Combining the wavelet transform and forecasting models to predict gas forward prices

This paper presents a forecasting technique for forward energy prices, one day ahead. This technique combines a wavelet transform and forecasting models such as multi- layer perceptron, linear regression or GARCH. These techniques are applied to real data from the UK gas markets to evaluate their performance. The results show that the forecasting accuracy is improved significantly by using the wavelet transform. The methodology can be also applied to forecasting market clearing prices and electricity/gas loads.

On the annealed VC entropy for margin classifiers: A statistical mechanics study

Using techniques from Statistical Physics, the annealed VC entropy for hyperplanes in high dimensional spaces is calculated as a function of the margin for a spherical Gaussian distribution of inputs.

A generative probabilistic oriented wavelet model for texture segmentation

This Letter addresses image segmentation via a generative model approach. A Bayesian network (BNT) in the space of dyadic wavelet transform coefficients is introduced to model texture images. The model is similar to a Hidden Markov model (HMM), but with non-stationary transitive conditional probability distributions. It is composed of discrete hidden variables and observable Gaussian outputs for wavelet coefficients. In particular, the Gabor wavelet transform is considered. The introduced model is compared with the simplest joint Gaussian probabilistic model for Gabor wavelet coefficients for several textures from the Brodatz album [1]. The comparison is based on cross-validation and includes probabilistic model ensembles instead of single models. In addition, the robustness of the models to cope with additive Gaussian noise is investigated. We further study the feasibility of the introduced generative model for image segmentation in the novelty detection framework [2]. Two examples are considered: (i) sea surface pollution detection from intensity images and (ii) image segmentation of the still images with varying illumination across the scene.

A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Short-term electricity demand and gas price forecasts using wavelet transforms and adaptive models

This paper presents some forecasting techniques for energy demand and price prediction, one day ahead. These techniques combine wavelet transform (WT) with fixed and adaptive machine learning/time series models (multi-layer perceptron (MLP), radial basis functions, linear regression, or GARCH). To create an adaptive model, we use an extended Kalman filter or particle filter to update the parameters continuously on the test set. The adaptive GARCH model is a new contribution, broadening the applicability of GARCH methods. We empirically compared two approaches of combining the WT with prediction models: multicomponent forecasts and direct forecasts. These techniques are applied to large sets of real data (both stationary and non-stationary) from the UK energy markets, so as to provide comparative results that are statistically stronger than those previously reported. The results showed that the forecasting accuracy is significantly improved by using the WT and adaptive models. The best models on the electricity demand/gas price forecast are the adaptive MLP/GARCH with the multicomponent forecast; their MSEs are 0.02314 and 0.15384 respectively.

A novel entropy measure for analysis of the electrocardiogram

There has been much recent research into extracting useful diagnostic features from the electrocardiogram with numerous studies claiming impressive results. However, the robustness and consistency of the methods employed in these studies is rarely, if ever, mentioned. Hence, we propose two new methods; a biologically motivated time series derived from consecutive P-wave durations, and a mathematically motivated regularity measure. We investigate the robustness of these two methods when compared with current corresponding methods. We find that the new time series performs admirably as a compliment to the current method and the new regularity measure consistently outperforms the current measure in numerous tests on real and synthetic data.

From cardinal spline wavelet bases to highly coherent dictionaries

Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a dictionary, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterize the correlation of the dictionary elements by measuring their 'coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation.

Analysis of nocturnal oxygen saturation recordings using kernel entropy to assist in sleep apnea-hypopnea diagnosis

In this study, a new entropy measure known as kernel entropy (KerEnt), which quantifies the irregularity in a series, was applied to nocturnal oxygen saturation (SaO 2) recordings. A total of 96 subjects suspected of suffering from sleep apnea-hypopnea syndrome (SAHS) took part in the study: 32 SAHS-negative and 64 SAHS-positive subjects. Their SaO 2 signals were separately processed by means of KerEnt. Our results show that a higher degree of irregularity is associated to SAHS-positive subjects. Statistical analysis revealed significant differences between the KerEnt values of SAHS-negative and SAHS-positive groups. The diagnostic utility of this parameter was studied by means of receiver operating characteristic (ROC) analysis. A classification accuracy of 81.25% (81.25% sensitivity and 81.25% specificity) was achieved. Repeated apneas during sleep increase irregularity in SaO 2 data. This effect can be measured by KerEnt in order to detect SAHS. This non-linear measure can provide useful information for the development of alternative diagnostic techniques in order to reduce the demand for conventional polysomnography (PSG). © 2011 IEEE.

The detection of p-waves in ambulatory ECG recordings by the use of wavelet transforms

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Rotation invariant iris feature extraction using Gaussian Markov random fields with non-separable wavelet

Rotation invariance is important for an iris recognition system since changes of head orientation and binocular vergence may cause eye rotation. The conventional methods of iris recognition cannot achieve true rotation invariance. They only achieve approximate rotation invariance by rotating the feature vector before matching or unwrapping the iris ring at different initial angles. In these methods, the complexity of the method is increased, and when the rotation scale is beyond the certain scope, the error rates of these methods may substantially increase. In order to solve this problem, a new rotation invariant approach for iris feature extraction based on the non-separable wavelet is proposed in this paper. Firstly, a bank of non-separable orthogonal wavelet filters is used to capture characteristics of the iris. Secondly, a method of Markov random fields is used to capture rotation invariant iris feature. Finally, two-class kernel Fisher classifiers are adopted for classification. Experimental results on public iris databases show that the proposed approach has a low error rate and achieves true rotation invariance. © 2010.

Wavelet packet decomposition-based fault diagnosis scheme for SRM drives with a single current sensor

Power converters are a key, but vulnerable component in switched reluctance motor (SRM) drives. In this paper, a new fault diagnosis scheme for SRM converters is proposed based on the wavelet packet decomposition (WPD) with a dc-link current sensor. Open- and short-circuit faults of the power switches in an asymmetrical half-bridge converter are analyzed in details. In order to obtain the fault signature from the phase currents, two pulse-width modulation signals with phase shift are injected into the lower-switches of the converter to extract the excitation current, and the WPD algorithm is then applied to the detected currents for fault diagnosis. Moreover, a discrete degree of the wavelet packet node energy is chosen as the fault coefficient. The converter faults can be diagnosed and located directly by determining the changes in the discrete degree from the detected currents. The proposed scheme requires only one current sensor in the dc link, while conventional methods need one sensor for each phase or additional detection circuits. The experimental results on a 750-W three-phase SRM are presented to confirm the effectiveness of the proposed fault diagnosis scheme.

Hybrid sampling on mutual information entropy-based clustering ensembles for optimizations

In this paper, we focus on the design of bivariate EDAs for discrete optimization problems and propose a new approach named HSMIEC. While the current EDAs require much time in the statistical learning process as the relationships among the variables are too complicated, we employ the Selfish gene theory (SG) in this approach, as well as a Mutual Information and Entropy based Cluster (MIEC) model is also set to optimize the probability distribution of the virtual population. This model uses a hybrid sampling method by considering both the clustering accuracy and clustering diversity and an incremental learning and resample scheme is also set to optimize the parameters of the correlations of the variables. Compared with several benchmark problems, our experimental results demonstrate that HSMIEC often performs better than some other EDAs, such as BMDA, COMIT, MIMIC and ECGA. © 2009 Elsevier B.V. All rights reserved.

Design concept evaluation based on rough number and information entropy theory

Concept evaluation at the early phase of product development plays a crucial role in new product development. It determines the direction of the subsequent design activities. However, the evaluation information at this stage mainly comes from experts' judgments, which is subjective and imprecise. How to manage the subjectivity to reduce the evaluation bias is a big challenge in design concept evaluation. This paper proposes a comprehensive evaluation method which combines information entropy theory and rough number. Rough number is first presented to aggregate individual judgments and priorities and to manipulate the vagueness under a group decision-making environment. A rough number based information entropy method is proposed to determine the relative weights of evaluation criteria. The composite performance values based on rough number are then calculated to rank the candidate design concepts. The results from a practical case study on the concept evaluation of an industrial robot design show that the integrated evaluation model can effectively strengthen the objectivity across the decision-making processes.