An ECG Signal Encryption and Classification Using Sparse Autoencoder and Optimized Neural Network Techniques

The advancement of healthcare systems in the digital era incorporates numerous technical innovations, aiming to improve patient care through enhanced data security measures and reducing the frequency of conventional one to one diagnosis and treatment practices. Telecommunication systems, telemedicine systems are introduced to get suggestions from physicians even from remote locations. People can access the specialists in the particular field by simply sitting in home and transmitting their medical data through internet. Healthcare devices are equipped to collect and consolidate the samples at a periodic interval and provide the same to physicians at the time of analysis. However, the data transmission in telecommunication channels introduces serious security threats which is a major concern in the present situation. Healthcare data, which includes personal and private information, should only be accessible to physicians and not to unauthorized individuals.

The electrocardiography is an important element in healthcare systems to detect abnormalities in patients. The worldwide diagnostic procedure for electrocardiography is similar and securing Electrocardiogram (ECG) signals gains more attention specifically after implementation of EU general data protection regulation (GDPR). ECG signals include user sensitive information also it can be used as a biometric. ECG features can be used as a cryptographic key in a few applications like pseudo-random number generators, shift generators [1], etc. These sensitive data should be accessed only the authorized persons and to achieve this privacy preserving methods should be adapted before transmitting the information in the communication channel. Researchers are increasingly focusing on securing healthcare data by introducing various security measures, including authentication, access controls [2], and watermarking [3], etc. However, these authentication and access control practices can be compromised if the cryptographic key is discovered or guessed. So, to bring an extra effort to secure the data before transmission, encryption procedures are introduced so that even the access controls are known to intruder, they cannot able to retrieve the encrypted message.

Recent methods for encrypting ECG signals include the Advanced Encryption Standard (AES) [4, 5], Dynamic AES [6], Selective Encryption (SE) [7], Chaos-based encryption [8], Wavelet and Chaotically Huffman Code [9], Logistic mapping-based stream encryption [10], Lightweight selective encryption (LWSE) [11], etc. However, the research towards identifying potential encryption model for ECG signal encryption is still in progress. The major objective of this research work is to bring an efficient and secure ECG signal encryption using deep learning technique. Since the feature merits of deep learning techniques are observed in various domains for feature extraction and classification and it is less explored in the encryption process. Specifically, the autoencoder in the deep learning model is mostly used for image-based applications, and limited works have evolved for signal processing. Specifically, healthcare signal processing is not explored using autoencoders which is the novelty of this proposed research work.

In addition to encryption, classification is also performed in this research work using optimized neural network. Various machine learning based ECG signal classification approaches are evolved which include support vector machines, random forests, decision trees, etc. [12, 13]. However, the feature extraction procedures adopted in those models lag in performance while selecting essential features. Similarly, if the classification model parameters are optimized then the performance of the classification models might get improvements. Considering these observations, in this research work for feature extraction, features of deep learning are utilized. Convolutional Neural Network (CNN) extracts the essential features from ECG signals. The extracted signals are processed using an optimized artificial neural network to categorize the patient status into normal, abnormal, Myocardial Infarction (MI), and History of MI. The major contribution of this research work is summarized as follows.

•We have presented a secure ECG encryption procedure for healthcare data transmission using a sparse auto-encoder with Chaotic Logistic Mapping.

•We have presented a classification model to detect the patient status from ECG signals using an optimized artificial neural network. The classification model incorporated the deep learning technique -CNN for efficient feature selection.

•We have presented an intense experimental analysis of the proposed encryption and classification model using a benchmark dataset

•We have presented a performance analysis of the proposed model with existing models to demonstrate better performance.

The remaining part of the article is structured as follows. A vast literature analysis is presented in section 2 by discussing the existing encryption and classification procedures in ECG signal analysis. The proposed encryption and classification model are presented in section 3. Experimental results and their relevant discussion are presented in section 4, and finally, the observations are concluded in section 5.

The proposed ECG signal analysis is presented in this section in two phases. In the first phase, the encryption model is presented and the optimized classification model is presented in the second phase. Techniques like sparse autoencoder and Chaotic Logistic Mapping are used in the encryption process. The use of sparse autoencoders for ECG signal encryption is relatively novel as sparse autoencoders are typically employed in image processing or noise reduction tasks. However, their application in encrypting ECG signals represents its uniqueness from standard encryption techniques like AES or RSA. Similarly, the integration of chaotic logistic mapping in the proposed work provides improved security features through its dynamic encryption which is sensitive to initial conditions. This makes the method highly resistant to standard cryptography attacks. The classification process of the proposed model includes the genetic algorithm and artificial neural network to classify ECG signals to detect the current status of the patient. The application of optimization techniques specifically genetic algorithms to fine-tune the parameters of an artificial neural network (ANN) for ECG signal classification is novel and it not only improves accuracy but also ensures that the model generalizes well on unseen data by preventing overfitting.

Figure 1 depicts the overview of the proposed encryption model, and Figure 2 shows the classification model.

The proposed model integrates both encryption and classification process in ECG signal analysis to ensure better signal security and accurate diagnosis of patient’s conditions. The ECG signals are initially encrypted using sparse autoencoder which is combined with chaotic logistic mapping. This encrypted data protects the sensitive information of patients during transmission. In the classification phase, the encrypted data are initially decrypted and preprocessed to ensure the signal integrity and remove noise factors which introduced in signals during transmission process. The preprocessed signals are then fed into convolutional neural network for feature extraction and then classified using an optimized neural network. This combines process ensures the better transition of data between decryption and classification, also it provides reliable diagnostic results without compromising the security.

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Figure 1. Overview of the proposed encryption process

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Figure 2. Overview of the proposed classification process

3.1 Encryption using sparse autoencoder and chaotic logistic mapping

The ECG signal encryption starts by encoding the input signal using sparse autoencoder. Generally, autoencoders are unsupervised learning algorithms which has the ability to handle and represent the large amount of unlabeled data. The encoding refers to the representation of middle layer with respect to the actual data as the input. The middle-hidden layers are used to decode the intermediate layer features so that actual input can be obtained at the output layer. The autoencoder reconstructs the signal considering the reconstruction error in the encoding and decoding process. Autoencoders reconstruct the signal without any supervisory measure since the features of the data can be learned automatically which avoids additional processing elements. The general structure of autoencoder is similar to feed-forward neural network so that the network is trained to learn the input features and produce the corresponding outputs rather than producing classification outputs.

The sparse autoencoder (SAE) in the research helps to reduce data redundancy and enhancing the efficiency when managing complex datasets. In the sparse autoencoder the majority of the hidden layer neurons will be inactive. This is because of the feasibly saturated condition of the neurons for most of the inputs. This results in the sparsity of features so that most of the elements of the features are considered as close to zero or zero. The sparsity is accomplished by the penalty term to mention the sparsity value. To obtain better clarity about sparse autoencoder the mathematical model is summarized in this section. Figure 3 depicts an illustration of sparse autoencoder with input, hidden and output layers.

Consider the input vector $n\in {{x}^{{{D}_{n}}}}$ and it is mapped by the autoencoder as a new vector $m\in {{x}^{{{D}^{\left( 1 \right)}}}}$. The new vector is expressed in terms of weight matrix and bias factors as follows.

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Figure 3. Sparse autoencoder

${{m}^{\left( 1 \right)}}={{k}^{\left( 1 \right)}}\left( {{w}^{\left( 1 \right)}}n+{{\beta }^{\left( 1 \right)}} \right)$              (1)

where, ${{k}^{\left( 1 \right)}}:{{x}^{{{D}^{\left( 1 \right)}}}}\to {{x}^{{{D}^{\left( 1 \right)}}}}$ represents the transfer function, the weight matrix is represented as ${{w}^{\left( 1 \right)}}\in {{x}^{{{D}^{\left( 1 \right)}}}}$ and the bias vector is represented as ${{\beta }^{\left( 1 \right)}}\in {{x}^{{{D}^{\left( 1 \right)}}}}$. The first layer of the autoencoder is represented using the superscript $\left( 1 \right)$. In the next step the encoded representation $m$ is transferred to reconstruct the input $n$ by the decoder as per the following formulation.

$\hat{n}={{k}^{\left( 2 \right)}}\left( {{w}^{\left( 2 \right)}}n+{{\beta }^{\left( 1 \right)}} \right)$                       (2)

where, ${{k}^{\left( 2 \right)}}:{{x}^{{{D}^{\left( 2 \right)}}}}\to {{x}^{{{D}^{\left( 2 \right)}}}}$ represents the transfer function, the weight matrix is represented as ${{w}^{\left( 2 \right)}}\in {{x}^{{{D}^{\left( 2 \right)}}}}$ and the bias vector is represented as ${{\beta }^{\left( 2 \right)}}\in {{x}^{{{D}^{\left( 2 \right)}}}}$. The second layer of the autoencoder is represented using the superscript $\left( 2 \right)$. In this stage, an adapted cost function is included in the autoencoder in the form of a regularization term to introduce the sparsity in the autoencoder. The activation functions are averaged to estimate the regularization term for each neuron $i$ and it is expressed as:

${{\hat{\sigma }}_{i}}=\frac{1}{l}\underset{j=1}{\overset{l}{\mathop \sum }}\,m_{i}^{\left( 1 \right)}\left( {{n}_{j}} \right)$            (3)

${{\hat{\sigma }}_{i}}=\frac{1}{l}\underset{j=1}{\overset{l}{\mathop \sum }}\,k\left( w_{i}^{\left( 1 \right)T}{{n}_{j}}+\beta _{i}^{\left( 1 \right)} \right)$              (4)

where, the total number of training samples is represented as $l$, ${{n}_{j}}$ indicates the input training sample, $w_{i}^{\left( 1 \right)T}$ represents the weight matrix of the first layer in transpose form, $\beta _{i}^{\left( 1 \right)}$ represents the neural network bias vector. For high output activation function the neuron will be fired however for low activation value, only small number of input samples will be processed by the neuron which motivates the autoencoder to learn the features. So, in this stage, a limitation term is included with the activation function output that encourages the neuron to learn from the limited features. Similarly, the other neurons are motivated to learn from the small features so that every neuron will be responsible for individual features of the inputs. In order to measure the relativity of the targeted activation function $\sigma$ and the actual activation function $\hat{\sigma }$ a sparsity regularize value is introduced. The Kullback-Leibler divergence function that defines the difference between the distributions are formulated as:

${{\text{ }\!\!\Omega\!\!\text{ }}_{Spars}}=\underset{i=1}{\overset{{{D}^{\left( 1 \right)}}}{\mathop \sum }}\,KL\left( \sigma \parallel {{{\hat{\sigma }}}_{i}} \right)$                           (5)

${{\text{ }\!\!\Omega\!\!\text{ }}_{Spars}}=\underset{i=1}{\overset{{{D}^{\left( 1 \right)}}}{\mathop \sum }}\,\sigma \log \frac{\sigma }{{{{\hat{\sigma }}}_{i}}}+\left( 1-\sigma  \right)\log \left( \frac{1-\sigma }{1-{{{\hat{\sigma }}}_{i}}} \right)$                          (6)

where, KL represents the divergence function and $\sigma$ represents the activation function. In order to make the distribution close to each other the cost function is decreased and it is expressed using mean square error as follows:

 $E=\frac{1}{L} \\ \underset{l=1}{\overset{L}{\mathop \sum }}\,\underset{v=1}{\overset{V}{\mathop \sum }}\,\left[ {{\left( {{N}_{vl}}+{{{\hat{N}}}_{vl}} \right)}^{2}} \right]+\left[ \rho *{{\text{ }\!\!\Omega\!\!\text{ }}_{w}} \right]+\left[ B*{{\text{ }\!\!\Omega\!\!\text{ }}_{Spars}} \right]$                (7)

where, the first element in the equation indicates the mean square error, the second element indicates the layer regularization term added to the cost function and the third element indicates the sparse regularization. The layer regularization value is added to avoid the sparsity regularization value being small in the training process when there is an increase in weight and decrease in mapped vector $m$ and it is expressed as:

${{\text{ }\!\!\Omega\!\!\text{ }}_{w}}=\frac{1}{2}\underset{h}{\overset{H}{\mathop \sum }}\,\underset{j}{\overset{l}{\mathop \sum }}\,\underset{i}{\overset{v}{\mathop \sum }}\,{{\left( w_{ij}^{\left( 1 \right)} \right)}^{2}}$                         (8)

where, the hidden layers are represented as $H$, the total number of input samples is represented as $L$, the number of classes is represented as $V$.

The encoded input is shuffled in the next step as scrambling and shuffling are the basic and primary steps of encryption process. The encryption process can involve one or more actions like scrambling the data, shuffling it, or using a combination of both to enhance security. However, instead of scrambling, the row-column shuffling is widely preferred as it is simple, fast, and efficient. While shuffling the row-column, the input is considered as a matrix function with j rows and k columns. The secret key is generated by selecting two tables in which one table is used for shuffling the rows and another table is used for shuffling the columns. Based on the shuffle table the rows and columns are shuffled. Similarly, for column shuffling is also performed. A simple pseudo random number generator is used to explain the shuffling process as the attack is irrespective to the shuffling table and the function is mathematically expressed as:

${{x}_{i+1}}=x_{i}^{2}+{{x}_{i}}+S~\left( mod~n \right)$ for $i=0,1,2\ldots$                 (9)

where, the random initial seed is represented as $S$, $n$ indicates the large number. The row shuffling table for is mathematically formulated as:

$a={{x}_{i}}\left( mod~h \right)$                 (10)

${{T}_{r}}\left( i \right)=a+z$                 (11)

where, ${{T}_{r}}$ represents the row shuffling table, minimum non-negative integer is represented as $z$. As per Eq. (11), shuffling is performed for row $i$ for the values $0,1,2..h-1$. Similarly, the column shuffle is also performed to enhance the security of the encryption process. Further, the shuffled data is encrypted using Chaotic Logistic Mapping. The mathematics behind the chaotic theory considers the dynamic behavior of the sensitive systems. Chaos theory defines that a minor variation in the initial condition will introduce serious uncorrelation in the final sequence. When it is applied for the encryption process the entire sequence will be unpredictable if a suitable bifurcation parameter is selected for the encryption. Compared to other encryption procedures, the chaotic theory is simple, impregnable, and computationally faster. The logistic map which produces two-dimensional chaotic sequences that are non-periodic is mathematically expressed as:

${{p}_{\left( n+1 \right)}}=\mu {{p}_{n}}\left( 1-{{p}_{n}} \right)$                          (12)

where, the bifurcation parameter is represented as $u$ and its range is from $1<\mu <4$ and the initial value is represented as ${{p}_{0}}$and the generated sequence elements are $\left\{ {{p}_{1}},{{p}_{2}},{{p}_{3}}\ldots {{p}_{n}} \right\}$. Generally, the bifurcation range is selected between $3.56<\mu \le 4$ to obtain a better chaotic nature. In a completely chaotic state, the logistic map can be used as a pseudo-random number generator. The methods of probability and statistics can also be used to understand the characteristics of chaotic sequences.

The doubling of sequences completes when the value $\mu =3.569$ and the system becomes chaotic. For a small range of $\mu$ values the system exhibits periodic behavior and this region is called a periodic window.

In the periodic window, an intermittency property is exhibited by the logistic map which is similar to periodic behavior interrupted by the chaotic bursts. Lyapunov exponent method is used to determine the chaotic nature and it is explained using the following formulation:

$\mathcal{L}=\frac{1}{}\left( \ln \left| f_{\mu }^{'}\left( {{p}_{1}} \right) \right|+\ln \left| f_{\mu }^{'}\left( {{p}_{2}} \right) \right|+\ldots +\ln \left| f_{\mu }^{'}\left( {{p}_{n}} \right) \right| \right)$                             (13)

where, the differentiation function of $p$ is represented as $f_{\mu }^{'}$ and the successive iterations are given as ${{p}_{1}},{{p}_{2}},\ldots ,{{p}_{n}}$. The exponent function can be computed from the samples obtained from the near points. Bifurcation occurs in a system when the average Lyapunov exponent is zero. The encryption process using chaotic logistic mapping considers the image dimension and layers. Let us consider an image $I\left( x,y,\ell  \right)$ in which $x$ indicates the number of rows and $y$ indicates the number of columns and the layer is represented as $\ell$. A permutation process is applied in the encryption process followed by the diffusion process. The diffusion process is illustrated in Figure 4. The image pixels are rearranged in the permutation process as follows:

${{p}_{i}}=\left[ p\times {{10}^{3}} \right]~mod~x$                 (14)

${{q}_{i}}=\left[ q\times {{10}^{3}} \right]~mod~y$                          (15)

where, ${{p}_{i}}$ and ${{q}_{i}}$ are the vectors which are obtained based on the condition given in Eq. (12). In the permutation process, the image exchanges its pixel with the vectors ${{p}_{i}}$ and ${{q}_{i}}$. For the diffusion process, Eq. (12) is modified as follows to obtain the vector ${{p}_{k}}$ and it is given as:

${{p}_{k}}=\left[ p\times {{10}^{10}} \right]~mod~256$                                (16)

where, the vector ${{p}_{k}}$ and permutated matrix are processed to obtain the final results.

The results obtained from the diffusion process are stored in ${{C}_{k}}$. The process starts with the input vector ${{p}_{k}}$and matrix ${{M}_{k}}$ with mod 256. The results are recombined with XOR along with the delay function ${{D}^{-2}}$ and ${{D}^{-3}}$. The final expression is given as:

${{C}_{k}}={{p}_{k}}Xor\\ \left( \left( {{M}_{k}}+{{p}_{k}} \right)mod256 \right)\ldots Xor{{C}_{k}}\left( {{D}^{-3}} \right)Xor{{C}_{k}}\left( {{D}^{-2}} \right)$                            (17)

The encryption process increases the diffusion level which increases the data security against cryptographic attacks.

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Figure 4. Diffusion process

3.2 Classification using optimized artificial neural network

The classification model presented in the proposed work includes Cat Swarm Optimization (CS) and Modified Decision Tree (MDT) Classifier for efficient classification. The parameters of DT are optimized by the CS to attain maximum classification accuracy and minimum loss. Before classification, the features are extracted using convolutional neural network so that optimal features are processed by the classification model to attain better performance.

3.2.1 Feature extraction using convolutional neural network (CNN)

Convolutional neural network (CNN) is a familiar deep learning architecture that includes an automated feature extraction process and a fully connected network for classification process. In this research work, the essential features are obtained using CNN and classified using genetic optimized artificial neural network instead of fully connected network to obtain maximum accuracy. Before feature extraction, the ECG signals are preprocessed since the data is collected generally from different environments which include frequency interference, EMG interference baseline drift, etc. So, it is essential to denoise the signal before classification. Generally, filters are used in the preprocessing steps to remove the noises. In this research work a wavelet transform approach is adopted before filtering. The wavelet transform decomposes the nonstationary signal into different frequency bands. Then an adaptive threshold filter is employed to select the wavelet function. These simple preprocessing steps are enough for the classification models as the essential features are directly extracted by the CNN model.

The convolutional neural network model used in the proposed work includes an input layer, three convolution layer and 3 pooling layer and a fully connected layer with a classifier. The convolution and pooling layer extract and maps the features from input to enhance the learning speed and avoids data overfitting. An average pooling layer is preferred in the proposed architecture instead of max-pooling to preserve the input data features. The architecture of the proposed CNN model used for feature extraction is depicted in Figure 5. The convolutional kernel convolutes the feature map which is obtained from the previous layer. Offsetting the convolution kernel and transferring it as a non-linear activation function the output of the convolution layer is obtained as follows:

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Figure 5. CNN architecture

$y_{i}^{m,n}=f\left( b_{i}^{m,n}+\underset{h=1}{\overset{H}{\mathop \sum }}\,w_{h,i}^{m,n}*k_{i+h-1}^{m-1,n} \right)$                  (18)

where, the output of the ${{i}^{th}}$ neuron in layer $m$ is represented as $y_{i}^{m,n}$, the function $f()$ indicates the activation function. The offset of the neuron for layer $m$ is represented as $b_{i}^{m,n}$ and the output of the neuron for layer $m-1$ is represented as $k_{i+h-1}^{m-1,n}$. The convolution kernel for ${{m}^{th}}$ layer is represented as $w_{h,i}^{m,n}$.

The pooling layer in the proposed architecture included next to the convolution layer and it reduces the convolution layer output data dimension. This helps to reduce the network complexity and avoids overfitting. The pooling layer function is mathematically expressed as

$\mathcal{O}_{i}^{m,n}=f\left( \delta _{i}^{m,n}pool~\left( k_{i}^{m-1,n} \right)+b_{i}^{m,n} \right)$                 (19)

where, the ${{i}^{th}}$ neuron output for layer $m$ is represented as $\mathcal{O}_{i}^{m,n}$, the function $f()$ indicates the activation function. The offset of the neuron for layer $m$ is represented as $b_{i}^{m,n}$ and the sampling weight coefficient is represented as $\delta _{i}^{m,n}$. The pooling function is represented as $pool()$ and the output of the $m-1$ is represented as $k_{i}^{m-1,n}$. Generally, a dropout layer is included before the fully connected layer. Based on the probability in the CNN training process, few neurons will be disconnected in the dropout layer. This dropout prevents data overfitting and enhance the network generalization ability. The layer details of proposed CNN architecture are depicted in Table 1.

Further, the obtained features are classified using genetic optimized artificial neural network for maximum accuracy.

Table 1. Layer details of CNN model

3.2.2 Genetic optimized artificial neural network

The feature benefits of artificial intelligence technique like artificial neural networks are explored by various researchers. Though ANN solves complex problems, the slow learning rate and local minima are the major demerits observed. In this research work, to overcome this optimization models are incorporated so that the weight and bias conditions of artificial neural networks are adjusted to obtain optimal performance. Figure 6 depicts the process flow of optimized Neural Network for ECG signal classification.

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Figure 6. Process flow of proposed optimized ANN

So, an objective function or fitness function should be obtained. Here the reason for introducing optimization in the classification process is to obtain minimum cost network which should provide better performance with minimum computational parameters. Mean square error (MSE) is generally used as network objective function. The error function which controls the ANN performances are training error $\left( {{e}_{train}} \right)$ and generalization error $({{e}_{gen}})$. Along with these error function, architecture criterion $\left( {{\mathcal{A}}_{c}} \right)$, solution consistency $({{\mathcal{S}}_{c}})$ and learning time constants $({{L}_{t}})$ are considered to obtain the objective function for the optimized ANN model. Mathematically the objective function is formulated as:

${{f}_{obj}}=\left[ {{e}_{train}}+{{e}_{gen}} \right]*\left[ {{\mathcal{A}}_{c}} \right]*\left[ {{\mathcal{S}}_{c}} \right]*\left[ {{L}_{t}} \right]$                (20)

The training error $\left( {{e}_{train}} \right)$ defines the memorization ability of the network. In the training process the learning progress of the network is measured and it is formulated as:

${{e}_{train}}=\frac{\mathop{\sum }_{i=1}^{n}\left| \left( {{y}_{ti}}-{{y}_{ri}} \right)/{{y}_{ti}} \right|}{n}$                 (21)

where, the absolute relative error average is represented as ${{e}_{train}}$ and the training data vector target value is represented as ${{y}_{ti}}$. The network response to the training data is represented as ${{y}_{ri}}$ and the total number of training data samples is represented as $n$. The generalization error is the measure that defines the response-ability of the network. The response of the network for similar but not identical samples is defined in terms of generalization error. Mathematically the generalization error is formulated as:

${{e}_{gen}}=\frac{\mathop{\sum }_{i=1}^{m}\left| \left( {{y}_{ti}}-{{y}_{ri}} \right)/{{y}_{ti}} \right|}{m}$                     (22)

where, the generalization error is represented as ${{e}_{gen}}$ and the testing data vector target value is represented as ${{y}_{ti}}$. The network response to the testing data is represented as ${{y}_{ri}}$ and the total number of training data samples is represented as $m$. The architecture criteria define the architecture through the penalty function. Since smaller architectures avoid data overfitting the training phase and increase the generalization ability. With minimum neurons and weight factors, the training process can be accelerated better than a conventional setup. So, in the architecture criteria, the weights and biases are considered and it is expressed as an exponential function as follows.

${{\mathcal{A}}_{c}}=\alpha {{e}^{f\left( k \right)}}$                              (23)

where, the total number of biases (k) and weights are represented as a function $f\left( k \right)$ and $\alpha$ is constant factor and its value is 1. The value of $f\left( k \right)=0.01\times k$. Though the generalization error is essential but it is not sufficient to persuade the network. since the generalization error provides the mean for all testing data. However, there may be a chance for low generalization error for special cases when the network prediction accuracy is lesser than the desired accuracy. To handle this situation a solution criterion is introduced in the objective function which computes the prediction error for the test data. When outlier cases are observed a penalty is applied which produces a high prediction error and based on that the network model is redirected to obtain accurate solutions using solution criteria. Mathematically the solution criteria are formulated as:

${{\mathcal{S}}_{c}}=1+\psi x+\varrho y$                 (24)

where, the test case average quality prediction is represented as $x$ and the unacceptable quality prediction is represented as $y$. Two adjustment factors are used to define the attributes such as $\psi$ and $\varrho$ and its values are considered as 0.33 and 1 respectively. The learning time constants are introduced considering the total epochs which required for training. This function is expressed as:

${{L}_{t}}=a*e+b$                          (25)

where, $a$ and $b$ are the linear function constants and its values are 2×10^-5 and 1 respectively and the total training epoch is represented as $e$.