Epilepsy EEG classification using morphological component analysis

Abstract

In this paper, we have proposed an application of sparse-based morphological component analysis (MCA) to address the problem of classification of the epileptic seizure using time series electroencephalogram (EEG). MCA was employed to decompose the EEG signal segments considering its morphology during epileptic events using undecimated wavelet transform (UDWT), local discrete cosine transform (LDCT), and Dirac bases forming the over-complete dictionary. Frequency-modulated time frequency features were extracted after applying the Hilbert transform. Feature root mean instantaneous frequency square (RMIFS) and its parameters and parameters ratio are used in two different pairs for classification using support vector machine (SVM), showing good and comparable results.

Introduction

Hyperactivity of neural subnetwork resulting into dysfunctioning of the brain from few seconds to several minutes can be considered as epileptic seizure [1]. Epileptic seizure has broad classification based on various causes and symptoms or signs [2]. EEG have been used for early diagnosis and detection of seizures. It carries valuable complex information of brain activity. Manual inspection of patient’s EEG is time consuming, and secondly, it is not accurate. Therefore, seizure diagnosis and detection system discriminating seizure data from nonseizure and interictal EEG providing information about data for diagnosis come handy. Seizure detection or classification system mainly consists of two parts. First, preprocessing, filter or decompose the EEG for feature computation and extraction, and second, use these data from the first part for the classification by some supervised algorithm [3]. This decomposition process and feature extraction in the first part plays a pivotal role. As EEG is a graphical representation of summation of neuronal activity recorded using electrodes over the scalp. It is important to decompose it into oscillatory modes risen from different brain activity. Seizure detection requires good features showing prominent difference for different brain activity. Classification of seizure against nonseizure healthy EEG helps in diagnosis of epileptic seizure occurrence in the subject, whereas classification of epileptic seizure (ictal) from interictal (the period between two consecutive seizures) is important for seizure warning and detection system [4]. In the past, various methods have been proposed and developed for seizure classification based on frequency domain such as Fourier [5, 6]. Short-time Fourier transform (STFT) methods based on time-frequency methods were also used [7] for this purpose. In STFT, window size is a crucial factor for deciding the tradeoff between frequency and time resolution [8]. Utilizing wavelet analysis [8, 9] and its variant like discrete wavelet transform for classification as employed by Guo et al. [10] to pre-analyze the EEG signals for epilepsy. Chen et al. [11] did similar work using dual tree complex wavelet (DTCWT) for decomposition to extract feature based on the logarithm of fast Fourier transform (FFT). Nearest neighbor (NN) classifier was used upon extracted features.

Various machine learning techniques have been used in conjunction with feature extraction for the classification of ictal from interictal and healthy nonseizure EEG. Feature extraction is an important part of this process and influence the discrimination power of the model [12]. Features like approximate entropy (ApEn) with autoregressive model and principal component analysis (PCA) were applied by Liang et al. [4]. K nearest neighbor (KNN), support vector machine (SVM), least square support vector machine (LS-SVM), decision trees, and naive Bayes are used on features derived from cross-correlation and power spectral density of signals [13, 14]. Genetic algorithm was used by Guo et al. [10] for feature extraction and classification purpose from feature database created by using discrete wavelet transform. SVM assembly implementation using median Teager energy and Limpel-Ziv entropy feature from five different frequency sub-bands computed from band-pass Gabor filter bank is presented in [15]. Permutation entropy feature was used in [16] to create seizure detection system. Complex network based ictal classification done by Zhu et al. [17]. Tempko et al. [18] had used a total of 55 features from time, frequency, energy, and entropy domain for classification of epileptic seizure.

Empirical mode decomposition (EMD) by Huang et al. [19] was used for EEG decomposition and feature computation and extraction for epilepsy classification. Features like weighted frequency [20], standard deviation, mean, variance, skew, and centroid [21, 22] are extracted using EMD for classification. Bandwidth based features from intrinsic mode functions (IMFs) of EMD were fed to LS-SVM in [23]. RMS frequency feature extracted from IMFs used upon SVM for classification of seizure was presented in [24]. Phase space representation in Sharma et al. [25] was utilized for discrimination of ictal has also shown good results. Sparse-based decomposition [26] and classification [27] are also proposed lately.

In epilepsy, the commonly observed behavior or morphology is spike train and sharp waves. The sudden transient burst of spikes and high-frequency oscillations in interictal recordings are also used for the localization of the epileptic seizures. Both disparity in background activity and EEG paroxysms make the automated analysis complicated. Artifacts in filtered data can give rise to false positives [28,29,30]. Recently, signal decomposition by focusing on morphological components are getting highlighted due to its applicability to nonlinear and non-stationary signal properties [31,32,33]. The mixing of sources causes the EEG signal to be nonlinear and non-stationary in nature. Due to this, separation of sources from desired mixed signal become more difficult in time or frequency domain. MCA uses the linear combination of coefficients similar to independent component analysis (ICA). PCA and ICA [34] are popular methods used for separation of sources or removal of artifacts. Both the methods works on a statistical approach and aim to find the linear projection of the signals, i.e., statistically independent [34]. The subspace projection is used to extract EEG components on time/space basis. PCA is a sophisticated method to reduce the artifacts and specifies principal components (PC) to reconstruct overall data structure and to remove the components with small amplitudes and irregular changes. It is very difficult to specify remaining PCs to represent such signal. To identify PC requires the prior knowledge of the artifacts [35]. In ICA, different estimation procedures such as mutual information minimization, maximization of non-Gaussianity, maximization of likelihood, SOBI, and Fastica are used for separation. Since ICA is based on the measure of statistical independence, the noise of the input is amplified by ICA and it makes the detection of the signal components difficult due to Gaussian noise spread over the component in an undesired way [36]. ICA generates spikes and bumps, if the sample size is not sufficient [37, 38]. Basic ICA is a multichannel source separation technique and does not work on single channel unlike MCA which can work perfectly with single channel [39]. Although MCA is well known in image processing domain [40, 41], it had found few applications in biomedical signal processing even after showing promising results in removing artifacts from EEG [39, 42, 43]. MCA identify the components of the signal based on sparsity in time frequency domain. It decompose the signal and then accurately reconstruct the signal using redundant transforms (mathematical function) called explicit dictionary. This combination of explicit dictionary forming over-complete dictionary is important for representation of different morphologies of EEG signal. Sparse-based reconstruction of EEG signal has an advantage of using minimum coefficients which gives it the advantage to be easily transferred it over the Internet. Every method has advantages and disadvantages and yet to reach the stage for real-time analysis as a single method.

The objective of this work is to present an approach considering the morphology of the EEG during an epileptic event for diagnosing and detection of the epileptic seizure. In this work, we have used MCA with undecimated wavelet transform (UDWT), local discrete cosine transform (LDCT), and Dirac bases composing the dictionary for decomposition. UDWT identifies the slow components in the EEG, LDCT identifies the spectral components, and Dirac identifies the spikes in the EEG. Root mean instantaneous frequency square (RMIFS) and the ratio of its consisting parameters from Dirac component are computed and given to SVM as input for classification. RMIFS is defined as square root over the sum of the time average squared bandwidth ${\sigma}_T^2$ and the center frequency square <ω>². These two parameters, ${\sigma}_T^2$ extracted from Dirac component and <ω>² from LDCT component, are also used for classification. These two sets of features show considerable high accuracy and sensitivity comparable with other existing works.

This paper is organized as MCA followed by the Hilbert transform, computation of feature, SVM, and dataset used followed by simulation and describing the physical relevance of the features, then Section 9 and Section 10 at the end.

Method and material

In the subsequent subsections, MCA is elaborated first, followed by features computed from its output decomposition. Briefly explained the SVM and the material and the data used in this work.

Morphological component analysis

Morphological component analysis uses the concept of sparsity and independent redundant transforms to decompose an EEG signal by adapting to the prevailing types of morphologies simultaneously. Representing EEG as a sparse linear contribution of coefficients, MCA uses over-complete dictionary ɸ ∈ R^n × k, where k is the morphological components of an EEG signal S ∈ Rⁿ decomposed by constructing source components {∅_k}_k ∈ Γ, where Γ representing the type of explicit dictionaries. An EEG signal can be represented as a sparse linear combination of coefficients. Over-complete dictionary ɸ is a set of explicit dictionary, defined by a set of mathematical functions to represent the specific morphologies of EEG [44]. Signal can be represented as

$$ {\displaystyle \begin{array}{l}S={\sum}_{i=0}^k{\beta}_i{\varnothing}_i+\zeta \\ {}={\beta}_1{\varnothing}_1+{\beta}_2{\varnothing}_2\dots +{\beta}_k{\varnothing}_k+\zeta \\ {}\cong {s}_1+{s}_2\dots +{s}_k\left(\zeta \ll 1\right)\\ {}={S}^{\hbox{'}}\end{array}} $$

(1)

where ∅_k represents a set of basis elements and β is the target coefficients to reconstruct the original EEG signal. ζ is assumed to be negligible noise tend to zero. By using three dictionaries, undecimated wavelet transform (UDWT), local discrete cosine transform (LDCT), and Dirac (Kronecker basis) [39, 45, 46] in this work, coefficients are optimized as

$$ \left\{{\beta}_0^{opt},{\beta}_1^{opt},{\beta}_2^{opt}\right\}=\underset{\beta_0,\cdots, {\beta}_2}{\arg \min}\sum \limits_{i=0}^2\parallel {\beta}_i{\parallel}_0 $$

(2)

subject to ${S}^{\prime }={\sum}_{i=0}^k{\beta}_i{\varnothing}_i,\mathrm{k}=2\ \mathrm{in}\ \mathrm{this}\ \mathrm{work}.$

The basis pursuit solution [47] was used to represent the sparse component which describes Eq. (1) as

$$ \left\{{\beta}_0^{opt},{\beta}_1^{opt},{\beta}_2^{opt}\right\}=\underset{\beta_0,\cdots, {\beta}_2}{\arg \min}\sum \limits_{i=0}^2\parallel {\beta}_i{\parallel}_1+\lambda \parallel S-\sum \limits_{i=0}^2{\varnothing}_i{\beta}_i{\parallel}_2^2 $$

(3)

Equation (3) is optimized by block coordinate relaxation (BCR) method [48] in finite time. The algorithm given in [39] is as follows:

The number of iteration I_max=100 is used. Balbir et al. [39] had varied the value of λ from 3 to 5 depending on the type of hard and soft threshold. In this work, λ = 3 is used. Figure 1 depicts the working of MCA as described in Algorithm 1. From Figs. 2 and 3, it can be observed that UDWT is showing slow component of EEG whereas LDCT showing spectral component. Dirac basis is showing its ability to capture the spike morphology of EEG, capturing the negative spike train of seizure or ictal in Fig. 3.

Fig. 1

Block diagram of MCA decomposition of EEG signal

Fig. 2

MCA decomposition of interictal EEG signal [52]

Fig. 3

MCA decomposition of ictal EEG signal [52]

Hilbert transform over decompositions

Hilbert transform was applied to the components produced by MCA. Representing real valued component c(t) into analytic form s(t) onto the real axis of the complex domain as

$$ s(t)=c(t)+j{c}_H(t), $$

(4)

Hilbert transform over c(t) produce c_H(t). The analytical form signifies that there is a shift or phase difference of $\frac{\pi }{2}$ between the positive and the negative frequency. Imaginary part representing negative frequency is ignored, and only the real part representing the positive frequency is considered for working due to Hermitian symmetry. Equation (4) can be represented as in [19]

$$ s(t)=a(t){e}^{j\varphi (t)} $$

(5)

Instantaneous phase φ(t) and amplitude a(t) can be given by

$$ \varphi (t)=\mathit{\arctan}\left[\frac{c_H(t)}{c(t)}\right]. $$

(6)

$$ a(t)=\sqrt{c^2(t)+{c}_H^2(t),} $$

(7)

Instantaneous frequency is defined as derivative of instantaneous phase as in [49]

$$ \omega (t)={\varphi}^{\prime }(t). $$

(8)

Prime is representing differentiation in this work.

Computation of root mean instantaneous frequency square

Equation (9a) can be expressed in another way by using Hermitian time frequency operator $\left(\frac{1}{j}\frac{d}{dt}\right)$. Center frequency can be written as in [50]

$$ <\omega >=\int \omega {\left|S\left(\omega \right)\right|}^2 d\omega, \kern0.5em $$

(9a)

$$ =\int {s}^{\ast }(t)\frac{1}{j}\frac{d}{dt}s(t) dt, $$

(9b)

$$ =\int \left({\varphi}^{\prime }(t)+\frac{1}{j}\frac{a^{\prime }(t)}{a(t)}\right){a}^2(t) dt, $$

(9c)

$$ <\omega >=\int {\varphi}^{\prime }(t){a}^2(t) dt, $$

(9d)

Imaginary part is ignored as zero, s^∗(t) is complex conjugate signal, and a²(t) is density in time [51].

Therefore, center frequency, as in [50], can be given by

$$ <\omega >=\int {\varphi}^{\prime }(t){a}^2(t) dt, $$

(10)

The S(ω) is the Fourier transform of the signal s(t).

$$ S\left(\omega \right)=\frac{1}{\sqrt{2}}\int {e}^{- i\omega t}s(t) dt. $$

(11)

Amplitude is normalized, and using Parseval’s theorem, ∫|S(ω)|²dω =  ∫ |s(t)|²dt = 1. All integrals computed are between time interval [0, 23.6] as EEG signal segments [52] used in this work is of 23.6 s as described in Section 7.

By referring to [51, 53], when time-averaged square bandwidth ${\sigma}_T^2$ also known as bandwidth frequency modulation (BFM) [51] is expanded, this can be represented as in Eq. (12b). Rearranging Eq. (12b) gives us a root mean instantaneous frequency square (RMIFS) frequency. <. >_T means time domain.

$$ {\sigma}_T^2=\int {\left({\varphi}^{\prime }(t)-<\omega >\right)}^2{a}^2(t) dt, $$

(12a)

$$ {\sigma}_T^2=<{\varphi}^{\prime 2}(t)>-<\omega {>}^2, $$

(12b)

$$ {\sigma}_T^2=<{\omega}^2>-<\omega {>}^2, $$

(12c)

$$ <{\omega}^2>={\sigma}_T^2+<\omega {>}^2, $$

(12d)

$$ {f}_R=\sqrt{\sigma_T^2+<\omega {>}^2}. $$

(12e)

${\sigma}_T^2$ and <ω>² are parameters, as can be seen in Eq. (12d), and their ratio can be given by

$$ {E}_{\mathrm{MIFS}}=\frac{<\omega {>}^2}{\sigma_T^2}. $$

(13)

Features extracted from components are depicted in Table 1 and in Fig. 4.

Table 1 Feature extracted from components

Fig. 4

Features a RMIFS frequency from Dirac component. b Parameters ratio ($\frac{<\omega {>}^2}{\sigma_T^2}$) from Dirac component. c Bandwidth frequency modulation (BFM) from Dirac component. d Center frequency square (CFS). Set F; Set N; Set O; Set S; and Set Z

SVM

Support vector machine (SVM), introduced by Vapnik [54], is used as classifier. SVM discriminate two different classes by creating a hyperplane which maximizes distance between among them. Radial basis function (RBF) kernel is used in this work represented:

$$ G\left({x}_i,{x}_j\right)={\mathit{\exp}}^{\left(\frac{{\left\Vert {x}_i,-{x}_j\right\Vert}^2}{2{\sigma}^2}\right)}, $$

(14)

where σ is a positive number.

Dataset

EEG dataset [52] commonly known as Bonn dataset was used to apply the method. Five subsets F, N, O, S, and Z make the dataset. All subsets consist of 100 signal segments, each of 23.6 s duration recorded with 173.61 Hz of sampling frequency containing 4097 samples. Subsets O and Z are recorded extracranially with eye open and with eyes closed from healthy subjects having no previous seizure history. Subsets F, N, and S have signal segments from intracranial experiments. Subsets F and N have interictal recording. Subset N is from the epileptic zone, and F is from the hippocampal formation of the opposite hemisphere. Subset S contains ictal EEG recording. In this work, six combinations of subsets are created for classification. First one is with sets F, S, second with N, S, third with O against S, fourth with Z against S, fifth with F, N together versus S, and sixth with O, Z against S for classification.

Every subset contains 100 data from each feature calculated upon 100 signal segments. These data are normalized using standard deviation and mean. Training and test set are prepared in 70:30 ratio for SVM. For one subset versus another individual subset’s classification, 70 samples are picked randomly without replacement from each set to create training set. Test set is made from the remaining 30 data samples. For F, N versus S, 35 samples are taken randomly without replacement from each F, N subsets and 70 random samples were picked without replacement from S set to make SVM training set. For test set, 15 samples are picked randomly from remaining 65 data samples from the subsets F, N and 30 remaining samples are taken from S set. The step of picking equal number of data samples from interictal and ictal sets was taken to avoid any bias and overfitting. Same process was adapted for classification of O, Z against S. Using grid search, best kernel parameters were searched, i.e., similar to cross-validation. But in most of the case, default kernel parameters have shown good results as presented in Table 2. We repeated this process hundred times means taking 100 trials following Bajaj et al. [23] who has taken 10 trials.

Table 2 Classification results from 100 trials on all six combinations of subsets

Simulation

In MCA methodology, sparsity play a vital role in separating the components having different time-frequency properties or morphology of constructing of individual source components. The combination of explicit dictionaries forming an over-complete dictionary makes the MCA more powerful methods for denoising and source component separation [39]. Mostly, decomposition-based methods like PCA and ICA required prior knowledge about the decomposed components. MCA-based decomposition has an advantage in the accurate reconstruction of the original component because the source component has a low probability of occurrence simultaneously. This method relies on the sparsity and the over-completeness of the dictionary ɸ ∈ R^n × k, a set of k redundant transforms, which represent the specific morphologies of different components of signal. Due to the concept of sparsity and the over-completeness, the dictionary extended the traditional signal decomposition to feature extractions of multiple types of morphology simultaneously. EEG signal contains specific morphology depending on the activity in the brain. Therefore, EEG time course data can be decomposed by one explicit dictionary and cannot be decomposed by other explicit dictionaries. It estimates the components accurately as the decomposed components are sparse and independent. The S is the linear combination of different brain activity, where β is the brain activity and ɸ is the mixing matrix. Different basis functions were trialed in different combinations to create the epileptic-specific dictionary from a set of UDWT, discrete sine transform (DST), discrete cosine transform (DCT), LDCT, and Dirac basis functions, and finally, UDWT, LDCT, and Dirac were used depending on the significant difference shown by the extracted, proposed features. UDWT has not been used directly for feature extraction but has been kept in the dictionary to make LDCT spectral component remain free from slow-moving components. Dirac basis was used to capture the spike morphology of the epileptic seizure. Dirac basis is also useful in capturing the transient spikes in interictal which can help in localizing the epileptic zone.

After using MCA for decomposition, Hilbert transform was applied over the components which take the real value signal decomposition to complex time frequency domain. Real signal gives symmetrical density in frequency making mean or center frequency zero. Using analytic representation, we will have identical spectrum for positive frequencies and zero for negative frequencies [50]. Feature RMIFS (f_R) and the parameters ratio ($\frac{<\omega {>}^2}{\sigma_T^2}$) are computed from Dirac component. RMIFS is defined as root over sum of the time-averaged bandwidth square ${\sigma}_T^2$ and the center frequency square <ω>². ${f}_R^2$ is always greater than <ω>² by ${\sigma}_T^2$. This feature is expressed completely in terms of frequency modulation ${\sigma}_T^2$ and average or center frequency square <ω>² in time domain which is advantageous as it is free from any amplitude-based component that is prone to noise. Computing f_R directly as $\sqrt{<{\varphi}^{\prime 2}(t)>}$ or as $\sqrt{\sigma_T^2+<\omega {>}^2}$ gives same value. The parameters ratio ($\frac{<\omega {>}^2}{\sigma_T^2}$) shows how dominant center frequency square is over time-averaged bandwidth square. For example, from Fig. 4c, in the case of interictal ${\sigma}_T^2$ is at higher range making the parameters ratio at lower range whereas for ictal the behavior is opposite means during the ictal event, the frequency modulation is small compared to interictal as also observed by Bajaj et al. [23]. Frequency modulation ${\sigma}_T^2$ from Dirac component is at higher range in nonseizure and interictal than ictal, and center frequency from LDCT component is highest in nonseizure than in ictal and lowest in interictal. As time-averaged bandwidth can be taken as the standard deviation of instantaneous frequency around the center frequency and center frequency as the mean, f_R satisfies the definition of root mean square. Value of f_R will be close to center frequency when instantaneous frequencies are close to center frequency leading to small ${\sigma}_T^2$. That is, signal decomposition during epileptic event showing small frequency modulation will result in ${f}_R^2$ influenced by center frequency square <ω>². Dirac component was chosen for computation of RMIFS frequency because, firstly, it represents the spike morphology of the EEG and, secondly, it shows more significant difference than when f_R is computed from LDCT component. For classification using <ω>² and ${\sigma}_T^2$, <ω>² is computed from LDCT component and ${\sigma}_T^2$ from Dirac component simultaneously because LDCT represents the frequency component better than Dirac which shows modulation better.

Center frequency square <ω>² calculated from LDCT component are in range from higher delta wave to lower alpha wave in interictal sets F, N, whereas in healthy nonseizure sets O, Z, it is between higher theta wave to alpha wave. Center frequency in ictal set S was dispersed between lower theta wave to lower beta wave. RMIFS f_R on an average is in beta range for all the subsets of the Bonn dataset as presented in Fig. 4.

Results and discussion

These features are normalized using mean and standard deviation then fed to SVM in a set of two pairs separately to elaborate its significance in classification of seizures. These pairs of features are selected as they are showing opposite behavior which helps SVM to create the hyperplane discriminating the classes. Performance of the SVM classifier is evaluated by using the statistical parameters from previous works, i.e., specificity (SPE), sensitivity (SEN), and accuracy (Acc) [4, 23].

$$ \mathrm{SPE}=\frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{FP}}\times 100, $$

(15)

$$ \mathrm{SEN}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}\times 100, $$

(16)

$$ \mathrm{Acc}=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}\times 100, $$

(17)

where true positive and true negative events are denoted by TP and TN, i.e., detecting ictal and interictal correctly. FN and FP stands for false negative and false positive, respectively.

Classification of result of set F versus set S using both pairs of feature, i.e., f_R, ($\frac{<\omega {>}^2}{\sigma_T^2}$) and ${\sigma}_T^2$, <ω>² shows similar result of average accuracy of 96.48 and 97.13% and average sensitivity of 93.53 and 94.26%. Average specificity using both the features are very high at 99.43 and 100.0%. Results are shown in Table 2.

Classification accuracy of both the pairs of feature for set N against S is good at 99.41 and 99.48%. Average sensitivity and specificity are 99.46, 99.90, 99.36, and 99.66%. For set O versus Z, features f_R, ($\frac{<\omega {>}^2}{\sigma_T^2}$) show average accuracy of 99.91%, but ${\sigma}_T^2$, <ω>² achieved lowly at 87.98%. Similar accuracy result is observed for set Z versus S with 99.63% using f_R, ($\frac{<\omega {>}^2}{\sigma_T^2}$), whereas 90.30% using $\kern0.50em {\sigma}_T^2$, <ω>². SVM plot for set N versus S using ${\sigma}_T^2$, <ω>² and set O against S using f_R, ($\frac{<\omega {>}^2}{\sigma_T^2}$) is shown in Figs. 5 and 6. Average accuracy for set F, N together versus set S are at 93.05 and 93.61% for both sets of features, whereas average classification accuracy for set O, Z versus S are at 99.11 and 90.60%. We have compared this proposed work with previous work at Tables 3 and 4.

Table 3 Comparison of set F, N vs S results with other existing works on Bonn dataset

Table 4 Comparison with other works on Bonn dataset for classification between healthy nonseizure set O, Z and seizure or ictal set S

Fig. 5

Set N vs S classification using RBF kernel σ = 1.0, c = 1.0. 0 (Ictal Training); 1 (Interictal Training); Support Vectors; SVM Hyperplane; 0 (Ictal Classified); and 1 (Interictal Classified)

Fig. 6

Set O vs S classification using RBF kernel σ = 1.0, c = 1.0. 0 (Ictal Training); 1 (NonSeizure Training); Support Vectors; SVM Hyperplane; 0 (Ictal Classified); 1 (NonSeizure Classified)

For most of the time default kernel parameters proved to be better. Even with an optimized parameters that are found with grid search, were close to default setting and shows little improvement of at most 1–1.5%. Therefore, the cases where we found improvement less than 1%, default setting or default kernel parameters were used which helped in avoiding computing overload of kernel parameters search and makes the application more practical. Both the pairs of features have shown similar classification result for interictal set versus ictal or seizure set whereas feature f_R, ($\frac{<\omega {>}^2}{\sigma_T^2}$) has shown better results for healthy nonseizure classification against seizure set. Therefore, f_R, ($\frac{<\omega {>}^2}{\sigma_T^2}$) features combination for classification are found to better than ${\sigma}_T^2$, <ω>². Figure 4 clearly shows it is hard to have two-dimensional map helping SVM to create hyperplane to separate nonseizure and seizure sets using feature combination of ${\sigma}_T^2$, <ω>² as they are quite intermingled. Although classification of seizure set which is the result of intracranial experiment against noninvasive extracranial nonseizure healthy EEG set is inappropriate, classification has been done for comparison purpose of the proposed method with previous works. Detailed comparison of the proposed work with the previously done work on Bonn dataset is presented in Tables 3 and 4.

Conclusions

MCA gives definite number of decomposition depending on the number of set of basis used in over-complete dictionary. This dictionary can be formed based on problem requirements. Selection of basis functions in the dictionary plays an important role in creating problem-specific application. We found LDCT component is best suited for spectral feature extraction, whereas Dirac bases are good in showing spike morphology of the EEG. Default setting of SVM kernel is suitable for proposed feature combinations which makes it suitable for practical application. To make the method reliable, 100 random trials were taken on SVM. 99.78% of highest average accuracy was observed for classification of interictal set N against ictal set S, whereas 99.91% of average accuracy was observed for classification of nonseizure set O against ictal set S. In future, we will try to form a dictionary to remove different artifacts from EEG and will try to create seizure prediction system using MCA and proposed features with suitable basis for long-term EEG signals.