If clustering can be performed in a continuous system, there is potential usefulness in processing speed for larger scale clustering. We have proposed clustering method of coupled chaotic circuit networks with learning. In this study, we propose a method to extract the center of a cluster by stabilizing synchronization through learning in networks where synchronization is not stable due to chaos.

Most machine learning algorithms are based on the formulation of an optimization problem using a global loss criterion. The essence of this formulation is a top-down engineering thinking that might have some limitations on the way towards a general artificial intelligence. In contrast, self-organizing maps use cooperative and competitive bottom-up rules to generate low-dimensional representations of complex input data. Following similar rules to SOMs, we develop a self-organization approach for a system of classifiers that combines top-down and bottom-up principles in a machine learning system. We believe that such a combination will overcome the limitations with respect to autonomous learning, robustness and self-repair that exist for pure top-down systems. Here we present a preliminary study using simple subsystems with limited learning capacities. As proof of principle, we study a network of simple artificial neural classifiers on the MNIST data set. Each classifier is able to recognize only one single digit. We demonstrate that upon training, the different classifiers are able to specialize their learning for a particular digit and cluster according to the digits. The entire system is capable of recognizing all digits and demonstrates the feasibility of combining bottom-up and top-down principles to solve a more complex task, while exhibiting strong spontaneous organization and robustness.

As early as the 1960s, oscillation phenomena observed in nonlinear circuits were actively studied. More than half a century has passed since then, and research on nonlinear circuits and networks has developed in a variety of fields, including physics, biology, neuroscience, electronics, and economics. In systems of coupled nonlinear circuits, various fascinating nonlinear phenomena can be observed, such as spatiotemporal chaos, oscillation quenching or, in particular, synchronization. Recently, many researchers have turned their interest to coupled nonlinear systems with particular coupling elements (e.g. delay coupling, hysteresis coupling, dynamical coupling) and network topologies (e.g. scale-free, small-world, frustrated networks). The discovery and investigation of mechanisms and forms of synchronization in such systems lays the foundation for future engineering applications.

In recent years, research on synchronization between coupled chaotic circuits has attracted interest in a wide range of fields. This is because the synchronization of coupled chaotic circuits is a multidisciplinary phenomenon that occurs in various applications, such as broadband communication systems or secure communication. In this study, we propose a coupled chaotic circuit network model with stochastic couplings. We investigate the synchronization phenomena observed for the proposed network using different network structures such as fully-coupled, random, small world and scale-free networks. We find that the same synchronization characteristics can be obtained for these networks with a dynamic topology as when the coupling strength is changed in static networks.

In this study, we focus on an effect of frustration to triangular oscillatory network with stochastically coupling. We propose a coupled nonliear circuit network with stochastically coupling. Frustration as environmental factor is occurred by network topology which is composed from polygonal structure. We investigate synchronization of the proposed network using different frustration levels by changing the coupling strength. By using computer simulations, the effect of frustration to triangular oscillatory networks with stochastically coupling is shown.

In this study, we focus on an effect of frustration to polygonal oscillatory network with stochastically coupling. We propose a coupled nonliear circuit network with stochastically coupling. Frustration as environmental factor is occurred by network topology which is composed from polygonal structure. We investigate synchronization of the proposed network using different frustration levels by changing the coupling strength. By using computer simulations, the effect of frustration to polygonal oscillatory networks with stochastically coupling is shown.

Recently, nature-inspired metaheuristic optimization algorithms such as Artificial Bee Colony Algorithm (ABC) is developed. ABC is based on the feeding behavior of bee herds. ABC can not solve for time-varying function. In this study, we offer a new ABC for time-varying function. We propose ABC in which the scout bee is improved probability by normal distribution. We compare the best solution with ABC, previous method and the proposed method. Object function which optimal solution moves circle of shape is used. We investigate characteristic of proposed method according to variance of normal distribution. Best value and orbit of solutions for proposed method are better than those of other method.

In this paper, we focus on clustering phenomena in a network composed of coupled chaotic circuits. In this investigation, the coupling strength is reflected by the distance information when the chaotic circuits are placed in a two-dimensional grid. We observe various clustering phenomena in the network of coupled chaotic circuits when we vary the scaling parameters, including the coupling strength, the distance between coupled chaotic circuits and the density of the chaotic circuits.

Recently, nature-inspired metaheuristic optimization algorithms such as Artificial Bee Colony Algorithm (ABC) is developed. ABC is based on the feeding behavior of bee herds. ABC can not solve for time-varying function. In this study, we offer a new ABC for time-varying function. We propose ABC in which the scout bee is improved probability by normal distribution. We compare the best solution with ABC, previous method and the proposed method. Object function which optimal solution moves circle of shape is used. We investigate characteristic of proposed method according to variance of normal distribution. Best value and orbit of solutions for proposed method are better than those of other method.

In this study, we propose a method of generating complex networks by exploiting synchronization between coupled oscillatory circuits. To each node of a 2D fully connected network a van der Pol oscillator is assigned. We then study the topological evolution of the network in dependence on environmental conditions. These conditions are modeled by considering the distance between the oscillators and some small frequency errors that are added. By carrying out computer simulations, we confirm that different types of complex networks are obtained depending on different environmental conditions.

In 2011, Senthilnath et al. proposed to utilize the Firefly Algorithm for K-means clustering. The algorithm has shown better results than the standard Kmeans algorithm or other combinations with bio-inspired optimization heuristics. In this study, we propose a further improvement of the method, based on an improved firefly algorithm. As a key aspect, the randomization parameter in our proposed algorithm is changed when the assignment does not change. We compare the standard K-means algorithm, K-means using the conventional Firefly Algorithm and our proposed algorithm on the basis of a simple data distribution. Numerical experiments show that our proposed algorithm is more efficient than the other algorithms.

In 2011, K-means algorithm combined Firefly Algorithm has been proposed by Mr. Senthilnath. This clustering algorithm has obtained better results than K-means algorithm and the other algorithms combined bio-inspired algorithm. In this study, we propose a new clustering algorithm; K-means algorithm combined improved Firefly Algorithm. One parameter of our proposed algorithm is changed when the assignment does not change. We compare K-means algorithm, K-means algorithm combined Firefly Algorithm and our proposed algorithm using simple model. Numerical experiments show our proposed algorithm is more efficient algorithm than the other algorithms.

When dealing with high-dimensional measurements that often show non-linear characteristics at multiple scales, a need for unbiased and robust classification and interpretation techniques has emerged. Here, we present a method for mapping high-dimensional data onto low-dimensional spaces, allowing for a fast visual interpretation of the data. Classical approaches of dimensionality reduction attempt to preserve the geometry of the data. They often fail to correctly grasp cluster structures, for instance in high-dimensional situations, where distances between data points tend to become more similar. In order to cope with this clustering problem, we propose to combine classical multi-dimensional scaling with data clustering based on self-organization processes in neural networks, where the goal is to amplify rather than preserve local cluster structures. We find that applying dimensionality reduction techniques to the output of neural network based clustering not only allows for a convenient visual inspection, but also leads to further insights into the intraand inter-cluster connectivity. We report on an implementation of the method with Rulkov-Hebbian-learning clustering and illustrate its suitability in comparison to traditional methods by means of an artificial dataset and a real world example.

Value differences across cultures or social groups are usually framed in terms of different emphases a particular group puts on specific values. For example, Western cultures typically prioritize values like autonomy and freedom, whereas East-Asian cultures put more emphasis on harmony and community. We present an alternative approach for investigating such cultural differences based on thesaurus databases that reflect the use of value terms in everyday language. We present a methodology that integrates empirical value research with linguistics and novel computer visualization tools to map and visualize value spaces. The maps outline variations in the semantic neighborhood of value terms. Based on 460 value terms both for US-English and German, we created for each language a map of 78 value classes that were further validated in two surveys. The use of such maps could inform research in three ways: first, by allowing for a controlled variability in the usage of value terms when generating vignettes; second, by indicating potential difficulties when translating value terms that display considerable differences in their semantic neighborhood; and third, as heuristics for better understanding value plurality.

Micro-texts emerging from social media platforms have become an important source for research. Automatized classification and interpretation of such micro-texts is challenging. The problem is exaggerated if the number of texts is at a medium level, making it too small for effective machine learning, but too big to be efficiently analyzed solely by humans. We present a semi-supervised learning system for micro-text classification that combines machine learning techniques with the unmatched human ability for making demanding, i.e. nonlinear decisions based on sparse data. We compare our system with human performance and a predefined optimal classifier using a validated benchmark data-set.

From 2004 to 2015, the market perception of the sovereign risks of the euro area government bonds experienced several different phases, reflected in a clear time structure of the correlation matrix between the yield changes. "Core" and "peripheral" bonds cluster in a bloc-like structure, but the correlations between the blocs are time-dependent and even become negative in periods of stress. Using noise-filtered partial correlation influences, this time dependency can be evaluated and visualized using network graphs. Our results support the view that market-implied spillover risks have decreased since the European rescue and stability mechanisms came into force in 2011. EFSF bond issues have been trading as part of the "core" bloc since 2011. In 2015, spillover risks reappeared during the Eurogroup's negotiations with Greece, although the periphery yields did not show risk spreads that were as large as those in 2012.