A new clustering method based on multipartite networks.

The clustering problem is one of the most studied and challenging in machine learning, as it attempts to identify similarities within data without any prior knowledge. Among modern clustering algorithms, the network-based ones are some of the most popular. Most of them convert the data into a graph in which instances of the data represent the nodes and a similarity measure is used to add edges. This article proposes a novel approach that uses a multipartite network in which layers correspond to attributes of the data and nodes represent intervals for the data. Clusters are intuitively constructed based on the information provided by the paths in the network. Numerical experiments performed on synthetic and real-world benchmarks are used to illustrate the performance of the approach. As a real application, the method is used to group countries based on health, nutrition, and population information from the World Bank database. The results indicate that the proposed method is comparable in performance with some of the state-of-the-art clustering methods, outperforming them for some data sets.

A game-theoretic model for the classification of selected oil companies' price changes.

One of the essential properties of a machine learning model is to be able to capture nuanced connections within data. This ability can be enhanced by considering alternative solution concepts, such as those offered by game theory. In this article, the Nash equilibrium is used as a solution concept to estimate probit parameters for the binary classification problem. A non-cooperative game is proposed in which data variables are players that attempt to maximize their marginal contribution to the log-likelihood function. A differential evolution algorithm is adapted to solve the proposed game. The new method is used to study the price changes of the Romanian oil company, OMV Petrom SA Romania, relative to the price of oil (crude and Brent) and the evolution of two other major oil companies with influence in the region. Results show that the proposed method outperforms the baseline probit and classical classification approaches in predicting price changes.

Characterization and Detection of ϵ-Berge-Zhukovskii Equilibria.

The Berge-Zhukovskii equilibrium is an alternate solution concept in non-cooperative game theory that formalizes cooperation in a noncooperative setting. In this paper, the ϵ-Berge-Zhukovskii equilibrium is introduced and characterized by using a generative relation. The generative relation also provides a solution to the problem of computing the ϵ-Berge-Zhukovskii equilibrium for large games, by using evolutionary algorithms. Numerical examples illustrate the approach and provide a possible application for this equilibrium concept.

Game theory and extremal optimization for community detection in complex dynamic networks.

The detection of evolving communities in dynamic complex networks is a challenging problem that recently received attention from the research community. Dynamics clearly add another complexity dimension to the difficult task of community detection. Methods should be able to detect changes in the network structure and produce a set of community structures corresponding to different timestamps and reflecting the evolution in time of network data. We propose a novel approach based on game theory elements and extremal optimization to address dynamic communities detection. Thus, the problem is formulated as a mathematical game in which nodes take the role of players that seek to choose a community that maximizes their profit viewed as a fitness function. Numerical results obtained for both synthetic and real-world networks illustrate the competitive performance of this game theoretical approach.