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EEG signal classification for Epilepsy Seizure Detection using Improved Approximate Entropy  [cached]
Sharanreddy Mallikarjun Akareddy,P.K. Kulkarni
International Journal of Public Health Science , 2013, DOI: 10.11591/ijphs.v2i1.1836
Abstract: Epilepsy is a common chronic neurological disorder. Epilepsy seizures are the result of the transient and unexpected electrical disturbance of the brain. About 50 million people worldwide have epilepsy, and nearly two out of every three new cases are discovered in developing countries. Epilepsy is more likely to occur in young children or people over the age of 65 years; however, it can occur at any age. The detection of epilepsy is possible by analyzing EEG signals. This paper, presents a hybrid technique to classification EEG signals for identification of epilepsy seizure. Proposed system is combination of multi-wavelet transform and artificial neural network. Approximate Entropy algorithm is enhanced (called as Improved Approximate Entropy: IApE) to measure irregularities present in the EEG signals. The proposed technique is implemented, tested and compared with existing method, based on performance indices such as sensitivity, specificity, accuracy parameters. EEG signals are classified as normal and epilepsy seizures with an accuracy of ~90%.
Relative entropy minimizing noisy non-linear neural network to approximate stochastic processes  [PDF]
Mathieu N. Galtier,Camille Marini,Gilles Wainrib,Herbert Jaeger
Physics , 2014,
Abstract: A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear Inverse Modeling (LIM), under the common principle of relative entropy minimization. The power of the new method is demonstrated on a stochastic approximation of the El Nino phenomenon studied in climate research.
Efficient Approximation of the Conditional Relative Entropy with Applications to Discriminative Learning of Bayesian Network Classifiers  [PDF]
Alexandra M. Carvalho,Pedro Ad?o,Paulo Mateus
Entropy , 2013, DOI: 10.3390/e15072716
Abstract: We propose a minimum variance unbiased approximation to the conditional relative entropy of the distribution induced by the observed frequency estimates, for multi-classification tasks. Such approximation is an extension of a decomposable scoring criterion, named approximate conditional log-likelihood (aCLL), primarily used for discriminative learning of augmented Bayesian network classifiers. Our contribution is twofold: (i) it addresses multi-classification tasks and not only binary-classification ones; and (ii) it covers broader stochastic assumptions than uniform distribution over the parameters. Specifically, we considered a Dirichlet distribution over the parameters, which was experimentally shown to be a very good approximation to CLL. In addition, for Bayesian network classifiers, a closed-form equation is found for the parameters that maximize the scoring criterion.
Approximate tensorization of entropy at high temperature  [PDF]
Pietro Caputo,Georg Menz,Prasad Tetali
Mathematics , 2014,
Abstract: We show that for weakly dependent random variables the relative entropy functional satisfies an approximate version of the standard tensorization property which holds in the independent case. As a corollary we obtain a family of dimensionless logarithmic Sobolev inequalities. In the context of spin systems on a graph, the weak dependence requirements resemble the well known Dobrushin uniqueness conditions. Our results can be considered as a discrete counterpart of a recent work of Katalin Marton. We also discuss some natural generalizations such as approximate Shearer estimates and subadditivity of entropy.
Research of adaptive stochastic resonance based on approximate entropy

Li Qiang,Wang Tai-Yong,Leng Yong-Gang,He Gai-Yun,He Hui-Long,

物理学报 , 2007,
Abstract: Weak signal detection under the condition of adiabatic elimination in large parameters has been solved by step-changed stochastic resonance algorithm. Adaptive stochastic resonance based on approximate entropy measurement is proposed, and it can give the best result of the step-changed stochastic resonance adaptively. Because the approximate entropy of the periodic signal does not suffer from the change of its amplitude and phase, a periodic signal of frequency f0 with given signal-to-noise ratio which is to be detected can be made under the same condition as the raw data, and its approximate entropy is calculated as the criterion. By adjusting the structural parameters and calculation step automatically, a series output of the bistable system can be got, and an approximate entropy distance matrix can be constructed. After getting the minimum value of the matrix, the best parameters of the nonlinear dynamical system can be obtained.
Approximate Decoding Approaches for Network Coded Correlated Data  [PDF]
Hyunggon Park,Nikolaos Thomos,Pascal Frossard
Mathematics , 2011,
Abstract: This paper considers a framework where data from correlated sources are transmitted with help of network coding in ad-hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth bottlenecks. We first show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples about the possible of our algorithms that can be deployed in sensor networks and distributed imaging applications. In both cases, the experimental results confirm the validity of our analysis and demonstrate the benefits of our low complexity solution for delivery of correlated data sources.
Constrained Approximate Maximum Entropy Learning of Markov Random Fields  [PDF]
Varun Ganapathi,David Vickrey,John Duchi,Daphne Koller
Computer Science , 2012,
Abstract: Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning - maximizing entropy with moment matching constraints - and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piecewise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints.
The approximate entropy of the electromyographic signals of tremor correlates with the osmotic fragility of human erythrocytes
Paulo HG Mansur, Lacordaire KP Cury, José OB Leite, Adriano A Pereira, Nilson Penha-Silva, Adriano O Andrade
BioMedical Engineering OnLine , 2010, DOI: 10.1186/1475-925x-9-29
Abstract: This work sought correlations between the osmotic fragility of erythrocytes and features extracted from electromyographic (EMG) activity resulting from physiological tremor in healthy patients (N = 44) at different ages (24-87 years). The osmotic fragility was spectrophotometrically evaluated by the dependence of hemolysis, provided by the absorbance in 540 nm (A54o), on the concentration of NaCl. The data were adjusted to curves of sigmoidal regression and characterized by the half transition point (H50), amplitude of lysis transition (dx) and values of A540 in the curve regions that characterize the presence of lysed (A1) and preserved erythrocytes (A2). The approximate entropy was estimated from EMG signals detected from the extensor carpi ulnaris muscle during the movement of the hand of subjects holding up a laser pen towards an Archimedes spiral, fixed in a whiteboard. The evaluations were carried out with the laser pen at rest, at the center of the spiral, and in movement from the center to the outside and from outside to the center. The correlations among the parameters of osmotic fragility, tremor and age were tested.Negative correlations with age were found for A1 and dx. With the hand at rest, a positive correlation with H50 was found for the approximate entropy. Negative correlations with H50 were found for the entropy with the hand in movement, as from the center to the outside or from the outside to the center of the spiral.In healthy individuals, the increase in the erythrocyte osmotic fragility was associated with a decrease in the approximate entropy for rest tremor and with an increase of the entropy for movement tremor. This suggests that the neuromuscular degeneration associated with tremor entails also the mechanisms involved in the breakdown of structural homeostasis of the erythrocyte membrane.Tremor, the most common movement disorder, is defined as a rhythmic and involuntary oscillation of one part of the body, caused by reciprocally innervat
Entropy vectors and network codes  [PDF]
Terence Chan,Alex Grant
Mathematics , 2007,
Abstract: We consider a network multicast example that relates the solvability of the multicast problem with the existence of an entropy function. As a result, we provide an alternative approach to the proving of the insufficiency of linear (and abelian) network codes and demonstrate the utility of non-Shannon inequalities to tighten outer bounds on network coding capacity regions.
The entropy of randomized network ensembles  [PDF]
Ginestra Bianconi
Physics , 2007, DOI: 10.1209/0295-5075/81/28005
Abstract: Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same degree-correlations or the same community structure of any given real network. We characterize these randomized network ensembles by their entropy, i.e. the normalized logarithm of the total number of networks which are part of these ensembles. We estimate the entropy of randomized ensembles starting from a large set of real directed and undirected networks. We propose entropy as an indicator to assess the role of each structural feature in a given real network.We observe that the ensembles with fixed scale-free degree distribution have smaller entropy than the ensembles with homogeneous degree distribution indicating a higher level of order in scale-free networks.
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