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.

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.

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.

Cortical oscillatory activity associated with the perception of illusory and real visual contours

We used magnetoencephalography (MEG) to examine the nature of oscillatory brain rhythms when passively viewing both illusory and real visual contours. Three stimuli were employed: a Kanizsa triangle; a Kanizsa triangle with a real triangular contour superimposed; and a control figure in which the corner elements used to form the Kanizsa triangle were rotated to negate the formation of illusory contours. The MEG data were analysed using synthetic aperture magnetometry (SAM) to enable the spatial localisation of task-related oscillatory power changes within specific frequency bands, and the time-course of activity within given locations-of-interest was determined by calculating time-frequency plots using a Morlet wavelet transform. In contrast to earlier studies, we did not find increases in gamma activity (> 30 Hz) to illusory shapes, but instead a decrease in 10–30 Hz activity approximately 200 ms after stimulus presentation. The reduction in oscillatory activity was primarily evident within extrastriate areas, including the lateral occipital complex (LOC). Importantly, this same pattern of results was evident for each stimulus type. Our results further highlight the importance of the LOC and a network of posterior brain regions in processing visual contours, be they illusory or real in nature. The similarity of the results for both real and illusory contours, however, leads us to conclude that the broadband (< 30 Hz) decrease in power we observed is more likely to reflect general changes in visual attention than neural computations specific to processing visual contours.

Techniques to improve forecasting models: applications to energy demand and price

This thesis is a study of three techniques to improve performance of some standard fore-casting models, application to the energy demand and prices. We focus on forecasting demand and price one-day ahead. First, the wavelet transform was used as a pre-processing procedure with two approaches: multicomponent-forecasts and direct-forecasts. We have empirically compared these approaches and found that the former consistently outperformed the latter. Second, adaptive models were introduced to continuously update model parameters in the testing period by combining ?lters with standard forecasting methods. Among these adaptive models, the adaptive LR-GARCH model was proposed for the fi?rst time in the thesis. Third, with regard to noise distributions of the dependent variables in the forecasting models, we used either Gaussian or Student-t distributions. This thesis proposed a novel algorithm to infer parameters of Student-t noise models. The method is an extension of earlier work for models that are linear in parameters to the non-linear multilayer perceptron. Therefore, the proposed method broadens the range of models that can use a Student-t noise distribution. Because these techniques cannot stand alone, they must be combined with prediction models to improve their performance. We combined these techniques with some standard forecasting models: multilayer perceptron, radial basis functions, linear regression, and linear regression with GARCH. These techniques and forecasting models were applied to two datasets from the UK energy markets: daily electricity demand (which is stationary) and gas forward prices (non-stationary). The results showed that these techniques provided good improvement to prediction performance.

The spatial distribution and temporal dynamics of brain regions activated during the perception of object and non-object patterns

Both animal and human studies suggest that the efficiency with which we are able to grasp objects is attributable to a repertoire of motor signals derived directly from vision. This is in general agreement with the long-held belief that the automatic generation of motor signals by the perception of objects is based on the actions they afford. In this study, we used magnetoencephalography (MEG) to determine the spatial distribution and temporal dynamics of brain regions activated during passive viewing of object and non-object targets that varied in the extent to which they afforded a grasping action. Synthetic Aperture Magnetometry (SAM) was used to localize task-related oscillatory power changes within specific frequency bands, and the time course of activity within given regions-of-interest was determined by calculating time-frequency plots using a Morlet wavelet transform. Both single subject and group-averaged data on the spatial distribution of brain activity are presented. We show that: (i) significant reductions in 10-25 Hz activity within extrastriate cortex, occipito-temporal cortex, sensori-motor cortex and cerebellum were evident with passive viewing of both objects and non-objects; and (ii) reductions in oscillatory activity within the posterior part of the superior parietal cortex (area Ba7) were only evident with the perception of objects. Assuming that focal reductions in low-frequency oscillations (< 30 Hz) reflect areas of heightened neural activity, we conclude that: (i) activity within a network of brain areas, including the sensori-motor cortex, is not critically dependent on stimulus type and may reflect general changes in visual attention; and (ii) the posterior part of the superior parietal cortex, area Ba7, is activated preferentially by objects and may play a role in computations related to grasping. © 2006 Elsevier Inc. All rights reserved.

Functional neuroimaging and behavioural studies on global form processing in the human visual system

Magnetoencephalography (MEG), functional magnetic resonance imaging (fMRI) and behavioural experiments were used to investigate the neural processes underlying global form perception in human vision. Behavioural studies using Glass patterns examined sensitivity for detecting radial, rotational and horizontal structure. Neuroimaging experiments using either Glass patterns or arrays of Gabor patches determined the spatio-temporal neural responseto global form. MEG data were analysed using synthetic aperture magnetometry (SAM) to spatially map event-related cortical oscillatory power changes: the temporal sequencing of activity within a discrete cortical area was determined using a Morlet wavelet transform. A case study was conducted to determine the effects of strbismic amblyopia on global form processing: all other observers were normally-sighted. The main findings from normally-sighted observers were: 1) sensitivity to horizontal structure was less than for radial or rotational structure; 2) the neural response to global structure was a reduction in cortical oscillatory power (10-30 Hz) within a network of extrastriate areas, including V4 and V3a; 3) the extend of reduced cortical power was least for horizontal patters; 4) V1 was not identified as a region of peak activity with either MEG or fMRI. The main findings with the strabismic amblyope were: 1) sensitivity for detection of radial, rotational, and horizontal structure was reduced when viewed with the amblyopic- relative to the fellow- eye; 2) cortical power changes within V4 to the presentation of rotational Glass patterns were less when viewed with the amblyopic- compared with the fellow- eye. The main conclusions are: 1) a network of extrastriate cortical areas are involved in the analysis of global form, with the most prominent change in neural activity being a reduction in oscillatory power within the 10-30 Hz band; 2) in strabismic amblyopia, the neuronal assembly associated with form perception in extrastriate cortex may be dysfunctional, the nature of this dysfunction may be a change in the normal temporal pattern of neuronal discharges; 3) MEG, fMRI and behavioural measures support the notion that different neural processes underlie the perception of horizontal as opposed to radial or rotational structure.

Colour image coding with wavelets and matching pursuit

This thesis considers sparse approximation of still images as the basis of a lossy compression system. The Matching Pursuit (MP) algorithm is presented as a method particularly suited for application in lossy scalable image coding. Its multichannel extension, capable of exploiting inter-channel correlations, is found to be an efficient way to represent colour data in RGB colour space. Known problems with MP, high computational complexity of encoding and dictionary design, are tackled by finding an appropriate partitioning of an image. The idea of performing MP in the spatio-frequency domain after transform such as Discrete Wavelet Transform (DWT) is explored. The main challenge, though, is to encode the image representation obtained after MP into a bit-stream. Novel approaches for encoding the atomic decomposition of a signal and colour amplitudes quantisation are proposed and evaluated. The image codec that has been built is capable of competing with scalable coders such as JPEG 2000 and SPIHT in terms of compression ratio.

No-reference image quality assessment in contourlet domain

The target of no-reference (NR) image quality assessment (IQA) is to establish a computational model to predict the visual quality of an image. The existing prominent method is based on natural scene statistics (NSS). It uses the joint and marginal distributions of wavelet coefficients for IQA. However, this method is only applicable to JPEG2000 compressed images. Since the wavelet transform fails to capture the directional information of images, an improved NSS model is established by contourlets. In this paper, the contourlet transform is utilized to NSS of images, and then the relationship of contourlet coefficients is represented by the joint distribution. The statistics of contourlet coefficients are applicable to indicate variation of image quality. In addition, an image-dependent threshold is adopted to reduce the effect of content to the statistical model. Finally, image quality can be evaluated by combining the extracted features in each subband nonlinearly. Our algorithm is trained and tested on the LIVE database II. Experimental results demonstrate that the proposed algorithm is superior to the conventional NSS model and can be applied to different distortions. © 2009 Elsevier B.V. All rights reserved.