Identification and monitoring of brain activity based on stochastic relevance analysis of short–time EEG rhythms
 Leonardo DuqueMuñoz^{1}Email author,
 Jairo Jose EspinosaOviedo^{2} and
 Cesar German CastellanosDominguez^{3}
https://doi.org/10.1186/1475925X13123
© DuqueMuñoz et al.; licensee BioMed Central Ltd. 2014
Received: 19 December 2013
Accepted: 15 August 2014
Published: 28 August 2014
Abstract
Background
The extraction of physiological rhythms from electroencephalography (EEG) data and their automated analyses are extensively studied in clinical monitoring, to find traces of interictal/ictal states of epilepsy.
Methods
Because brain wave rhythms in normal and interictal/ictal events, differently influence neuronal activity, our proposed methodology measures the contribution of each rhythm. These contributions are measured in terms of their stochastic variability and are extracted from a Short Time Fourier Transform to highlight the non–stationary behavior of the EEG data. Then, we performed a variability–based relevance analysis by handling the multivariate short–time rhythm representation within a subspace framework. This maximizes the usability of the input information and preserves only the data that contribute to the brain activity classification. For neural activity monitoring, we also developed a new relevance rhythm diagram that qualitatively evaluates the rhythm variability throughout long time periods in order to distinguish events with different neuronal activities.
Results
Evaluations were carried out over two EEG datasets, one of which was recorded in a noise–filled environment. The method was evaluated for three different classification problems, each of which addressed a different interpretation of a medical problem. We perform a blinded study of 40 patients using the support–vector machine classifier cross–validation scheme. The obtained results show that the developed relevance analysis was capable of accurately differentiating normal, ictal and interictal activities.
Conclusions
The proposed approach provides the reliable identification of traces of interictal/ictal states of epilepsy. The introduced relevance rhythm diagrams of physiological rhythms provides effective means of monitoring epileptic seizures; additionally, these diagrams are easily implemented and provide simple clinical interpretation. The developed variability–based relevance analysis can be translated to other monitoring applications involving time–variant biomedical data.
Keywords
Stochastic relevance EEG rhythms Interictal/ictal classification Epilepsy monitoringIntroduction
Epilepsy is a chronic neurological disorder characterized by recurrent unprovoked seizures resulting from several brief and episodic neuronal hypersynchronous discharges with dramatically increased amplitudes affecting normal (i.e., background) brain activity. In the clinical setting, however, seizures without overt convulsions and the low probability of observing a seizure during standard recording times of 2040min greatly complicate diagnoses, as noted in [1]. Moreover, due to the excessive presence of artifacts, interference or overlapping symptomatology with other neurological disorders, the discrimination between normal brain activities and epileptiform activities for epilepsy diagnoses can be challenging, even from the visual inspection of an EEG by an experienced neurologist. Even the most highly trained neurology experts are not able to differentiate interictal EEG signals of epileptic from normal EEG data with over 80% accuracy. The complete review of recorded EEG signals by a trained professional is time–consuming, as explained in [2, 3]. Therefore, in clinical monitoring, automated EEG data techniques show promise in finding traces of interictal (between seizures) and ictal (during an epileptic seizure) states of epilepsy.
Generally, EEG data reflecting the electrical activity of different brain neuronal dynamics can be described as a collection of several sub–band waveform frequencies (or physiological rhythms) ranging between slow to fast activity (δ, θ, α, and β). For rhythm analyses, most of the known EEG–based detection systems require features extracted from time, frequency, or time–frequency domains to feed into a given classifier model [4]. Therefore, for epileptic seizure detection, features extracted in either time or frequency are assumed to have less computational complexity and burden [5]. However, due to the non–stationary behavior of EEG recordings, time–frequency domain methods typically lead to higher successes [6–9]. Moreover, it is known that the time–frequency representation ability to analyze different neural rhythm scales can be used as a reliable EEG marker; this ability has been shown to be a powerful tool for investigating small–scale neural brain oscillations [10, 11]. Accordingly, close relationships are often established between rhythms and epileptic seizures because they highly vary with changes in a nonictal/ictal state [12]. Particularly, the δ and θ rhythms that exhibit lower frequencies and higher magnitudes with respect to α waves may occur in epilepsy cases. Consequently, a quantitative contribution of each frequency sub–band must be clearly expressed toward automatic epileptic seizure identification and monitoring.
In order to measure the contribution of time–variant rhythms to the representation of brain activity, the following two stages must be carried out: i) the estimation of physiological rhythms highlighting the non–stationary behavior of EEG data, and ii) the construction of a measure appraising the concrete amount, or relevance, of each extracted rhythm dynamics in terms of discriminating different brain neuronal activities. In the former stage, several time–frequency decompositions have been proposed to encode EEG dynamics in extracted rhythms. These enhancing methods range from the recently introduced Empirical Mode Decomposition (EMD) [13–15] and the baseline Short Time Fourier Transform (STFT) [5, 6, 16] (including the use of several time–frequency distributions [7, 17]), to the Wavelet Transform (WT), which seems to be the most commonly used decomposition [1, 3, 5, 9, 16, 18–22].
In the latter stage, the knowledge of individual latent time–variant components has been proven to supply useful insight into EEG data analysis. In particular, as discussed in [1, 3, 7, 19, 23, 24], principal component analysis (PCA) has been used in feature enhancement for epilepsy classification. Additionally, to determine all clinically relevant EEG waveforms, independent component analyses [25] and more elaborate manifold learning techniques have been also applied [26]. Overall, it was found that based on a time–frequency EEG decomposition, one may measure the relevance of each frequency sub–band by an analysis or classification performance. However, during the relevance evaluation stage, none of these techniques take into account the non–stationary behavior of the epileptic–related rhythmic activity [7, 11, 27]. Therefore, to improve the classification accuracy, the identification of brain neuronal activities should be based on the stochastic relevance analysis of short–time EEG rhythms.
We aim to develop a methodology based on the stochastic relevance analysis that estimates the contribution of each time–variant EEG rhythm to discriminate between normal and ictal/interictal states. For this purpose, a subspace–based stochastic analysis of EEG rhythm dynamics is introduced. Thus, instead of a widely used scalar–valued parameter set extracted from a given EEG signal, neuronal states are detected throughout this analysis by using a vector set of short–time rhythms. The Short Time Fourier Transform is used as an enhancing decomposition to provide suitable temporal and spectral resolutions of extracted EEG rhythms [7, 28]. To show the robustness of the proposed training approach, the developed methodology is tested over two EEG datasets, one of which is recorded in a noisy (i.e., non–shielded) environment. We perform a blind study of 50 patients using the supportvectormachine classifier cross–validation scheme under three epilepsy–related problems of medical interest. As a result, our methodology provides support to the identification of brain neural activity related to epileptic seizure diagnoses. Furthermore, we introduce the concept of the relevance rhythm diagram, which provides a simple clinical interpretability that is implementable in automated EEG monitoring systems. This paper is organized as follows: in section “Materials and methods”, we briefly introduce the estimation of short–time EEG rhythms and their stochastic relevance evaluations. In section “Experimental setup”, an experimental set–up illustrates the effectiveness of the proposed training approach. Finally, the discussion and conclusions of obtained results are given in sections “Discussion” and “Conclusions”, respectively.
Materials and methods
Short–time rhythm extraction from enhanced EEG representation
where n _{ M } is the desired Cepstral coefficient feature set, and s _{ m }(l) is the weighted sum of each frequency filter response set, defined as ${s}_{m}\left(l\right)={\sum}_{k=1}^{{n}_{K}}{S}_{y}(l,k){F}_{m}\left(k\right)$. Variables m, l and k are indices for filter ordinal, time, and frequency axes, respectively; n _{ K } is the number of samples in the frequency domain. Therefore, each Cepstral coefficient subseries is associated directly with one of four EEG rhythms, that is, z _{ i }→x _{ i }: ∀i=i,…,4.
We select the linear filterbank LFCC for representation of EEG signals because they may more accurately refined to each rhythm frequency bandwidth. Therefore, we use five cepstral coefficients associated with δ, θ, α, and β rhythms, extracted as dynamic features(which were also used for EEG analysis in [29, 30]).
As a result, instead of a widely used scalar–valued parameter set extracted from the EEG signal, neural activities relating to epileptic seizures are detected by using a vector set of short–time rhythms, $\{{\mathit{x}}_{i}\phantom{\rule{0.3em}{0ex}}\subset \phantom{\rule{0.3em}{0ex}}{\mathbb{R}}^{1\times T}\phantom{\rule{0.3em}{0ex}}:\phantom{\rule{0.3em}{0ex}}i\phantom{\rule{0.3em}{0ex}}\in \phantom{\rule{0.3em}{0ex}}p\}$ with t ∈ T, which carries temporal information on non–stationary EEG recordings. The variable p represents each rhythm, i.e., δ,θ,α,β waveforms are denoted as i=1,2,3,4, respectively. Therefore, the input stochastic feature set, {x _{ i }}, is represented by the observation ensemble comprising M objects in the following input observation matrix, X=[X _{1}⋯X _{ m }⋯X _{ M }]. In turn, each object, denoted as X _{ m }, m=1,…,M, is described by their respective observation set of short–time vectors, $\left\{{\mathit{x}}_{i}^{\left(m\right)}\right\}$, such that each column becomes ${X}_{m}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}{\left[{\mathit{x}}_{1}^{\left(m\right)}\cdots {\mathit{x}}_{i}^{\left(m\right)}\cdots {\mathit{x}}_{p}^{\left(m\right)}\right]}^{\top}\phantom{\rule{0.3em}{0ex}},$ for ${X}_{m}\phantom{\rule{0.3em}{0ex}}\subset \phantom{\rule{0.3em}{0ex}}{\mathbb{R}}^{1\times \mathit{\text{pT}}},$ where each vector, ${\mathit{x}}_{i}^{\left(m\right)}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{2.77626pt}{0ex}}\phantom{\rule{0.3em}{0ex}}\left[{x}_{i}^{\left(m\right)}\right(1)\dots \phantom{\rule{0.3em}{0ex}}{x}_{i}^{\left(m\right)}(t)\phantom{\rule{0.3em}{0ex}}\dots \phantom{\rule{0.3em}{0ex}}{x}_{i}^{\left(m\right)}(T\left)\right]$ is a measured EEG rhythm (equally sampled through time), and is ${x}_{i}^{\left(m\right)}\left(t\right),$ the i–th stochastic waveform of the m–th object for a given time t instant.
Stochastic relevance analysis of short–time rhythms
In order to analyze the ability of the rhythm discriminant to detect neural brain states, priority is placed on identifying the time evolution and the structure of the underlying short–time waveforms, i.e., their contribution over time to the classifier performance must be carefully analyzed and quantified [5]. In this regard, the relevance analysis of the time–variant signals is carried out.
The solution of Eq. (4) implies $\mathit{A}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}{\left[{\mathit{v}}_{1}^{\top}\phantom{\rule{0.3em}{0ex}}\dots ,{\mathit{v}}_{i}^{\top},\dots ,{\mathit{v}}_{q}^{\top}\right]}^{\top},$ where $\left\{{\mathit{v}}_{i}^{\top}\right\}$ is the eigenvector set of the diagonal covariance matrix Σ _{ X } with non–ranked singular values {λ _{ k } : k ∈ p}. In practice, the covariance matrix is estimated as ${\stackrel{~}{\Sigma}}_{\mathit{X}}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}\mathit{X}{\mathit{X}}^{\top}/M,$ with a size of p T × p T. In most cases, p T ≫ M; we cannot readily compute eigenvectors and eigenvalues of such a large matrix. However, the needed eigenvector set is computed, based on the rank property stating that ${\mathit{v}}_{i}^{\top}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}\mathit{X}{\widehat{v}}_{i}^{\top}/\parallel \widehat{v}\parallel ,$ where $\left\{{\widehat{v}}_{i}^{\top}\right\}$ the eigenvector set of the matrix X^{⊤} X with the same non–null eigenvalues as X X^{⊤}.
The numerical evaluation of Eq. (6) yields the relevance weight of the i–th stochastic feature. The main assumption of the proposed relevance analysis is that the larger the weight, the more relevant the stochastic feature. Consequently, the set of estimated weights {γ _{ i }} can be ordered by decreasing values of achieved relevance, i.e., $[\phantom{\rule{0.3em}{0ex}}{\widehat{\gamma}}_{1}\phantom{\rule{0.3em}{0ex}}\cdots \phantom{\rule{0.3em}{0ex}}{\widehat{\gamma}}_{i}\phantom{\rule{0.3em}{0ex}}\cdots \phantom{\rule{0.3em}{0ex}}{\widehat{\gamma}}_{p}],$ where ${\widehat{\gamma}}_{i1}\phantom{\rule{0.3em}{0ex}}\ge \phantom{\rule{0.3em}{0ex}}{\widehat{\gamma}}_{i},$ for ${\widehat{\gamma}}_{1}=\underset{\forall i}{\mathrm{max}}\left\{{\gamma}_{i}\right\},$ and ${\widehat{\gamma}}_{p}=\underset{\forall i}{\mathrm{min}}\left\{{\gamma}_{i}\right\}.$
Support vector machine classifier
where $c\subset {\mathbb{R}}^{+}$ is a tradeoff penalization parameter indicating the relative importance of the model complexity when compared with the training error, and ${e}_{m}\subset {\mathbb{R}}^{+}$ is the training error for the m–th sample.
Both parameters are adjusted using a particle swarm metaheuristic optimization, a bioinspired method used for SVM parameter determination, as carried out in [33]. In practice, the use of a Gaussian kernel is more desirable than Laplacian or Polynomial kernels because it creates a Reproducing Kernel Hilbert Space with universal approximating capabilities, as discussed in [34]. Polynomial kernels are less widely used than the RBF kernel. For similar training and testing costs, a polynomial kernel may not provide greater accuracy than the RBF kernel, as suggested in [35].
Experimental setup
Electroencephalographic recording datasets
In order to validate the proposed methodology of brain neural activity identification, this work uses the following two EEG data sources. The signals were obtained retrospectively during medical examinations, performed in accordance with the Declaration of Helsinki. The data were anonymized and stored in the output format (txt files). Database one was acquired in Klinik für Epileptology, Universitat Bonn, Germany. Database two was acquired under approbation of the Ethics Committee of the Instituto de Epilepsia y Parkinson del Eje Cafetero (Pereira, Colombia).
Database One (DB1):
This collection is publicly available. The complete data set consists of five subsets [22, 36] (A, B, C, D, and E). Each set is composed of 100 single–channel EEG segments of 23.6s duration. Sets A and B are taken from five healthy subjects with eyes opened and closed, respectively. All signals from sets C, D and E come from five epileptic subjects. Sets C and D comprise seizure–free interictal signals measured on the epileptic zone and on the hemisphere opposite to the hippocampal formation of the brain. Set E contains epileptic signals recorded from each aforementioned location during an ictal seizure. Sets C, D and E were recorded intracranially.
All EEG signals were digitized at 173.61 Hz and 12– bit resolution. To retain relevant EEG data signals were filtered through a low–pass filter with a 40 Hz cutoff frequency.

Bi–class Problem I, for which normal (Atype) and seizure (Etype) labeled recordings are distinguished.

Problem II, or a three–class problem, closely represents real medical applications, including three categories: normal (Atype EEG segments), seizure–free interictal (Dtype EEG segments), and seizure (Etype EEG segments).

Problem III, or a five–class problem, i.e., all five classes are investigated, wherein all EEG segment sets from the above described dataset is used: normal (Types A and B), interictal (Types C and D) and seizure (Type E).
Database Two (DB2):
Computed short–time rhythms
Estimated relevance weights of short–time EEG rhythms
Performed classification based on short–time rhythms
In order to validate the proposed training methodology, the accuracy of the SVM classifier was investigated, by using a conventional cross–validation procedure which tested each database 10 times.
The commonly used crossvalidation procedure performs 10 repetitions where 70% of the data is used for SVM training while the remaining 30% is used for testing. This strategy provides better parameter estimation because the variance of the resulting estimate is reduced as the number of repetitions is increased. The values of c and ς are iteratively optimized, so that both parameters change after each test. Once the SVM training concludes, parameter values maximizing the estimator accuracy are used for testing.
where N _{ c } is the number of correctly classified patterns, N _{ T } is the total number of patterns used to feed the classifier, N _{ TP } is the number of true positives (i.e., accurately classified objective classes), N _{ FN } is the number of false negatives (i.e., objective classes classified as reference classes), N _{ TN } is the number of true negatives, and N _{ FP } is the number of false positives.
SVM classifier performance results for bi–class problem I
DB  a _{ ac }[%]  a _{ se }[%]  a _{ sp }[%] 

DB1  100  100  100 
DB2  98.02±2.16  97.79±1.78  99.31±1.68 
DB2 ^{∗}  98.35±1.27  98.11±1.45  98.89±1.47 
SVM classifier performance results for the classification problems II and III
Set  a _{ ac }[%]  a _{ se }[%]  a _{ sp }[%] 

A  100  100  100 
D  100  100  
E  100  100  
A  96.58±3.09  96.18±4.32  99.38±1.12 
B  96.56±2.19  99.16±0.96  
C  94.21±4.65  98.32±1.21  
D  90.86±4.16  98.54±2.25  
E  99.12±1.06  99.13±0.96 
Results for patients classification
Class  Patient  1  2  3  4  5  6  7  8  9  10 

Normal  Error seg.  0  8  3  0  0  0  0  0  0  2 
a _{ ac }[ %]  100  83.3  93.7  100  100  100  100  100  100  95.8  
Patient  11  12  13  14  15  16  17  18  19  20  
Error seg.  2  3  0  4  0  0  4  0  0  1  
a _{ ac }[ %]  95.8  93.7  100  91.6  100  100  91.6  100  100  97.9  
Seizure  Patient  1  2  3  4  5  6  7  8  9  10 
Error seg.  0  0  0  0  0  0  0  3  0  0  
a _{ ac }[ %]  100  100  100  100  100  100  100  93.75  100  100  
Patient  11  12  13  14  15  16  17  18  19  20  
Error seg.  6  0  0  0  0  0  0  4  0  3  
a _{ ac }[ %]  87.5  100  100  100  100  100  100  91.6  100  93.7 
Relevance rhythm diagrams in neural activity monitoring
Estimated relevance weights per class from considered short–time rhythms for both underlying data bases
DB  δ  θ  α  β  

DB1  Seizure  10.03  0.93±0.06  0.52±0.06  0.26±0.09 
Normal  0.71±0.05  0.82±0.06  10.03  0.42±0.12  
Diff  +  +      
DB2  Seizure  10.07  0.85±0.08  0.58±0.12  0.25±0.09 
Normal  0.69±0.05  0.78±0.02  10.07  0.36±0.12  
Diff  +  +     
For epileptic events, the shape of the seizure–related diamond becomes strained, i.e., the vertical axis is longer while the horizontal axis tends to be shorter. The same situation was observed for the labeled DB2 set; however, a few overlapping values were presented in α and β corners. Low rhythm bands (i.e., δ and θ) increased their contribution to overall rhythms, while high rhythm bands (i.e., α and β) presented diminished activity.
Discussion

The first aspect concerns the EEG enhancement method, from which short–time rhythms are extracted. The stochastic feature vector estimated from STFT is used because it is able to reveal nonstationary dynamics of EEG signals. Although a large amount of filterbankbased features have been proposed to characterize sub–band rhythms, the LFCC parameters are chosen as the feature vectors because of their simple, but effective, combination of frequency and magnitude from the shortterm power spectrum of EEG signals. LFCC parameters can be accurately calibrated to each rhythm frequency band. However, this stochastic relevance analysis strategy should be tested on nonlinear methods of feature extraction (e.g., entropies, fractal dimension, and recurrence quantification) that have been found to be effective for more accurate diagnose of epilepsy [39].

Moreover, the classifier performance of neural activities is similar to values reported in the literature for other commonly used enhanced representation approaches (e.g., WT and EMD), as shown in Table 5. However, because the purpose of the discussed training methodology is the brain activity monitoring, only a few strategies are suitable for a concrete time–frequency EEG decomposition approach. The criteria used for the STFT window may greatly influence classifier performance and the estimation of the RRD. Another shortcoming of the STFT is its computational burden that over–exceeds the WT by one order of magnitude. However, matching each WT level with the appropriate rhythm frequency sub–band depends at least, on proper sampling frequencies; this deficiency is discussed in detail in [10]. The possible disadvantages of EMD may be related to low–frequency mixing issues and the non–differentiability of the phase function that may be observed with a strong artifacts.
Classification accuracy (%) for the detection of epileptic seizures as reported by the discussed stochastic relevance method and by other recent works
Authors  Features/Classifier  Subset  a _{ ac }[%] 

[28]  TFR2DPCA/knn  A,E  100 
[42]  tf analysis/RNN  A,E  99.60 
[43]  WT/PNN  A,E  99.99 
[44]  PCA FFT/AIRS  A,E  100 
[41]  CC+PSD/voting of classifiers  A,E  100 
[7]  tf analysis/ANN  A,E  100 
This work  short–time rhythms/knn  A,E  99.50 
This work  short–time rhythms/SVM  A,E  100 
[19]  PCARBF/ANN  A,D,E  96.60 
[40]  EV/MLP NN  A,D,E  97.50 
[45]  PSD+CLZ/SVMA  A,D,E  98.72 
[28]  TFR2DPCA/knn  A,D,E  98.80 
[7]  tf analysis/ANN  A,D,E  100 
This work  short–time rhythms/knn  A,D,E  98.12 
This work  short–timerhythms/SVM  A,D,E  100 
[7]  tf analysis/ANN  A,B,C,D,E  89.00 
[28]  TFR2DPCA/knn  A,B,C,D,E  94.40 
[6]  (WT + eigenvectors)/SVM  A,B,C,D,E  99.20 
This work  short–time rhythms/knn  A,B,C,D,E  95.78 
This work  short–time rhythms/SVM  A,B,C,D,E  96.58 

The next consideration is related to the stochastic relevance analysis of time–evolving rhythm waveforms, which was proven to maintain a discriminant capability for neural activity detection and monitoring. As seen in Table 4, estimated rhythm weights do not significantly change over different databases, indicating their robustness toward noisy acquired EEG data. To the best of our knowledge, there are no known approaches that measure the concrete contribution of each physiological rhythm to discriminate neural states (normal, interictal, and ictal). The proposed stochastic relevance analysis may help medical specialists concretely determine the contribution of physiological rhythms for the identification and monitoring of brain neural activity during long time periods.

There are two main reasons for choosing the proposed diagnosis strategy for epilepsy: clinical interpretability (clinicians are familiar with the rhythm concept) and easy implementation (feature extraction and classifier processes are based on simple inference and do not require complex calibration). The methodology benefits from a deeper study of the signals over time.

Based on the estimated rhythm relevance weights, classifier performance is carried out, as shown from Table 1. For Problem I, the highest classifier accuracy is obtained (namely, a _{ ac }=100%, a _{ se }=100% a _{ sp }=100%) for DB1. For the noisy DB2, high classifier performance is also obtained (a _{ ac }=98.02%, a _{ se }=97.79%, a _{ se }=99.31). However, because practicing neurologists have difficulty in differentiating between interictal and healthy EEG recordings, solving Problem II (instead of Problem I) is more relevant to the medical community [40]. As shown in Table 2, the proposed training methodology achieves 100% accuracy, making it more suitable for the implementation of EEG monitoring systems.

The accuracy values of the proposed training approach and other recent approaches are compared in Table 5, using DB1 and problems (I,II, and III). Although this comparison may not be completely fair due to different details on the testing procedures (there is a wide dispersion in the choice of the analysis window; see [4–8]), it seems to be the best possible option. For bi–class and three–class problems, our obtained SVM classifier offers the best accuracy. It is worth noting that rhythm waveforms, have direct clinical interpretability. Furthermore, our classification approach still produces high accuracy when employing a simple k–nearest neighbor classifier, which simplifies the training design complexity. The optimal value was k=3, which is close to the k values in similar works [7, 41].– In addition to the conventional quantitative discrimination analysis (based on classifier performance), another practical consideration uses the relevance evaluation of short–time EEG rhythms to the qualitative identification of brain neuronal activity. However, few studies have determined proper physiological EEG rhythm parameters for use as classifier inputs. The discussed methodology for the relevance evaluation of EEG rhythm waveforms may provide a qualitative identification of epileptic seizures. From the assessed stochastic relevance analysis, the introduced relevance rhythm diagrams permit the qualification of the contribution of neural dynamics for each patient’s condition, enabling improved clinical interpretations of obtained results (Figures 7 and 8).

Therefore, as particular cases of piecewise linear methods, short–time rhythms can be highly relevant and similarly effective than nonlinear methods for the characterization of neuronal dynamics, in terms of classifier performance. Because of their straightforward interpretation, this characterization may yield valuable diagnostic information. However, there are no standard frequency ranges for determining these different bands [41]. Certain variability should be considered between subjects.

The average computational time for extracting the feature vector from a single EEG segment was 0.9293s. To reduce computational burden, the use of feature extraction based on faster filterbank decompositions (particularly, wavelets) should be strongly considered. This approach was suggested in [46] in which a biclass problem is addressed where the computation of the feature vector over a single EEG segment was nearly 100 times faster.
Conclusions
This work proposes a methodology to quantitatively evaluate each waveform contribution to the neuronal activity related to either normal or epileptic seizure states. A relevance evaluation is based on a time–evolving, latent variable decomposition of electroencephalogram signals. The discussed methodology is simple and can interpret the assessed feature set. The methodology is based on the hypothesis that using relevance–based analysis over enhanced representations of EEG signals permits measurements of rhythm contributions in each clinical case. The proposed methodology uses STFT as a decomposition method to extract sufficient information from the short–time EEG rhythms. In turn, measured rhythm relevance weights provide high classifier performances in terms of distinguishing between brain neural activities.
These results can be used in future studies focusing on finding alternative methods for monitoring and diagnosing epileptic seizures using less costly and noninvasive equipment. The introduced rhythm relevance weights have the added benefit of providing easier clinical interpretations, we additionally introduced the relevance rhythm diagram, which provides a qualitatively measure of the rhythm contribution to the neural activity. This may be used during EEG data monitoring. The proposed methodology of stochastic relevance analysis can be translated to other monitoring applications involving time–variant biomedical data.
Future areas of research include the application of the discussed methodology to analyze other brain activities and to determine the feasibility of seizure prediction. More elaborate and higher accuracy EEG analysis techniques (e.g., neural activity mapping) can also be considered for the diagnosis of epilepsy.
Declarations
Acknowledgments
The authors acknowledge Dr Diana Gómez Meza, who is working with the Instituto de Epilepsia y Parkinson del Eje Cafetero (Pereira, Colombia), for her assistance in delivering and organizing EEG data acquisition. This research was carried out under the grant research project 111045426008 “Desarrollo de un sistema automatico de mapeo cerebral y monitoreo intraoperatorio cortical y profundo: Aplicacion a la neurocirugia”, sponsored by COLCIENCIAS, also project P13259 “Implementación de una metodología para la interpretación de comandos mentales mediante el procesamiento de electroencefalografía para el desarrollo de interfaces cerebro computador” from Instituto Tecnológico Metropolitano.
Authors’ Affiliations
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