266 research outputs found
Extended LaSalle's invariance principle for full-range cellular neural networks
In several relevant applications to the solution of signal processing tasks in real time, a cellular neural network (CNN) is required to be convergent, that is, each solution should tend toward some equilibrium point. The paper develops a Lyapunov method, which is based on a generalized version of LaSalle's invariance principle, for studying convergence and stability of the differential inclusions modeling the dynamics of the full-range (FR) model of CNNs. The applicability of the method is demonstrated by obtaining a rigorous proof of convergence for symmetric FR-CNNs. The proof, which is a direct consequence of the fact that a symmetric FR-CNN admits a strict Lyapunov function, is much more simple than the corresponding proof of convergence for symmetric standard CNNs
Nonlinear dynamics of full-range CNNs with time-varying delays and variable coefficients
In the article, the dynamical behaviours of the full-range cellular neural networks (FRCNNs) with variable coefficients and time-varying delays are considered. Firstly, the improved model of the FRCNNs is proposed, and the existence and uniqueness of the solution are studied by means of differential inclusions and set-valued analysis. Secondly, by using the Hardy inequality, the matrix analysis, and the Lyapunov functional method, we get some criteria for achieving the globally exponential stability (GES). Finally, some examples are provided to verify the correctness of the theoretical results
Convergence of Discrete-Time Cellular Neural Networks with Application to Image Processing
The paper considers a class of discrete-time cellular neural networks (DT-CNNs) obtained by applying Euler's discretization scheme to standard CNNs. Let T be the DT-CNN interconnection matrix which is defined by the feedback cloning template. The paper shows that a DT-CNN is convergent, i.e. each solution tends to an equilibrium point, when T is symmetric and, in the case where T + En is not positive-semidefinite, the step size of Euler's discretization scheme does not exceed a given bound (En is the n × n unit matrix). It is shown that two relevant properties hold as a consequence of the local and space-invariant interconnecting structure of a DT-CNN, namely: (1) the bound on the step size can be easily estimated via the elements of the DT-CNN feedback cloning template only; (2) the bound is independent of the DT-CNN dimension. These two properties make DT-CNNs very effective in view of computer simulations and for the practical applications to high-dimensional processing tasks. The obtained results are proved via Lyapunov approach and LaSalle's Invariance Principle in combination with some fundamental inequalities enjoyed by the projection operator on a convex set. The results are compared with previous ones in the literature on the convergence of DT-CNNs and also with those obtained for different neural network models as the Brain-State-in-a-Box model. Finally, the results on convergence are illustrated via the application to some relevant 2D and 1D DT-CNNs for image processing tasks
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Higher-Order Representations for Visual Recognition
In this thesis, we present a simple and effective architecture called Bilinear Convolutional Neural Networks (B-CNNs). These networks represent an image as a pooled outer product of features derived from two CNNs and capture localized feature interactions in a translationally invariant manner. B-CNNs generalize classical orderless texture-based image models such as bag-of-visual-words and Fisher vector representations. However, unlike prior work, they can be trained in an end-to-end manner. In the experiments, we demonstrate that these representations generalize well to novel domains by fine-tuning and achieve excellent results on fine-grained, texture and scene recognition tasks. The visualization of fine-tuned convolutional filters shows that the models are able to capture highly localized attributes. We present a texture synthesis framework that allows us to visualize the pre-images of fine-grained categories and the invariances that are captured by these models.
In order to enhance the discriminative power of the B-CNN representations, we investigate normalization techniques for rescaling the importance of individual features during aggregation. Spectral normalization scales the spectrum of the covariance matrix obtained after bilinear pooling and offers a significant improvement. However, the computation involves singular value decomposition, which is not computationally efficient on modern GPUs. We present an iteration-based approximation of matrix square-root along with its gradients to speed up the computation and study its effect on fine-tuning deep neural networks. Another approach is democratic aggregation, which aims to equalize the contributions of individual feature vector into the final pooled image descriptor. This achieves a comparable improvement, and can be approximated in a low-dimensional embedding unlike the spectral normalization. Therefore, this approach is friendly to aggregating higher-dimensional features. We demonstrate that the two approaches are closely related, and we discuss their trade-off between performance and efficiency
Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to
predict. This makes the design of accurate and stable reduced-order models
challenging. The overarching objective of this paper is to propose a nonlinear
decomposition of the turbulent state for a reduced-order representation of the
dynamics. We divide the turbulent flow into a spatial problem and a temporal
problem. First, we compute the latent space, which is the manifold onto which
the turbulent dynamics live (i.e., it is a numerical approximation of the
turbulent attractor). The latent space is found by a series of nonlinear
filtering operations, which are performed by a convolutional autoencoder (CAE).
The CAE provides the decomposition in space. Second, we predict the time
evolution of the turbulent state in the latent space, which is performed by an
echo state network (ESN). The ESN provides the decomposition in time. Third, by
assembling the CAE and the ESN, we obtain an autonomous dynamical system: the
convolutional autoncoder echo state network (CAE-ESN). This is the
reduced-order model of the turbulent flow. We test the CAE-ESN on a
two-dimensional flow. We show that, after training, the CAE-ESN (i) finds a
latent-space representation of the turbulent flow that has less than 1% of the
degrees of freedom than the physical space; (ii) time-accurately and
statistically predicts the flow in both quasiperiodic and turbulent regimes;
(iii) is robust for different flow regimes (Reynolds numbers); and (iv) takes
less than 1% of computational time to predict the turbulent flow than solving
the governing equations. This work opens up new possibilities for nonlinear
decompositions and reduced-order modelling of turbulent flows from data
Functional data learning using convolutional neural networks
In this paper, we show how convolutional neural networks (CNN) can be used in
regression and classification learning problems of noisy and non-noisy
functional data. The main idea is to transform the functional data into a 28 by
28 image. We use a specific but typical architecture of a convolutional neural
network to perform all the regression exercises of parameter estimation and
functional form classification. First, we use some functional case studies of
functional data with and without random noise to showcase the strength of the
new method. In particular, we use it to estimate exponential growth and decay
rates, the bandwidths of sine and cosine functions, and the magnitudes and
widths of curve peaks. We also use it to classify the monotonicity and
curvatures of functional data, algebraic versus exponential growth, and the
number of peaks of functional data. Second, we apply the same convolutional
neural networks to Lyapunov exponent estimation in noisy and non-noisy chaotic
data, in estimating rates of disease transmission from epidemic curves, and in
detecting the similarity of drug dissolution profiles. Finally, we apply the
method to real-life data to detect Parkinson's disease patients in a
classification problem. The method, although simple, shows high accuracy and is
promising for future use in engineering and medical applications.Comment: 38 pages, 23 figure
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