70,381 research outputs found
A new class of wavelet networks for nonlinear system identification
A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions
Lattice dynamical wavelet neural networks implemented using particle swarm optimization for spatio-temporal system identification
In this brief, by combining an efficient wavelet representation with a coupled map lattice model, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNNs), is introduced for spatio-temporal system identification. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the OPP algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, however, may be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. An example for a real spatio-temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework
Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification
Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNN), is introduced for spatiotemporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimisation (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet-neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated waveletneurons are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares (OLS) algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet-neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet-neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework
Innovative Second-Generation Wavelets Construction With Recurrent Neural Networks for Solar Radiation Forecasting
Solar radiation prediction is an important challenge for the electrical
engineer because it is used to estimate the power developed by commercial
photovoltaic modules. This paper deals with the problem of solar radiation
prediction based on observed meteorological data. A 2-day forecast is obtained
by using novel wavelet recurrent neural networks (WRNNs). In fact, these WRNNS
are used to exploit the correlation between solar radiation and
timescale-related variations of wind speed, humidity, and temperature. The
input to the selected WRNN is provided by timescale-related bands of wavelet
coefficients obtained from meteorological time series. The experimental setup
available at the University of Catania, Italy, provided this information. The
novelty of this approach is that the proposed WRNN performs the prediction in
the wavelet domain and, in addition, also performs the inverse wavelet
transform, giving the predicted signal as output. The obtained simulation
results show a very low root-mean-square error compared to the results of the
solar radiation prediction approaches obtained by hybrid neural networks
reported in the recent literature
The Effects of International F/X Markets on Domestic Currencies Using Wavelet Networks: Evidence from Emerging Markets
This paper proposes a powerful methodology wavelet networks to investigate the effects of international F/X markets on emerging markets currencies. We used EUR/USD parity as input indicator (international F/X markets) and three emerging markets currencies as Brazilian Real, Turkish Lira and Russian Ruble as output indicator (emerging markets currency). We test if the effects of international F/X markets change across different timescale. Using wavelet networks, we showed that the effects of international F/X markets increase with higher timescale. This evidence shows that the causality of international F/X markets on emerging markets should be tested based on 64-128 days effect. We also find that the effects of EUR/USD parity on Turkish Lira is higher on 17-32 days and 65-128 days scales and this evidence shows that Turkish lira is less stable compare to other emerging markets currencies as international F/X markets effects Turkish lira on shorten time scale.F/X Markets; Emerging markets; Wavelet networks; Wavelets; Neural networks
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
Deep Convolutional Neural Networks Based on Semi-Discrete Frames
Deep convolutional neural networks have led to breakthrough results in
practical feature extraction applications. The mathematical analysis of these
networks was pioneered by Mallat, 2012. Specifically, Mallat considered
so-called scattering networks based on identical semi-discrete wavelet frames
in each network layer, and proved translation-invariance as well as deformation
stability of the resulting feature extractor. The purpose of this paper is to
develop Mallat's theory further by allowing for different and, most
importantly, general semi-discrete frames (such as, e.g., Gabor frames,
wavelets, curvelets, shearlets, ridgelets) in distinct network layers. This
allows to extract wider classes of features than point singularities resolved
by the wavelet transform. Our generalized feature extractor is proven to be
translation-invariant, and we develop deformation stability results for a
larger class of deformations than those considered by Mallat. For Mallat's
wavelet-based feature extractor, we get rid of a number of technical
conditions. The mathematical engine behind our results is continuous frame
theory, which allows us to completely detach the invariance and deformation
stability proofs from the particular algebraic structure of the underlying
frames.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT),
Hong Kong, China, June 2015, to appea
Choosing Wavelet Methods, Filters, and Lengths for Functional Brain Network Construction
Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into
time series representing neurophysiological activity in fixed frequency bands.
Using these time series, one can estimate frequency-band specific functional
connectivity between sensors or regions of interest, and thereby construct
functional brain networks that can be examined from a graph theoretic
perspective. Despite their common use, however, practical guidelines for the
choice of wavelet method, filter, and length have remained largely
undelineated. Here, we explicitly explore the effects of wavelet method (MODWT
vs. DWT), wavelet filter (Daubechies Extremal Phase, Daubechies Least
Asymmetric, and Coiflet families), and wavelet length (2 to 24) - each
essential parameters in wavelet-based methods - on the estimated values of
network diagnostics and in their sensitivity to alterations in psychiatric
disease. We observe that the MODWT method produces less variable estimates than
the DWT method. We also observe that the length of the wavelet filter chosen
has a greater impact on the estimated values of network diagnostics than the
type of wavelet chosen. Furthermore, wavelet length impacts the sensitivity of
the method to detect differences between health and disease and tunes
classification accuracy. Collectively, our results suggest that the choice of
wavelet method and length significantly alters the reliability and sensitivity
of these methods in estimating values of network diagnostics drawn from graph
theory. They furthermore demonstrate the importance of reporting the choices
utilized in neuroimaging studies and support the utility of exploring wavelet
parameters to maximize classification accuracy in the development of biomarkers
of psychiatric disease and neurological disorders.Comment: working pape
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