One-shot Learning for iEEG Seizure Detection Using End-to-end Binary Operations: Local Binary Patterns with Hyperdimensional Computing

This paper presents an efficient binarized algorithm for both learning and classification of human epileptic seizures from intracranial electroencephalography (iEEG). The algorithm combines local binary patterns with brain-inspired hyperdimensional computing to enable end-to-end learning and inference with binary operations. The algorithm first transforms iEEG time series from each electrode into local binary pattern codes. Then atomic high-dimensional binary vectors are used to construct composite representations of seizures across all electrodes. For the majority of our patients (10 out of 16), the algorithm quickly learns from one or two seizures (i.e., one-/few-shot learning) and perfectly generalizes on 27 further seizures. For other patients, the algorithm requires three to six seizures for learning. Overall, our algorithm surpasses the state-of-the-art methods for detecting 65 novel seizures with higher specificity and sensitivity, and lower memory footprint.Comment: Published as a conference paper at the IEEE BioCAS 201

A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands

This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem

Analysis of noise-induced temporal correlations in neuronal spike sequences

This is a copy of the author 's final draft version of an article published in the journal European physical journal. Special topics. The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60024-6We investigate temporal correlations in sequences of noise-induced neuronal spikes, using a symbolic method of time-series analysis. We focus on the sequence of time-intervals between consecutive spikes (inter-spike-intervals, ISIs). The analysis method, known as ordinal analysis, transforms the ISI sequence into a sequence of ordinal patterns (OPs), which are defined in terms of the relative ordering of consecutive ISIs. The ISI sequences are obtained from extensive simulations of two neuron models (FitzHugh-Nagumo, FHN, and integrate-and-fire, IF), with correlated noise. We find that, as the noise strength increases, temporal order gradually emerges, revealed by the existence of more frequent ordinal patterns in the ISI sequence. While in the FHN model the most frequent OP depends on the noise strength, in the IF model it is independent of the noise strength. In both models, the correlation time of the noise affects the OP probabilities but does not modify the most probable pattern.Peer ReviewedPostprint (author's final draft

Decoupling of Fourier Reconstruction System for Shifts of Several Signals

We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f_1,\ldots,f_k$ from the Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S_r$ to be a subset of the common set of zeroes of the Fourier transforms {\cal F}(f_\l), \ \l \ne r, on which ${\cal F}(f_r)\ne 0$. We show that in this way the reconstruction system is reduced to $k$ separate systems, each including only one of the signals $f_r$. Each of the resulting systems is of a ``generalized Prony'' form. We discuss the problem of unique solvability of such systems, and provide some examples