels of nodes and communities, respectively. The proposed algorithm takes microgranules as input and outputs meaningful communities in rough macrocommunity form. For this purpose, the microgranules are drawn toward each other based on a new rough similarity measure defined in this paper. As a result, the structure of communities is revealed and adapted over time, according to the interactions observed in the network, and the number of communities is extracted automatically. The proposed model can deal with both the low and the sharp changes in the network. The algorithm is evaluated in multiple dynamic datasets and the results confirm the superiority of the proposed algorithm in various measures and scenarios

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Clustering of nonstationary data streams: a survey of fuzzy partitional methods

YesData streams have arisen as a relevant research topic during the past decade. They are real‐time, incremental in nature, temporally ordered, massive, contain outliers, and the objects in a data stream may evolve over time (concept drift). Clustering is often one of the earliest and most important steps in the streaming data analysis workflow. A comprehensive literature is available about stream data clustering; however, less attention is devoted to the fuzzy clustering approach, even though the nonstationary nature of many data streams makes it especially appealing. This survey discusses relevant data stream clustering algorithms focusing mainly on fuzzy methods, including their treatment of outliers and concept drift and shift.Ministero dell‘Istruzione, dell‘Universitá e della Ricerca

GBMST: An Efficient Minimum Spanning Tree Clustering Based on Granular-Ball Computing

Most of the existing clustering methods are based on a single granularity of information, such as the distance and density of each data. This most fine-grained based approach is usually inefficient and susceptible to noise. Therefore, we propose a clustering algorithm that combines multi-granularity Granular-Ball and minimum spanning tree (MST). We construct coarsegrained granular-balls, and then use granular-balls and MST to implement the clustering method based on "large-scale priority", which can greatly avoid the influence of outliers and accelerate the construction process of MST. Experimental results on several data sets demonstrate the power of the algorithm. All codes have been released at https://github.com/xjnine/GBMST

A finder and representation system for knowledge carriers based on granular computing

In one of his publications Aristotle states ”All human beings by their nature desire to know” [Kraut 1991]. This desire is initiated the day we are born and accompanies us for the rest of our life. While at a young age our parents serve as one of the principle sources for knowledge, this changes over the course of time. Technological advances and particularly the introduction of the Internet, have given us new possibilities to share and access knowledge from almost anywhere at any given time. Being able to access and share large collections of written down knowledge is only one part of the equation. Just as important is the internalization of it, which in many cases can prove to be difficult to accomplish. Hence, being able to request assistance from someone who holds the necessary knowledge is of great importance, as it can positively stimulate the internalization procedure. However, digitalization does not only provide a larger pool of knowledge sources to choose from but also more people that can be potentially activated, in a bid to receive personalized assistance with a given problem statement or question. While this is beneficial, it imposes the issue that it is hard to keep track of who knows what. For this task so-called Expert Finder Systems have been introduced, which are designed to identify and suggest the most suited candidates to provide assistance. Throughout this Ph.D. thesis a novel type of Expert Finder System will be introduced that is capable of capturing the knowledge users within a community hold, from explicit and implicit data sources. This is accomplished with the use of granular computing, natural language processing and a set of metrics that have been introduced to measure and compare the suitability of candidates. Furthermore, are the knowledge requirements of a problem statement or question being assessed, in order to ensure that only the most suited candidates are being recommended to provide assistance

Streaming Feature Grouping and Selection (Sfgs) For Big Data Classification

Real-time data has always been an essential element for organizations when the quickness of data delivery is critical to their businesses. Today, organizations understand the importance of real-time data analysis to maintain benefits from their generated data. Real-time data analysis is also known as real-time analytics, streaming analytics, real-time streaming analytics, and event processing. Stream processing is the key to getting results in real-time. It allows us to process the data stream in real-time as it arrives. The concept of streaming data means the data are generated dynamically, and the full stream is unknown or even infinite. This data becomes massive and diverse and forms what is known as a big data challenge. In machine learning, streaming feature selection has always been a preferred method in the preprocessing of streaming data. Recently, feature grouping, which can measure the hidden information between selected features, has begun gaining attention. This dissertation’s main contribution is in solving the issue of the extremely high dimensionality of streaming big data by delivering a streaming feature grouping and selection algorithm. Also, the literature review presents a comprehensive review of the current streaming feature selection approaches and highlights the state-of-the-art algorithms trending in this area. The proposed algorithm is designed with the idea of grouping together similar features to reduce redundancy and handle the stream of features in an online fashion. This algorithm has been implemented and evaluated using benchmark datasets against state-of-the-art streaming feature selection algorithms and feature grouping techniques. The results showed better performance regarding prediction accuracy than with state-of-the-art algorithms

A methodology for automatic parameter-tuning and center selection in density-peak clustering methods

The density-peak clustering algorithm, which we refer to as DPC, is a novel and efficient density-based clustering approach. The method has the advantage of allowing non-convex clusters, and clusters of variable size and density, to be grouped together, but it also has some limitations, such as the visual location of centers and the parameter tuning. This paper describes an optimization-based methodology for automatic parameter/center selection applicable both to the DPC and to other algorithms derived from it. The objective function is an internal/external cluster validity index, and the decisions are the parameterization of the algorithm and the choice of centers. The internal validation measures lead to an automatic parameter-tuning process, and the external validation measures lead to the so-called optimal rules, which are a tool to bound the performance of a given algorithm from above on the set of parameterizations. A numerical experiment with real data was performed for the DPC and for the fuzzy weighted k-nearest neighbor (FKNN-DPC) which validates the automatic parameter-tuning methodology and demonstrates its efficiency compared to the state of the art.El algoritmo de agrupamiento de picos de densidad, al que nos referimos como DPC , es un enfoque de agrupamiento basado en la densidad novedoso y eficiente. El método tiene la ventaja de permitir agrupar clústeres no convexos y clústeres de tamaño y densidad variables, pero también tiene algunas limitaciones, como la ubicación visual de los centros y el ajuste de parámetros. Este artículo describe una metodología basada en la optimización para la selección automática de parámetros/centros aplicable tanto al DPC como a otros algoritmos derivados de él. La función objetivo es un índice de validez de clúster interno/externo, y las decisiones son la parametrización del algoritmo y la elección de los centros. Las medidas de validación interna conducen a un proceso automático de ajuste de parámetros, y las medidas de validación externa conducen al llamadoreglas óptimas , que son una herramienta para limitar el rendimiento de un algoritmo dado desde arriba en el conjunto de parametrizaciones. Se realizó un experimento numérico con datos reales para el DPC y para el k -vecino más cercano ponderado difuso ( FKNN-DPC ) que valida la metodología de ajuste automático de parámetros y demuestra su eficiencia en comparación con el estado del arte

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches