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

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

Electroencephalography (EEG) is an important tool for studying the human brain activity and epileptic processes in particular. EEG signals provide important information about epileptogenic networks that must be analyzed and understood before the initiation of therapeutic procedures. Very small variations in EEG signals depict a definite type of brain abnormality. The challenge is to design and develop signal processing algorithms which extract this subtle information and use it for diagnosis, monitoring and treatment of patients with epilepsy. This paper presents a review of wavelet techniques for computer-aided seizure detection and epilepsy diagnosis with an emphasis on research reported during the past decade. A multiparadigm approach based on the integration of wavelets, nonlinear dynamics and chaos theory, and neural networks advanced by Adeli and associates is the most effective method for automated EEG-based diagnosis of epilepsy.

Wavelet-based EEG processing for computer-aided seizure detection and epilepsy diagnosis.

http://www.psy.vanderbilt.edu/postdocs/gregoryrsl/cv/assets/ddg13nbr.pdf

Moment-to-moment brain signal variability: A next frontier in human brain mapping?

A novel wavelet-based algorithm for real-time detection of epileptic seizures using scalp EEG is proposed. In a moving-window analysis, the EEG from each channel is decomposed by wavelet packet transform. Using wavelet coefficients from seizure and nonseizure references, a patient-specific measure is developed to quantify the separation between seizure and nonseizure states for the frequency range of 1-30 Hz. Utilizing this measure, a frequency band representing the maximum separation between the two states is determined and employed to develop a normalized index, called combined seizure index (CSI). CSI is derived for each epoch of every EEG channel based on both rhythmicity and relative energy of that epoch as well as consistency among different channels. Increasing significantly during ictal states, CSI is inspected using one-sided cumulative sum test to generate proper channel alarms. Analyzing alarms from all channels, a seizure alarm is finally generated. The algorithm was tested on scalp EEG recordings from 14 patients, totaling 75.8 h with 63 seizures. Results revealed a high sensitivity of 90.5% , a false detection rate of 0.51 h-1 and a median detection delay of 7 s. The algorithm could also lateralize the focus side for patients with temporal lobe epilepsy.

Automated Real-Time Epileptic Seizure Detection in Scalp EEG Recordings Using an Algorithm Based on Wavelet Packet Transform

A novel patient-specific seizure prediction method based on the analysis of positive zero-crossing intervals in scalp electroencephalogram (EEG) is proposed. In a moving-window analysis, the histogram of these intervals for the current EEG epoch is computed, and the values corresponding to specific bins are selected as an observation. Then, the set of observations from the last 5 min is compared with two reference sets of data points (preictal and interictal) through novel measures of similarity and dissimilarity based on a variational Bayesian Gaussian mixture model of the data. A combined index is then computed and compared with a patient-specific threshold, resulting in a cumulative measure which is utilized to form an alarm sequence for each channel. Finally, this channel-based information is used to generate a seizure prediction alarm. The proposed method was evaluated using ~ 561 h of scalp EEG including a total of 86 seizures in 20 patients. A high sensitivity of 88.34% was achieved with a false prediction rate of 0.155 h-1 and an average prediction time of 22.5 min for the test dataset. The proposed method was also tested against a Poisson-based random predictor.

Predicting Epileptic Seizures in Scalp EEG Based on a Variational Bayesian Gaussian Mixture Model of Zero-Crossing Intervals

Electroencephalography (EEG) has an important role in the diagnosis and classification of epilepsy. It can provide information for predicting the response to antiseizure drugs and to identify the surgically remediable epilepsies. In temporal lobe epilepsy (TLE) seizures could originate in the medial or lateral neocortical temporal region, and many of these patients are refractory to medical treatment. However, majority of patients have had excellent results after surgery and this often relies on the EEG and magnetic resonance imaging (MRI) data in presurgical evaluation. If the scalp EEG data is insufficient or discordant, invasive EEG recording with placement of intracranial electrodes could identify the seizure focus prior to surgery. This paper highlights the general information regarding the use of EEG in epilepsy, EEG patterns resembling epileptiform discharges, and the interictal, ictal and postictal findings in mesial temporal lobe epilepsy using scalp and intracranial recordings prior to surgery. The utility of the automated seizure detection and computerized mathematical models for increasing yield of non-invasive localization is discussed. This paper also describes the sensitivity, specificity, and predictive value of EEG for seizure recurrence after withdrawal of medications following seizure freedom with medical and surgical therapy.

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Electroencephalography in Mesial Temporal Lobe Epilepsy: A Review

We describe a novel algorithm for the prediction of epileptic seizures using scalp EEG. The method is based on the analysis of the positive zero-crossing interval series of the EEG signal and its first and second derivatives as a measure of brain dynamics. In a moving-window analysis, we estimated the probability density of these intervals and computed the differential entropy. The resultant entropy time series were then inspected using the cumulative sum (CUSUM) procedure to detect decreases as precursors of upcoming seizures. In the next step, the alarm sequences resulting from analysis of the EEG waveform and its derivatives were combined. Finally, a seizure prediction index was generated based on the spatio-temporal processing of the combined CUSUM alarms. We evaluated our algorithm using a dataset of ∼21.5 hours of multichannel scalp EEG recordings from four patients with temporal lobe epilepsy, resulting in 87.5% sensitivity, a false prediction rate of 0.28/hr, and an average prediction time of 25 min.

An entropy-based approach to predict seizures in temporal lobe epilepsy using scalp EEG

A novel real-time patient-specific algorithm to predict epileptic seizures is proposed. The method is based on the analysis of the positive zero-crossing intervals in the scalp electroencephalogram (EEG), describing the brain dynamics. In a moving-window analysis, the histogram of these intervals in each EEG epoch is computed, and the distribution of the histogram value in specific bins, selected using interictal and preictal references, is estimated based on the values obtained from the current epoch and the epochs of the last 5 min. The resulting distribution for each selected bin is then compared to two reference distributions (interictal and preictal), and a seizure prediction index is developed. Comparing this index with a patient-specific threshold for all EEG channels, a seizure prediction alarm is finally generated. The algorithm was tested on ∼15.5 hours of multichannel scalp EEG recordings from three patients with temporal lobe epilepsy, including 14 seizures. 86% of seizures were predicted with an average prediction time of 20.8 min and a false prediction rate of 0.12/hr.

Manouchehr Javidan

Papers

Automated Real-Time Epileptic Seizure Detection in Scalp EEG Recordings Using an Algorithm Based on Wavelet Packet Transform

Predicting Epileptic Seizures in Scalp EEG Based on a Variational Bayesian Gaussian Mixture Model of Zero-Crossing Intervals

Electroencephalography in Mesial Temporal Lobe Epilepsy: A Review

An entropy-based approach to predict seizures in temporal lobe epilepsy using scalp EEG

Predicting temporal lobe epileptic seizures based on zero-crossing interval analysis in scalp EEG