There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

A review on empirical mode decomposition in fault diagnosis of rotating machinery

Deep convolutional neural network for the automated detection and diagnosis of seizure using EEG signals.

In this paper, we present a new method for classification of electroencephalogram (EEG) signals using empirical mode decomposition (EMD) method. The intrinsic mode functions (IMFs) generated by EMD method can be considered as a set of amplitude and frequency modulated (AM-FM) signals. The Hilbert transformation of IMFs provides an analytic signal representation of the IMFs. The two bandwidths, namely amplitude modulation bandwidth (BAM) and frequency modulation bandwidth (BFM), computed from the analytic IMFs, have been used as an input to least squares support vector machine (LS-SVM) for classifying seizure and nonseizure EEG signals. The proposed method for classification of EEG signals based on the bandwidth features (BAM and BFM) and the LS-SVM has provided better classification accuracy than the method adopted by Liang and coworkers in their study published in 2010. The experimental results with the recorded EEG signals from a published dataset are included to show the effectiveness of the proposed method for EEG signal classification.

Classification of Seizure and Nonseizure EEG Signals Using Empirical Mode Decomposition

We propose new features for classification of epileptic seizure EEG signals.Features were extracted from PSR of IMFs of EEG signals.We define ellipse area of 2D PSR and IQR of Euclidian distance of 3D PSR as features.LS-SVM classifier has been used for classification with the proposed features.Results were compared with other existing methods studied on the same EEG dataset. Epileptic seizure is the most common disorder of human brain, which is generally detected from electroencephalogram (EEG) signals. In this paper, we have proposed the new features based on the phase space representation (PSR) for classification of epileptic seizure and seizure-free EEG signals. The EEG signals are firstly decomposed using empirical mode decomposition (EMD) and phase space has been reconstructed for obtained intrinsic mode functions (IMFs). For the purpose of classification of epileptic seizure and seizure-free EEG signals, two-dimensional (2D) and three-dimensional (3D) PSRs have been used. New features based on the 2D and 3D PSRs of IMFs have been proposed for classification of epileptic seizure and seizure-free EEG signals. Two measures have been defined namely, 95% confidence ellipse area for 2D PSR and interquartile range (IQR) of the Euclidian distances for 3D PSR of IMFs of EEG signals. These measured parameters show significant difference between epileptic seizure and seizure-free EEG signals. The combination of these measured parameters for different IMFs has been utilized to form the feature set for classification of epileptic seizure EEG signals. Least squares support vector machine (LS-SVM) has been employed for classification of epileptic seizure and seizure-free EEG signals, and its classification performance has been evaluated using different kernels namely, radial basis function (RBF), Mexican hat wavelet and Morlet wavelet kernels. Simulation results with various performance parameters of classifier, have been included to show the effectiveness of the proposed method for classification of epileptic seizure and seizure-free EEG signals.

Classification of epileptic seizures in EEG signals based on phase space representation of intrinsic mode functions

A new approach to characterize epileptic seizures using analytic time-frequency flexible wavelet transform and fractal dimension

Objective : This paper investigates the multivariate oscillatory nature of electroencephalogram (EEG) signals in adaptive frequency scales for epileptic seizure detection. Methods : The empirical wavelet transform (EWT) has been explored for the multivariate signals in order to determine the joint instantaneous amplitudes and frequencies in signal adaptive frequency scales. The proposed multivariate extension of EWT has been studied on multivariate multicomponent synthetic signal, as well as on multivariate EEG signals of Children's Hospital Boston-Massachusetts Institute of Technology (CHB-MIT) scalp EEG database. In a moving-window-based analysis, 2-s-duration multivariate EEG signal epochs containing five automatically selected channels have been decomposed and three features have been extracted from each 1-s part of the 2-s-duration joint instantaneous amplitudes of multivariate EEG signals. The extracted features from each oscillatory level have been processed using a proposed feature processing step and joint features have been computed in order to achieve better discrimination of seizure and seizure-free EEG signal epochs. Results : The proposed detection method has been evaluated over 177 h of EEG records using six classifiers. We have achieved average sensitivity, specificity, and accuracy values as 97.91%, 99.57%, and 99.41%, respectively, using tenfold cross-validation method, which are higher than the compared state of art methods studied on this database. Conclusion : Efficient detection of epileptic seizure is achieved when seizure events appear for long duration in hours long EEG recordings. Significance : The proposed method develops time–frequency plane for multivariate signals and builds patient-specific models for EEG seizure detection.

A Multivariate Approach for Patient-Specific EEG Seizure Detection Using Empirical Wavelet Transform

The brain is a complex structure made up of interconnected neurons, and its electrical activities can be evaluated using electroencephalogram (EEG) signals. The characteristics of the brain area affected by partial epilepsy can be studied using focal and non-focal EEG signals. In this work, a method for the classification of focal and non-focal EEG signals is presented using entropy measures. These entropy measures can be useful in assessing the nonlinear interrelation and complexity of focal and non-focal EEG signals. These EEG signals are first decomposed using the empirical mode decomposition (EMD) method to extract intrinsic mode functions (IMFs). The entropy features, namely, average Shannon entropy (ShEnAvg), average Renyi’s entropy (RenEnAvg ), average approximate entropy (ApEnAvg), average sample entropy (SpEnAvg) and average phase entropies (S1Avg and S2Avg), are computed from different IMFs of focal and non-focal EEG signals. These entropies are used as the input feature set for the least squares support vector machine (LS-SVM) classifier to classify into focal and non-focal EEG signals. Experimental results show that our proposed method is able to differentiate the focal and non-focal EEG signals with an average classification accuracy of 87% correct.

https://www.mdpi.com/1099-4300/17/2/669/pdf

Ram Bilas Pachori

Papers

Classification of Seizure and Nonseizure EEG Signals Using Empirical Mode Decomposition

Classification of epileptic seizures in EEG signals based on phase space representation of intrinsic mode functions

A new approach to characterize epileptic seizures using analytic time-frequency flexible wavelet transform and fractal dimension

A Multivariate Approach for Patient-Specific EEG Seizure Detection Using Empirical Wavelet Transform

Application of Entropy Measures on Intrinsic Mode Functions for the Automated Identification of Focal Electroencephalogram Signals