Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm.

Model predictive control (MPC) has become one of the well-established modern control methods for three-phase inverters with an output LC filter, where a high-quality voltage with low total harmonic distortion (THD) is needed. Although it is an intuitive controller, easy to understand and implement, it has the significant disadvantage of requiring a large number of online calculations for solving the optimization problem. On the other hand, the application of model-free approaches such as those based on artificial neural networks approaches is currently growing rapidly in the area of power electronics and drives. This paper presents a new control scheme for a two-level converter based on combining MPC and feed-forward ANN, with the aim of getting lower THD and improving the steady and dynamic performance of the system for different types of loads. First, MPC is used, as an expert, in the training phase to generate data required for training the proposed neural network. Then, once the neural network is fine-tuned, it can be successfully used online for voltage tracking purpose, without the need of using MPC. The proposed ANN-based control strategy is validated through simulation, using MATLAB/Simulink tools, taking into account different loads conditions. Moreover, the performance of the ANN-based controller is evaluated, on several samples of linear and non-linear loads under various operating conditions, and compared to that of MPC, demonstrating the excellent steady-state and dynamic performance of the proposed ANNbased control strategy.Index Terms-Three-phase inverter, model predictive control, artificial neural network, UPS systems.

The class of mapping networks is a general family of tools to perform a wide variety of tasks. This paper presents a standardized, uniform representation for this class of networks, and introduces a simple modification of the multilayer perceptron with interesting practical properties, especially well suited to cope with pattern classification tasks. The proposed model unifies the two main representation paradigms found in the class of mapping networks for classification, namely, the surface-based and the prototype-based schemes, while retaining the advantage of being trainable by backpropagation. The enhancement in the representation properties and the generalization performance are assessed through results about the worst-case requirement in terms of hidden units and about the Vapnik-Chervonenkis dimension and cover capacity. The theoretical properties of the network also suggest that the proposed modification to the multilayer perceptron is in many senses optimal. A number of experimental verifications also confirm theoretical results about the model's increased performances, as compared with the multilayer perceptron and the Gaussian radial basis functions network.

We discuss the graded possibilistic model. We review some clustering algorithms derived from the basic c-Means and introduce a formalism to provide an alternative, unified perspective on these clustering algorithms, focused on the memberships rather than on the cost function. An interesting case is the concept of graded possibility. Its formulation includes as the two extreme cases the "probabilistic" assumption and the "possibilistic" assumption. A possible formulation can be stated as an interval equality constraint enforcing both the normality condition and the required graded possibilistic condition. We outline a basic example of graded possibilistic clustering algorithm.The experimental demonstrations presented aim at highlighting the different properties attainable through appropriate implementation of a suitable graded possibilistic model.