Wavelet design by means of multi-objective GAs for motor imagery EEG analysis

Wavelet-based analysis has been broadly used in the study of brain-computer interfaces (BCI), but in most cases these wavelet functions have not been designed taking into account the requirements of this field. In this study we propose a method to automatically generate wavelet-like functions by means of genetic algorithms. Results strongly indicate that it is possible to generate (evolve) wavelet functions that improve the classification accuracy compared to other well-known wavelets (e.g. Daubechies and Coiflets)

Evolutionary Computing and Second generation Wavelet Transform optimization: Current State of the Art

The Evolutionary Computation techniques are exposed to number of domains to achieve optimization. One of those domains is second generation wavelet transformations for image compression. Various types of Lifting Schemes are being introduced in recent literature. Since the growth in Lifting Schemes is in an incremental way and new types of Lifting Schemes are appearing continually. In this context, developing flexible and adaptive optimization approaches is a severe challenge. Evolutionary Computing based lifting scheme optimization techniques are a valuable technology to achieve better results in image compression. However, despite the variety of such methods described in the literature in recent years, security tools incorporating anomaly detection functionalities are just starting to appear, and several important problems remain to be solved. In this paper, we present a review of the most well-known EC approaches for optimizing Secondary level Wavelet transformations

Optimal design and control of stationary electrochemical double-layer capacitors for light railways

The optimisation algorithm has been further investigated to understand the influence of the weight coefficients that affect the solution of all the optimisation problems and it is very often overlooked in the traditional approach. In fact, the choice of weight coefficients leading to the optimum among different optimal solutions also presents a challenge and this specific problem does not give any a priori indications. This challenge has been tackled using both genetic algorithms and particle swarm optimisations, which are the best methods when there are multiple local optima and the number of parameters is large. The results show that, when the optimal set of coefficients are used and the optimal positions and capacitances of EDLCs are selected, the energy savings can be up to 42%. The second problem of the control of the storage has been tackled with a linear state of charge control based on a piece-wise linear characteristic between the current and the voltage deviation from the nominal voltage of the supply at the point of connection of the storage. The simulations show that, regardless of the initial state of charge, the control maintain the state of charge of EDLCs within the prescribed range with no need of using the on-board braking resistor and, hence, dissipating braking energy. The robustness of the control algorithm has been verified by changing the characteristics of the train loading and friction force, with an energy saving between 26 - 27%

Adaptive Conjoint Wavelet-Support Vector Classifiers

Combined wavelet - large margin classifiers succeed in solving difficult signal classification problems in cases where solely using a large margin classifier like, e.g., the Support Vector Machine may fail. This thesis investigates the problem of conjointly designing both classifier stages to achieve a most effective classifier architecture. Particularly, the wavelet features should be adapted to the Support Vector classifier and the specific classification problem. Three different approaches to achieve this goal are considered: The classifier performance is seriously affected by the wavelet or filter used for feature extraction. To optimally choose this wavelet with respect to the subsequent Support Vector classification, appropriate criteria may be used. The radius - margin Support Vector Machine error bound is proven to be computable by two standard Support Vector problems. Criteria which are computationally still more efficient may be sufficient for filter adaptation. For the classification by a Support Vector Machine, several criteria are examined rating feature sets obtained from various orthogonal filter banks. An adaptive search algorithm is devised that, once the criterion is fixed, efficiently finds the optimal wavelet filter. To extract shift invariant wavelet features, Kingsbury's dual-tree complex wavelet transform is examined. The dual-tree filter bank construction leads to wavelets with vanishing negative frequency parts. An enhanced transform is established in the frequency domain for standard wavelet filters without special filter design. The translation and rotational invariance is improved compared with the common wavelet transform as shown for various standard wavelet filters. So the framework well applies to adapted signal classification. Wavelet adaptation for signal classification is a special case of feature selection. Feature selection is an important combinatorial optimisation problem in the context of supervised pattern classification. Four novel continuous feature selection approaches directly minimising the classifier performance are presented. In particular, they include linear and nonlinear Support Vector classifiers. The key ideas of the approaches are additional regularisation and embedded nonlinear feature selection. To solve the optimisation problems, difference of convex functions programming which is a general framework for non-convex continuous optimisation is applied. This optimisation framework may also be interesting for other applications and succeeds in robustly solving the problems, and hence, building more powerful feature selection methods