 Research
 Open Access
Performance analysis of wavelet transforms and morphological operatorbased classification of epilepsy risk levels
 Rajaguru Harikumar^{1}Email author and
 Thangavel Vijayakumar^{1}
https://doi.org/10.1186/16876180201459
© Harikumar and Vijayakumar; licensee Springer. 2014
 Received: 24 August 2013
 Accepted: 10 April 2014
 Published: 3 May 2014
Abstract
The objective of this paper is to compare the performance of singular value decomposition (SVD), expectation maximization (EM), and modified expectation maximization (MEM) as the postclassifiers for classifications of the epilepsy risk levels obtained from extracted features through wavelet transforms and morphological filters from electroencephalogram (EEG) signals. The code converter acts as a level one classifier. The seven features such as energy, variance, positive and negative peaks, spike and sharp waves, events, average duration, and covariance are extracted from EEG signals. Out of which four parameters like positive and negative peaksand spike and sharp waves, events and average duration are extracted using Haar, dB2, dB4, and Sym 8 wavelet transforms with hard and soft thresholding methods. The above said four features are also extracted through morphological filters. Then, the performance of the code converter and classifiers are compared based on the parameters such as performance index (PI) and quality value (QV).The performance index and quality value of code converters are at low value of 33.26% and 12.74, respectively. The highest PI of 98.03% and QV of 23.82 are attained at dB2 wavelet with hard thresholding method for SVD classifier. All the postclassifiers are settled at PI value of more than 90% at QV of 20.
Keywords
 EEG signals
 Morphological operators
 Wavelet transforms
 Code converter
 Singular value decomposition
 Expectation maximization
 Modified expectation maximization
1 Introduction
The electroencephalogram (EEG) is a measure of cumulative firing of neurons in various parts of the brain [1]. It contains information regarding changes in the electrical potential of the brain obtained from a given set of recording electrodes. These data include the characteristic waveforms with accompanying variations in amplitude, frequency, phase, etc., as well as brief occurrence of electrical patterns such as spindles, sharps, and spike waveforms [2]. EEG patterns have shown to be modified by a wide range of variables including biochemical, metabolic, circulatory, hormonal, neuroelectric, and behavioral factors in [3]. In the past, the encephalographer, by visual inspection, was able to qualitatively distinguish normal EEG activity from either the localized or generalized abnormalities contained within relatively long EEG records [4]. The most important activity possibly detected from the EEG is the epilepsy [5]. Epilepsy is characterized by an uncontrolled excessive activity or potential discharge by either a part or all of the central nervous system [5]. The different types of epileptic seizures are characterized by different EEG waveform patterns [6]. With realtime monitoring to detect epileptic seizures gaining widespread recognition, the advent of computers has made it possible to effectively apply a host of methods to quantify the changes occurring based on the EEG signals [4]. The EEG is an important clinical tool for diagnosing, monitoring, and managing neurological disorders related to epilepsy [7]. This disorder is characterized by sudden recurrent and transient disturbances of mental function and/or movements of body that results in excessive discharge group of brain cells [8]. The presence of epileptiform activity in the EEG confirms the diagnosis of epilepsy, which sometimes may be confused with other disorders producing similar seizurelike activity [9]. Between seizures, the EEG of a patient with epilepsy may be characterized by occasional epileptic form transientsspikes and sharp waves [10]. Seizures are featured by short episodic neural synchronous discharges with considerably enlarged amplitude. This uneven synchrony may happen in the brain accordingly, i.e., partial seizures can be visible only in few channels of the EEG signal or generalized seizures, that are seen in every channel of the EEG signal involving the whole brain [11]. Epileptic seizure is an abnormality in EEG gathering and is featured by short and episodic neuronal synchronous discharges with severely high amplitude. This anomalous synchrony may happen in the brain locally (partial seizures) and is visible only in fewer channels of the EEG signal or including the entire brain, i.e., visible in all the channels of the EEG signal [12].
1.1 Related works
In the last three decades, the analysis and classification of epilepsy from EEG signal has become a fascinating research. A huge volume of research has already been performed which includes spike detection, classification epilepsy seizures, ictal and inter ictal analysis, nonlinear and linear analysis and soft computing methods. Gotman [9] discussed the improvement of epileptic seizure detection and evaluation. Pang et al. [10] summarized the history and evaluation of various spike detecting algorithms. The authors in [13] have discussed the different neural networks as a function approximation and universal approximation for epilepsy diagnosis. Rezasarang [14] encapsulated the performance of spike detecting algorithms in terms of sensitivity, specificity, and average detection. Rezasarang [14] orders the performance of spike detecting algorithms in terms of good detection ratio (GDR). McSharry et al. [8] discussed and enumerated the nonlinear methods and its relevance to predict epilepsy by considering EEG samples as time series. Majumdar [15] reviews various soft computing approaches of EEG signals which emphasize more on pattern recognition techniques. The paper [15] mainly focuses on dimensionality reduction, SNR problems, linear and soft computing techniques for EEG signal processing. Majumdar concludes that the neural network and Bayesian approaches are two popular choices even though linear statistical discriminants are easier to implement. Great deals of support vector machines (SVM) are also discussed in this paper for their classification accuracy. Hence, the EEG signal occupies a great deal of data regarding the work of the brain. However, classification and estimation of the signals are inadequate. As there is no explicit category suggested by the experts, visual examination of EEG signals in time domain may be deficient. Routine clinical diagnosis necessitates the analysis of EEG signals [13]. Hence, automation and computer methods have been utilized for this reason. Current multicenter clinical analysis indicates confirmation of premonitory symptoms in 6.2% of 500 patients with epilepsy [16]. Another interviewbased study found that 50% of 562 patients felt ‘auras’ before seizures. Those clinical data provide a motivation to search for premonitoring alterations on EEG recordings from the brain and to employ a device that can act without human intervention to forewarn the patient [17]. On the other hand, despite decades of research, existing techniques do not yield to better performance. This paper addresses the application and comparison of singular value decomposition (SVD), expectation maximization (EM), and modified expectation maximization (MEM) classifiers towards optimization of code converter outputs in the classification of epilepsy risk levels.
Weber et al. [18] have proposed the threestage design of an EEG seizure detection system. The first stage of the seizure detector compresses the raw data stream and transforms the data into variables which represent the state of the subject's EEG. These state measures are referred to as context parameters. The second stage of the system is a neural network that transforms the state measures into smaller number of parameters that are intended to represent measures of recognized phenomena such as small seizure in the EEG [9, 10]. The third stage consists of a few simple rules that confirm the existence of the phenomena under consideration. Similarly, this paper also presents a threestage design for epilepsy risk level classification. The first stage extracts the seven required distinct features from raw EEG data stream of the patient in time domain. The next stage transforms these features into a code word through a code converter with seven alphabets which represents the patient's state in five distinct risk levels for a 2s epoch of EEG signal per channel. The last stage is a SVD, EM, or MEM which optimizes the epilepsy risk level of the patient. The organization of the paper is as follows. Section 1 introduces the paper and materials, and its methods are discussed in Section 2. Section 3 describes about the SVD, EM, and MEM as postclassifiers for epilepsy risk level classification. Results are discussed in Section 4, and the paper is concluded in Section 5.
2 Materials and methods
2.1 Data acquisition of EEG signals
 1.For every epoch, the energy is calculated as [4]$\mathit{E}={\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\mathit{x}}_{\mathit{i}}^{2}}$(1)
 2.One of the simplest linear statistics that may be used for investigating the dynamics of underlying the EEG is the variance of the signal calculated in consecutive nonoverlapping windows. The variance (σ) is given by${\mathit{\sigma}}^{2}=\frac{{\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\left({\mathit{x}}_{\mathit{i}}\mathit{\mu}\right)}^{2}}}{\mathit{n}}$(2)
 3.For the average variance, the covariance of duration is determined by using the equation below:$\mathrm{CD}=\frac{{\displaystyle \sum _{\mathit{i}=1}^{\mathit{p}}{\left(\mathit{D}{\mathit{t}}_{\mathit{i}}\right)}^{2}}}{\mathit{p}{\mathit{D}}^{2}}$(3)
 1.
The total number of positive and negative peaks is found above the threshold.
 2.
For a zero crossing function, if it lies between 20to 70 ms, then the spikes can be detected. If the zero crossing function lies between 70to 200 ms then the sharp waves are detected when the zero crossing function lies between 70 to 200 ms.
 3.
After having detected, the total number of spikes and sharp waves were determined as the events.
 4.
The duration for these waves is determined by the relation:
2.2 Wavelet transforms for feature extraction
The brain signals are nonstationary in nature. In order to capture the transients and events of the waveforms, we are in dire state to visualize the time and frequency simultaneously. Hence, the wavelet transforms are the better choice to extract the transient features and events from the EEG signals. The wavelet transformbased feature extraction is discussed as follows:
where ψ* (t) is the complex conjugate of the wavelet function ψ (t).
where a is the dilation parameter and b is the translation parameter.
where T is the threshold level.
Parameter ranges for various risk levels
Normalized parameters  Risk levels  

Normal  Low  Medium  High  Very high  
Energy  0 to 1  0.7 to 3.6  2.9 to 8.2  7.6 to 11  9.2 to 30 
Variance  0 to 0.3  0.15 to 0.45  0.4 to 2.2  1.6 to 4.3  3.8 to 10 
Peaks  0 to 2  1 to 4  3 to 8  6 to 16  12 to 20 
Events  0 to 2  1 to 5  4 to 10  7 to 16  15 to 28 
Sharp waves  0 to 2  1 to 5  4 to 8  7 to 11  10 to 12 
Average duration  0 to 0.3  0.15 to 0.45  0.4 to 2.4  1.8 to 4.6  3.6 to 10 
Covariance  0 to 0.05  0.025 to 0.1  0.09 to 0.4  0.28 to 0.64  0.54 to 1 
The output of code converter is encoded into the strings of seven codes corresponding to each EEG signal parameter based on the epilepsy risk levels threshold values as set in Table 1. The expert defined threshold values as containing noise in the form of overlapping ranges. Therefore, we have encoded the patient risk level into the next level of risk instead of a lower level. Likewise, if the input energy is at 3.4, then the code converter output will be at medium risk level instead of low level [26].
2.3 Code converter as a preclassifier
Representation of risk level classifications
Risk level  Coded representation 

Normal  U 
Low  W 
Medium  X 
High  Y 
Very high  Z 
Output of code converter for patient 2
Epoch1  Epoch2  Epoch3 

WYYWYYY  WYYWYYY  WZYYWWW 
YZZYXXX  YYYYXXX  YYYXYYY 
ZZZYYYY  YYYYYYY  YYYYYYY 
YYZXYYY  XZZXYYY  YYYYYYY 
ZZZYYYY  WYYYXXX  YYYXYYY 
YYZXXXX  WYZYYYY  YZZYYYY 
ZZZYYYY  YYYYYYY  ZZZYYYY 
YYYYXXX  YYYYXXX  YYYXZYY 
Binary representation of risk levels
Risk level  Code  Binary string  Weight  Probability 

Very high  Z  10000  16/31 = 0.51612  0.086021 
High  Y  01000  8/31 = 0.25806  0.043011 
Medium  X  00100  4/31 = 0.12903  0.021505 
Low  W  00010  2/31 = 0.06451  0.010752 
Normal  U  00001  1/31 = 0.03225  0.005376 
11111 = 31  Σ = 1 
Where PI is the performance index, PC is the perfect classification, MC is the missed classification and FA is the false alarm.
The performance of code converter is 44.81%. The perfect classification represents when the physician agrees with the epilepsy risk level. Missed classification represents a high level as low level. False alarm represents a low level as high level with respect to the physician's diagnosis. The other performance measures are also defined as below:
Performance of code converter output based on wavelet transform along hard thresholding
Wavelets  Perfect classification  Missed classification  False alarm  Performance index 

Haar  61.45  15.625  22.91  37.58 
Db2  61.18  16.14  22.65  36.44 
Db4  64.57  12.49  22.91  44.72 
Sym8  63.52  11.44  23.95  44.81 
2.4 Rhythmicity of code converter
Rhythmicity of code converter for wavelets with hard thresholding
Wavelets  Number of categories of patterns  Rhythmicity 

R = C/D  
Haar  31  0.032292 
Db2  41  0.042708 
Db4  30  0.03125 
Sym8  45  0.046875 
2.5 Morphological filtering for feature extraction of EEG signals
Morphological filtering was chosen over other methods such as the temporal approach of the EEG signal and waveletbased approach due to the fact that morphological filtering can precisely determine the spikes with a very high accuracy rate [14]. Let us call it as a function f (t). Let us also take into account a structuring element g (t) which together with f (t) be the subsets of Euclidean space E.
Accordingly, the Minkowski addition and subtraction [6] for the function f (t) is given by the relation
The opening and closing functions of the morphological filter is given as:
where x (t) is the spiky part of the signal.
Performance index, sensitivity, and specificity of code converter outputs through morphological filterbased feature extraction arrived at the low value of 33.46%, 76.23%, and 77.42%, respectively. This scenario impacts the optimization of code converter outputs using postclassifier to accomplish a singleton result. The following section describes about the outcome of SVD, EM, and MEM techniques as postclassifier.
3. Singular value decomposition, expectation maximization, and modified EM as postclassifier for classification of epilepsy risk levels
In this section, we discuss the possible usage of SVD, EM, and MEM as a postclassifier for classification of epilepsy risk levels. The SVD was established in 1870s by Beltrami and Jordan for real square matrices [27]. It is used mainly for dimensionality reduction and determining the modes of a complex linear dynamical system [27]. Since then, SVD is regarded as one of the most important tools of modern numerical analysis and numerical linear algebra.
3.1 SVD theorem
where A∈Rm × n (with m ≥ n), U∈Rm × n, V∈Rn × n, And S is a diagonal matrix of size Rn × n.
The columns of U are called the left singular vectors of matrix A, and the columns of V are called the right singular vectors of A. P = min (m, n) and ∑ is called as the singular value matrix with along the diagonal.
We have taken the EEG records of 20 patients for our study. Each patient's sample is composed of a 16 × 3 matrix as code converter outputs depicted in Table 3. Considering this to be as matrix A, SVD is computed. The so obtained eigenvalue is eventually regarded as the patient's epilepsy risk level. The similar procedure is carried out in finding out the remaining eigenvalues of other patients as well.
3.2 Expectation maximization as a postclassifier

Expectation step (E Step): Say for data x, having an estimate of the parameter and the observed data, the expected value is initially computed [29]. For a given measurement,y_{1} and based on the current estimate of the parameter, the expected value of x_{1} is computed as given below:${\mathit{x}}_{1}^{\left[\mathit{k}+1\right]}=\mathit{E}\phantom{\rule{2pt}{0ex}}\left[{\mathit{x}}_{1}{\mathit{y}}_{1},{\mathit{p}}^{\mathit{k}}\right]$(26)This implies${\mathit{x}}_{1}^{\left[\mathit{k}+1\right]}={\mathit{y}}_{1}\frac{1/4}{{\scriptscriptstyle \frac{1}{4}}+{\scriptscriptstyle \frac{{\mathit{p}}^{\left[\mathit{k}\right]}}{2}}}$(27)

Maximization step (M Step): From the expectation step, we use the data which were actually measured to determine the maximum likelihood (ML) estimate of the parameter.

Considering the code converter output, let us take a set of unit vectors to be as ?. We will have to find out the parameters µ and ? of the distribution Md (µ, k). Accordingly, we can form the equation as [30]$?=\left\{{\mathit{X}}_{\mathit{i}}{\mathit{X}}_{\mathit{i}}^{~}\mathrm{Md}\phantom{\rule{0.25em}{0ex}}\left(\mu ,\mathit{k}\right)\phantom{\rule{0.25em}{0ex}}\mathrm{for}\phantom{\rule{0.25em}{0ex}}1=\mathit{i}=\mathit{n}\right\}$(28)

Considering x_{i}??, the likelihood of ? is:$\begin{array}{l}\mathit{P}\left(?\mu ,\mathit{k}\right)=\mathit{P}\left({\mathit{x}}_{\mathit{i}}\dots \dots ..\mathit{xn}\mu ,\mathit{k}\right)={\displaystyle {?}_{\mathit{i}=1}^{\mathit{n}}\mathit{f}({\mathit{x}}_{\mathit{i}}}\mathit{\mu},\mathit{k})\\ \phantom{\rule{4.5em}{0ex}}={\displaystyle {?}_{\mathit{i}=1}^{\mathit{n}}{\mathit{c}}_{\mathit{d}}}\left(\mathit{k}\right){\mathit{e}}^{\mathit{k}{\mathit{\mu}}^{\mathit{T}}{\mathit{x}}_{\mathit{i}}}\end{array}$(29)

The log likelihood of Equation 25 can be written as:$\mathit{L}\phantom{\rule{0.25em}{0ex}}\left(?\mu ,\mathit{k}\right)=ln\mathit{P}\phantom{\rule{0.25em}{0ex}}\left(?\mu ,\mathit{k}\right)=\mathit{n}\phantom{\rule{1pt}{0ex}}ln\mathrm{cd}\phantom{\rule{0.25em}{0ex}}\left(\mathit{k}\right)+\mathit{k}\phantom{\rule{0.25em}{0ex}}\mu \mathrm{Tr}$(30)
where r?=??_{ i }x_{ i }.

In order to obtain the likelihood parameters µ and ?, we will have to maximize Equation 28 with the help of Lagrange operator ?. The equation can be written as:$\mathit{L}\phantom{\rule{0.25em}{0ex}}\left(\mu ,\mathit{?},\mathit{?},?\right)=\mathit{n}\phantom{\rule{1pt}{0ex}}ln\mathrm{cd}\phantom{\rule{0.25em}{0ex}}\left(\mathit{k}\right)+\mathit{k}\phantom{\rule{0.25em}{0ex}}\mu \mathrm{Tr}+\mathit{?}\phantom{\rule{0.25em}{0ex}}\left(1\mu \mathit{T}\phantom{\rule{0.25em}{0ex}}\mu \right)$(31)

Derivating Equation 29 with respect to µ, ?, and ? and equating these to zero will yield the parameter constraints as$\widehat{\mathit{\mu}}=\frac{\widehat{\mathit{k}}}{2\widehat{\mathit{?}}}\mathit{r}$(32)${\widehat{\mathit{\mu}}}^{\mathit{T}}\widehat{\mathit{\mu}}=1$(33)$\frac{\mathit{n}{\mathit{c}}^{\text{'}}\left(\widehat{\mathit{k}}\right)}{{\mathit{c}}_{\mathit{d}}\left(\widehat{\mathit{k}}\right)}={\widehat{\mathit{\mu}}}^{\mathit{T}}\mathit{r}$(34)

In the expectation step, the threshold data are estimated, given the observed data and current estimate of the model parameters [31]. This is achieved using the conditional expectation, explaining the choice of terminology. In the M step, the likelihood function is maximized under the assumption that the threshold data are known. The estimate of the missing data from the E step is used in lieu of the actual threshold data.
3.3 Modified expectation maximization algorithm
In this paper, a ML approach uses a modified EM algorithm for pattern optimization. Similar to the conventional EM algorithm, this algorithm alternated between the estimation of the complete loglikelihood function (E step) and the maximization of this estimate over values of the unknown parameters (M step) [32]. Because of the difficulties in the evaluation of the ML function [33], modifications are made to the EM algorithm as follows.
The method of maximum likelihood corresponds to many wellknown estimation methods in statistics. For example, one may be interested in the heights of adult female giraffes, but been unable due to cost or time constraints, to measure the height of every single giraffe in a population. Assuming that the heights are normally (Gaussian) distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population.
 1.
Find the initial values of the maximum likelihood parameters which are mean, covariance, and mixing weights.
 2.
Assign each x _{ i } to its nearest cluster centerck by Euclidean distance (d).
 3.In maximization step, maximization can be used.The likelihood function is written as:$\begin{array}{l}\mathit{Q}\phantom{\rule{1pt}{0ex}}\left({\mathit{\theta}}^{\mathit{i}+1}{\mathit{\theta}}^{\mathit{i}}\right)=max\mathit{Q}\phantom{\rule{1pt}{0ex}}\left({\mathit{\theta}}^{\mathit{i}}\mathit{\theta}\right),{\mathit{\theta}}^{\mathit{i}+1}\\ \phantom{\rule{5.5em}{0ex}}=argmax\mathit{Q}\phantom{\rule{1pt}{0ex}}\left(\mathit{\theta},{\mathit{\theta}}^{\mathit{i}}\right)\end{array}$(35)$\mathit{d}\left(\mathit{p},\mathit{q}\right)=\mathit{d}\left(\mathit{p},\mathit{q}\right)=\sqrt{{\displaystyle {\sum}_{\mathit{i}+1}^{\mathit{n}}({\mathit{q}}_{\mathit{i}}}}{\mathit{p}}_{\mathit{i}}){2}^{}$(36)
 4.
Repeat iterations and do not stop the loop until it becomes small enough.
The algorithm terminates when the difference between the log likelihood for the previous iteration and current iteration fulfills the tolerance. For μ = 0 and σ = 1, the likelihood function was applied to the 16 × 3 matrix of the code converter output by having truncated to the known endpoints.
4. Results and discussion
To study the relative performance of these code converter and SVD, EM, and MEM, we measure two parameters, the performance index and the quality value. These parameters are calculated for each set of 20 patients and compared.
4.1 Performance index
Performance index for morphological based feature extraction
Classifiers  Morphological operators based feature extraction  

Perfect classification  Missed classification  False alarm  Performance index  
Code converter  62.6  18.25  19.13  33.26 
With SVD optimization  91.22  7.31  1.42  89.48 
With EM optimization  82.68  12.93  4.38  80.1 
With MEM optimization  85.32  10.95  3.72  83.35 
Performance analysis of wavelet transforms with hard thresholding
Classifiers  Perfect classification  Missed classification  False alarm  Performance index 

Haar wavelet  
Code converter  61.45  15.625  22.91  37.58 
With SVD optimization  96.58  3.42  0  96.4 
With EM optimization  82.68  12.93  4.38  80.1 
With MEM optimization  85.32  10.95  3.72  83.35 
DB 2 Wavelet  
Code converter  61.18  16.14  22.65  36.44 
With SVD optimization  98.13  0.9465  0.946  98.03 
With EM optimization  87.29  8.1  4.59  85.42 
With MEM optimization  89.58  5.81  4.61  87.81 
DB 4 Wavelet  
Code converter  64.57  12.49  22.91  44.72 
With SVD optimization  97.54  0.378  2.08  97.45 
With EM optimization  92.33  4.31  3.29  91.35 
With MEM optimization  93.86  2.3  3.84  93.17 
Sym8 Wavelet  
Code converter  63.52  11.44  23.95  44.81 
With SVD optimization  97.35  1.512  1.135  97.23 
With EM optimization  87.27  7.78  5.48  85.03 
With MEM optimization  88.71  6.9  5.67  86.95 
Performance analysis of Haar wavelet transforms with soft thresholding
Classifiers  Perfect classification  Missed classification  False alarm  Performance index 

Heursure soft thresholding  
Code Converter  66.1  19.18  11.93  52.82 
With SVD optimization  87.21  2.84  9.94  82.64 
With EM optimization  89.03  6.79  4.16  87.88 
With MEM optimization  90.46  4.6  4.93  89.82 
Minimax soft thresholding  
Code converter  64.63  20.59  15.1  44.52 
With SVD optimization  85.22  0  14.77  79.43 
With EM optimization  89.48  5.92  4.6  88.15 
With MEM optimization  93.97  2.74  3.5  93.4 
Rigsure soft thresholding  
Code converter  66.34  19.88  13.78  49.11 
With SVD optimization  88.49  0  11.5  84.18 
With EM optimization  90.9  3.84  5.48  89.93 
With MEM optimization  92.22  3.62  4.16  91.25 
Sqtwolog soft thresholding  
Code converter  65.34  27.69  6.96  46.89 
With SVD optimization  77.69  20.88  1.42  66.58 
With EM optimization  84.65  10.85  4.49  82.12 
With MEM optimization  88.38  8.88  2.74  86.87 
4.2 Quality value
Where C is the scaling constant, R_{fa} is the false alarm per set, T_{dly} is the average delay of onset classification, P_{dct} is the percentage of perfect classification, and P_{msd} is the percentage of perfect risk level missed.
Quality value of wavelet transforms with hard thresholding
Wavelets  Quality value  

Without optimization  With SVD optimization  With EM optimization  With MEM optimization  
Haar  11.56  23.5  18.32  19.24 
Db2  12.57  23.82  19.72  20.49 
Db4  12.49  23.15  21.32  22.11 
Sym8  12.84  23.37  19.52  20.3 
Performance analysis of twenty patients using db2 wavelet hard thresholding with SVD, EM, and MEM postclassifiers
Parameters  Code converter method before optimization  SVD optimization  With EM optimization  With MEM optimization 

Risk level classification rate (%)  61.45  98.13  87.29  89.58 
Weighted delay (s)  2.189  2.017  2.233  2.14 
Falsealarm rate/set  22.65  0.9463  4.59  4.6 
Performance index%  36.45  98.03  85.42  87.81 
Sensitivity  75.43  99.05  95.4  95.4 
Specificity  81.94  99.1  91.89  94.19 
Average detection  78.875  99.075  93.645  94.795 
Relative risk  1.166  0.9999  1.038  1.0128 
Quality value  12.57  23.82  19.72  20.49 
Quality value of Haar wavelet transforms with soft thresholding
Haar wavelet with soft thresholding  Quality value  

Code converter  With SVD optimization  With EM optimization  With MEM optimization  
Heursure  13.54  20.16  20.12  20.85 
Mini max  12.11  19.38  20.09  22.54 
Rigsure  12.91  20.44  20.32  21.42 
Sqtwolog  13.22  17.82  18.77  20.22 
Performance analysis of 20 patients using Haar wavelet in soft thresholding with SVD, EM, and MEM postclassifiers
Parameters  Code converter method before optimization  SVD optimization  With EM optimization  With MEM optimization 

Heursure soft thresholding  
Risk level classification rate (%)  66.1  87.21  89.03  90.46 
Weighted delay (s)  2.47  1.91  2.19  2.08 
Falsealarm rate/set  11.93  9.94  4.16  4.93 
Performance index%  52.82  82.64  87.88  89.82 
Sensitivity  85.39  90.05  96.27  95.07 
Specificity  78.28  97.16  92.76  95.4 
Average detection  78.875  93.61  94.51  95.23 
Relative risk  1.166  0.926  1.037  0.996 
Quality value  13.54  20.16  20.12  20.85 
Minimax soft thresholding  
Risk level classification rate (%)  64.63  85.22  89.48  93.97 
Weighted delay (s)  2.53  1.7  2.15  2.06 
Falsealarm rate/set  15.1  14.77  4.6  3.5 
Performance index%  44.52  79.43  88.15  93.4 
Sensitivity  82.31  85.25  95.4  96.71 
Specificity  76.81  100  94.08  97.26 
Average detection  78.875  92.625  94.74  96.98 
Relative risk  1.166  0.85  1.014  0.994 
Quality value  12.11  19.36  20.09  22.54 
Rigsure soft thresholding  
Risk level classification rate (%)  66.34  88.49  90.9  92.22 
Weighted delay (s)  2.52  1.77  2.01  2.1 
Falsealarm rate/set  13.78  11.5  5.48  4.16 
Performance index%  49.11  84.18  89.93  91.25 
Sensitivity  84.35  88.49  94.74  95.83 
Specificity  78.23  100  96.16  96.83 
Average detection  78.875  94.45  95.45  96.33 
Relative risk  1.166  0.88  0.992  0.989 
Quality value  12.91  20.44  20.32  21.42 
Sqtwolog soft thresholding  
Risk level classification rate (%)  65.34  77.69  84.65  88.38 
Weighted delay (s)  2.96  2.806  2.34  2.3 
Falsealarm rate/set  6.96  1.42  4.49  2.74 
Performance index%  46.89  66.58  82.12  86.87 
Sensitivity  91.34  98.57  95.5  97.26 
Specificity  70.82  79.11  89.15  91.12 
Average detection  78.875  88.84  92.325  94.19 
Relative risk  1.166  1.245  1.07  1.06 
Quality value  13.22  17.82  18.77  20.22 
Performance analysis of 20 patients using morphological filters with SVD, EM, and MEM postclassifiers
Parameters  Code converter method  SVD optimization  With EM optimization  With MEM optimization 

Risk level classification rate (%)  62.6  91.22  87.27  88.71 
Weighted delay (s)  2.34  2.26  2.2  2.18 
Falsealarm rate/set  19.13  1.42  5.47  5.67 
Performance index%  33.26  89.48  85.03  86.95 
Sensitivity  77.84  98.57  95.59  98.97 
Specificity  78.91  92.65  98.11  97.67 
Average detection  78.875  95.61  96.85  98.32 
Relative risk  1.166  1.063  0.974  1.013 
Quality value  12.74  20.62  19.52  20.3 
Performance analysis of postclassifiers in terms of weighted delay and quality value
Methods  Wavelets  SVD optimization  EM optimization  MEM optimization  

Weighted delay (s)  Quality value  Weighted delay (s)  Quality value  Weighted delay (s)  Quality value  
Hard threshold  Haar  2.14  23.5  2.431  18.32  2.36  19.24 
dB2  2.017  23.82  2.23  19.72  2.14  20.49  
dB4  1.974  23.15  2.11  21.32  2.01  22.11  
Sym8  2.038  23.37  2.2  19.52  2.18  20.3  
Soft threshold heursure  Haar  1.94  20.16  2.19  20.12  2.08  20.85 
dB2  2.82  16.01  2.37  20.24  2.27  20.54  
dB4  2.41  19.99  2.31  19.79  2.27  20.57  
Sym8  2.16  18.95  2.26  20.44  2.13  22  
Soft threshold minimax  Haar  1.7  19.36  2.15  20.09  2.06  22.54 
dB2  2.23  19.39  2.3  18.87  2.16  20.41  
dB4  1.97  20.13  2.17  19.97  2.14  20.66  
Sym8  2.51  19.51  2.27  20.2  2.22  20.73  
Soft threshold rigsure  Haar  1.77  20.44  2.01  20.32  2.1  21.42 
dB2  1.62  18.77  2.07  19.4  2.04  19.95  
dB4  1.53  16.74  2.08  20.42  2.08  22.04  
Sym8  1.65  19.51  2.18  20.02  2.09  21.06  
Soft threshold sqtwolog  Haar  2.08  17.82  2.34  18.77  2.3  20.22 
dB2  3.25  16.73  2.42  19.17  2.36  20.1  
dB4  2.76  19.1  2.37  19.62  2.36  19.35  
Sym8  2.97  17.52  2.41  18.74  2.39  19.97  
Morphological filters  2.26  20.62  2.2  19.52  2.18  20.3 
In the case of Table 15, the EM and MEM classifiers are either plugged into more missed classification or false alarms and subsequently leads to lower value of QV less than 20 in most of the wavelet transforms. In case of soft thresholding, dB2 wavelet in rigsure thresholding for MEM postclassifier outperforms other fifteen methods. Morphological filters are stacked at higher delay with QV set at near 20.
Summary of previous works for automated detection of normal and epileptic classes
Authors  Features  Classifier  Accuracy (%) 

Nigam and Graupe [35]  Nonlinear preprocessing filter  Diagnostic neural network  97.20 
Kannathal et al. [37]  Entropy measures adaptive neurofuzzy  Inference system (ANFIS)  92.22 
Srinivasan et al. [38]  Time andfrequency domain  Features Elman network  99.60 
Sadati et al. [39]  DWT adaptive neural  Fuzzy network  85.90 
Subasi [42]  DWT statistical measures  Mixture expert model (a modular neural network)  94.50 
Polat and Gunes [43]  FFTbased features  Decision tree  98.72 
Tzallas et al. [41]  Timefrequency methods  Artificial neural network  97.72 to 100 
Srinivasan et al. [40]  ApEn  Probabilistic neural network, Elman network  100 
Polat and Gunes [44]  FFTbased features  Artificial immune recognition system  100 
Polat and Gunes [45]  AR C4.5  Decision tree classifier  99.32 
Ocak [46]  DWTApEn  Thresholding  96.65 
Guo et al. [47]  Relative wavelet energy  ANN  95.85 
Guo et al. [48]  ApEn and wavelet Transform  ANN  99.85 
Guo et al. [49]  Line length features and wavelet transform  ANN  99.60 
Subasi and Gursoy [51]  DWTPCA, ICA, LDA  SVM  98.75(PCA) 
99.50(ICA)  
100(LDA)  
Ubeyli [52]  AR  SVM  99.56 
Lima et al. [53]  Wavelet transform  SVM  100 
Guo et al. [50]  Genetic programming based  KNN  99 
Wang et al. [54]  Wavelet packet entropy  KNN  100 
Iscan et al. [55]  Cross correlation and PSD  Several classifiers including SVM  100 
Proposed method by authors Harikumar  dB2 wavelet hard thresholding  SVD  98.03 
5 Conclusions
The objective of this paper is to classify the risk level of the epileptic patients from the EEG signals. The aim is to obtain high classification rate, performance index, quality value with low false alarm, and missed classification. Due to the nonlinearity obtained and also the poor performance found in the code converters, an optimization was vital for the effective classification of the signals. We opted SVD, EM, and MEM as postclassifiers. Morphological filters were also used for the feature extraction of the EEG signals. After having computed the values of PI and QV discussed under the results column, we found that SVD was working perfectly with a high classification rate of 91.22% and a false alarm as low as 1.42. Therefore, SVD was chosen to be the best postclassifier. The accuracy of the results obtained can be made even better by using extreme learning machine as a postclassifier, and further research will be in this direction.
Declarations
Acknowledgements
The authors express their sincere thanks to the Management and the Principal of Bannari Amman Institute of Technology, Sathyamangalam for providing the necessary facilities for the completion of this paper. This research is also funded by AICTE RPS: F. No 8023/BOR/RID/RPS41/200910, dated 10 Dec 2010.
Authors’ Affiliations
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