Prediction of Brain Stroke Severity Using Machine Learning

According to “United States centers for Disease Control and Prevention” around 7,95,000 people have been affected with strokes in the year 2018 [1]. On the other hand, when compared with Canadian statistics the overall death rate was around 15,409 people affected with stroke in the year 2000 [2]. Likewise, the statistical report in India given by “India Collaborative Acute Stroke Study” shows 2,162 people are affected with strokes in the year 2004 [3]. As per records of “Stroke Association United Kingdom”, every 5 children out of 100,000 are affected by stroke in the year 2012 [4].

1.1 Brain stoke

In an adult human being even when the body is set to rest 20% of the oxygen and glucose also about 2% of the entire body weight is constituted by the brain. The blood flow in the brain is said to extend when recreation of the neurons takes palace in certain parts of the brain. It is carried out through the internal carotid and vertebral arteries. The blood is then altered from head to heart through the internal jugular veins [5].

The loss of the blood might be observed in two scenarios in which the flow of blood among the blood tissues decreases results in the ischemic stroke whereas if internal bleeding occurs among the brain tissues known as hemorrhagic stroke [6] and the types of strokes are demonstrated in Figure 1.

The flow of the blood from arteries among the brain tissues leads to blockage or becomes slender [7, 8]. This blocking might also happen when the tiny parts of plaque that are caused through atherosclerosis damage thereby creating a clot in the blood vessel [9, 10]. Hemorrhagic stroke referred to as a severe stroke in which the blocked artery might damage resulting in the bleeding or explosion of the artery [11, 12]. When the blood is divulged and leaked it spreads out causing pressure on the brain [13].

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Figure 1. Stroke classification

1.2 Machine learning

Machine learning is a study of Artificial Intelligence (AI) and it is a part of computer science, it varies with different perspectives from traditional computations. Machine learning has a feature that permits the system to develop and control the data sets in producing the output values within the limited range [14]. In this technology, the algorithms are defined in the precise way of representing the data sets utilized by the computer in the evaluation of the problems. These algorithms can be implemented through supervised learning and unsupervised learning as shown in Figure 2 [15]. Supervised learning involves the data that is inputted by the humans by retrieving the concerning output. Whereas the backend part of running the algorithm for implementing the accurate results can be done through unsupervised learning without the labeled data by allowing it to find the architecture based upon the input given by the user.

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Figure 2. Types of machine learning

The remaining sections of this research work are organized as follows. Section-2 discusses ‘Related Work’, Section-3 presents the ‘Methods Used and Proposed Model’, Section-4 describes the ‘Experimental Results and Analysis’. Section-5 discusses ‘Conclusion and Future Scope.

This section comprises of different benchmark machine learning models with their limitations, the dataset used for this research work, and proposed architecture with its advantage over existing models.

3.1 Machine learning models

3.1.1 Gaussian Naïve Bayes

Supervised learning algorithm uses the Naïve Bayes Model, which depends on Bayes theorem involves resolving the different divisions of the errors. Among different types of Naive Bayes methodologies, we implement “Gaussian naïve Bayes” in this research work. The probabilities of the patients effected by hemorrhagic and ischemic strokes can be written as:

$P\left(\frac{A}{B}\right)=\sum_{w \in A \cap B} P\left(\frac{W}{B}\right)+\sum_{w \in A \cap B^{c}} P\left(\frac{W}{B}\right)$  (1)

$=\sum w \in A \cap B \frac{P(w)}{P(B)}$   (2)

$=\frac{P(A \cap B)}{P(B)}$   (3)

where, ‘A’ is probability of getting stroke and ‘B’ defines highest occurring value of every primary attribute in dataset.

The instances represented by solution vector x = (x1, x2, x3,……,xn) and P(Ck | x1, x2, x3,……,xn ), where, ‘Ck’ defines the ‘kth’ class and ‘k’ is the number of classes.

The conditional probability of Gaussian Naïve Bayes can be decomposed as follows:

$P\left(C_{k} \mid \mathrm{x}\right)=\frac{P\left(C_{k}\right) P\left(\mathrm{x} \mid C_{k}\right)}{P(\mathrm{x})}$   (4)

Using the probability on construction a model classifier is calculated as:

$\hat{y}=\operatorname{argmax}\left\{P\left(c_{1}\right) \prod_{i=1}^{n} P\left(\frac{x_{i}}{C_{1}}\right), P\left(c_{2}\right)\right.$$\left.\prod_{i=1}^{n} P\left(\frac{x_{i}}{C_{2}}\right)\right\}$   (5)

where, ‘n’ defines number of primary parameters (n=9), ‘C₁’ defines the low risk and ‘C₂’ defines the high risk.

3.1.2 Linear regression

The name itself is referred to as the precise correspondence among the dependent and independent variables considering few or more variables so-called linear regression. Since the linear regression represents in a precise way in its correspondence by predicting the change in the variables of dependent classes to that of the change of the variables in the independent classes is calculated as:

Y = b₀ + b₁*X₁+ b₂*X₂ + b₃*X₃ +……. + b_n*X_n      (6)

where, ‘Y’ is a dependent variable, X1……Xn are independent variables, b0.….bn are the regression coefficients. The number of attributes ‘n’ is written as:

$Y_{i}=\sum_{i=1}^{n} X n^{*} b_{n}+b_{0}$   (7)

In this research work, we consider the “Multilinear regression” technique from among the various types of linear regression modules. In general, taking the variables than the required sum in the independent class that is required in analyzing the binary dependent values. This process of linear regression is referred to as Multilinear regression and the sum of squares error (SSE) can be calculated as:

$S S E=\sum\left(Y_{i}-Y_{i}^{\mid}\right)^{2}$   (8)

where, Y_i is ‘Predicted Output’ and $Y_{i}^{\mid}$ is ‘expected output’.

3.1.3 Logistic regression

Logistic regression comes under the technique of supervised learning, which is used for analyzing the absolute dependent values by making use of the variable among the required blocks of the independent values. Analysis of the output values can be determined by the logistic regression of the absolute dependent values. Hence the solutions can be drawn as the absolute or the differential variables. It may be of any form either numerical or binary variables i.e., Yes or No, 0 or 1, true or false, etc. In the computer-determined language, the values are given in the 0 or a format but this model represents the feasible value that lies between 0 and 1. The usage of the values is the only difference between Logistic regression and Linear Regression. The retrogradation of the problems can be settled using linear regression whereas the categorization of the issues was carried out by the Logistic regressions is written as:

Sigmoid Function $\emptyset(z)=\frac{1}{1+e^{-z}}$   (9)

where, z = b₀ + b₁ * age + b₂ * systolicBP + b₃ * diastolicBP + …… + b₉ * cholesterol.

3.1.4 K-Means

Combining the group of unlabeled datasets into various forms, that binds the datasets into a collection that comes under an unsupervised learning algorithm that configures in K-Means grouping. In this research work, the variable K is represented as the number of existing groups that are required to be initialized in this technology. This required grouping the datasets into various combined variables from among the various groups and in an easy manner without considering the training process by identifying various datasets in the unlabeled classes in an independent way is calculated as:

$\sum_{j=1}^{k} \sum_{i=1}^{n}\left\|X_{i}^{(j)}-\mathrm{Cj}\right\|^{2}$  (10)

where, ‘k’ is number of clusters, ‘n’ is number of patients and ‘c_j’ defines risk factor can be low, medium, moderate, and risk.

3.1.5 Support vector machine

The main aim of this model is to develop the exact linear way or deterministic partition which separates n-proportional space into groups such that providing easy access of combining the data which is newly formed into their respective modules for further references. This type of sorting the data by an exact linear way can also be referred to as hyperplane.

Since considering these outermost vector points that are supportive in building the hyperplane are termed as support points and so the algorithm is named as Support vector algorithm. With the help of the demo graphs that are categorized into two variant ways which are divided considering the deterministic partition or a hyperplane.

The linear SVM is required in linearly differentiating the information/data, that represents dividing the dataset into two different classes by a unique linear separation. Data is termed to as the linear differential and the classifier is written as:

Class 1 (Low risk) $=(\mathrm{W} * \mathrm{X}+\mathrm{b}) \geq 1, \forall \mathrm{X}$   (11)

Class 2 (High risk) $=(\mathrm{W} * \mathrm{X}+\mathrm{b}) \leq-1, \forall \mathrm{X}$   (12)

where, ‘W’ is a vector to Hyper plane, ‘b’ is a bias and ‘x’ is a matrix from dataset.

The non-linear term itself referred to as the in deterministic data division, that represents a dataset that cannot be divided by the shortest route, that particular information is referred to as non-linear data and hence the classifier is written as:

$K(X, Y)=(1+X * Y)^{d}$   (13)

where, ‘X’ is data of low risk, ‘Y’ data of high risk and ‘d’ is degree of the polynomial.

The RBF kernel represents a consequence that gives points relies upon the measured interval from the initial origination or from any particular point is written as:

$K\left(X, X^{1}\right)=\exp \left(-\frac{\left\|X-X^{1}\right\|^{2}}{2 \sigma^{2}}\right)$  (14)

where, || X-X¹|| defines the distances between the two risk vectors and let $\gamma=\frac{1}{2 \sigma^{2}}$

$K\left(X, X^{I}\right)=\exp \left(-\gamma\left\|X-X^{1}\right\|^{2}\right)$   (15)

3.1.6 Decision tree

The decision tree consists of two apexes, those are Decision apex and the leaflet apex. Among these, the Decision apex shows the features of the number of limbs attached to it and are required in making decisions, on the other hand, the leaflet apexes represent the outcomes of these decision limbs and they do not have any limbs attached to them. The selection or implementation depends upon the type of dataset that is provided. Depending upon the required scenarios these are represented in the form of a graph by drawing all the possible outcomes based on the selection/complication. Since it starts with the source apex and diverges in various directions by developing a structure of the tree is calculated as:

Gini Index $(\mathrm{G})=\sum_{i=1}^{c} P_{\mathrm{i}}\left(1-P_{\mathrm{i}}\right)$   (16)

where, ‘c’ is number of classes, ‘p_i’ defines the probability of class ‘i’, and ‘G’ becomes the root node which having more value.

3.1.7 Random forest

Random forest is based on the theory of ensemble learning. It is a procedure that indulges various classifiers in resolving compounded drawbacks by enhancing the execution of this technology. Considering the average in enhancing in identifying the speed of the particular dataset by the random forest which consisting of multiple decision trees relying on different subset among the given dataset. Alternately rather than depending on a single decision tree, the random forest concludes every single tree and on the maximum identifications by finally displaying the identified outcome. The importance of each feature of a decision tree can be calculated as follows:

$f i_{i}=\frac{\sum_{{ j: node\,j\, splits\, on\,feature\, i }}^{n i_{j}}}{\sum_{k \in {all\, nodes }}^{ n i_{k}}}$                                            (17)

where, ‘fi_i’ defines the ‘i^th’ feature importance, ‘ni_j’ defines the importance of node ‘j’.

Algorithm 1: Random forest

Step 1: Apply bootstrapping procedure for creating subsets of data.

Step 2: Create decision tree for each subset generated at step 1.

Step 3: Test data given to each decision tree and decision trees produces values.

Step 4: The majority value associated to decision tree can be considered for final prediction.

3.1.8 Adaptive Boosting (AdaBoost)

Boosting is the technique of combining all the weak classifiers under single strong classifiers. During the instruction period, it produces n number of multiple decision trees. Once the final decision tree is formed the data record that has found incorrectly when first identified is considered to be the major priority. Based on this the output of these is gathered and sent for the next further decision model. This process iterates and repeats itself until we attain the required base learners recommended to create at the initial stage.

Algorithm 2: AdaBoost

Step 1: Initialize the weights for all training points by using:

W = $\frac{1}{N}$    (18)

Step 2: Calculate error rate for each “weak classifier” by using:

$\epsilon=\sum_{w e a k} w_{i}$   (19)

Step 3: Select the lowest error rate classifier.

Step 4: Find the $\alpha$ for the classifier by using:

$\alpha=\frac{1}{2} \log \frac{1-\epsilon}{\epsilon}$  (20)

Step 5: Check if the classifier is good or not by using:

$f\left(x_{i}\right)=\sum_{t=1}^{T} \alpha_{t} h_{t}\left(x_{i}\right)$   (21)

Step 6: Update weights of each classifier based on the previous classifiers.

Step 7: Go to step-2 to step-6 for number of iterations ‘T’.

3.1.9 Cross validation

Cross-validation is a technique, where the data is divided into ‘n’ variables depending upon the subsets. Once these variables are attained, the training process is initiated on all the ‘k’ folds except the last variable ‘k-1’ which is sent for the testing process.

3.2 Proposed improved random forest

The improvised random forest model predicts the stroke severity by using three hierarchical modules. The module-1 predicts the risk level of intracerebral and subarachnoid hemorrhagic based on the presence of ischemic stroke. Module-2 predicts the risk level of ischemic and subarachnoid hemorrhagic based on the presence of intracerebral hemorrhagic. Module-3 predicts the risk level of ischemic and intracerebral hemorrhagic based on the presence of subarachnoid hemorrhagic.

Adding to the high accuracy of the improvised random forest model, we have also developed a User Interface (UI) to take in data from the user. The UI ensures better understanding about the details the user needs to give and it also adds a pluggable look and feel to the whole process.

Additionally, our proposed model also has an exponentially better accuracy for predicting the occurrence of brain strokes given the age, Systolic BP, Diastolic BP, BMI, Glucose levels, Cholesterol and any existing smoking habits. We have spiked the accuracy of the system, by using multiple base estimators in the random forest algorithm unlike the single base estimators which are generally used. In addition to the multiple base estimators, we have also used cross folding to explore and find out the best features in the given dataset.

3.3 Proposed model architecture

The proposed model predicts the stroke severity in three different level factors such as low risk, moderate risk, and high risk based on the primary attributes followed by classification technique.

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Figure 3. Model architecture

Figure 3 shows the proposed model can extract the features based on NIHSS for data gathering processes. After data gathering, the machine learning model works depending on the training data (80%) and testing data (20%). Both the training data and the test data are sent as inputs into the Random Forest algorithm which has the base classifiers namely base decision tree, base logistic regression and base SVM. The risk factor is thereby generated from the above model architecture. The detailed work flow of the proposed architecture is demonstrated in the following steps:

Step 1: Data Collection and pre-processing is explained in Figure 4(a).

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Figure 4(a). Feature extraction based on stroke scale

Step 2: Risk Formation is explained in Figure 4(b).

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Figure 4(b). Risk formation based on best accuracy model

Step 3: Risk identification with different levels of stroke is represented in Figure 4(c).

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Figure 4(c). Stroke level prediction

3.4 Proposed improvised random forest algorithm

Algorithm 3: Stroke Prediction (SPN)

Step 1: If the model trained is ‘False’ then load the trained data and start training the model

Step 2: From the user data initialize the required data for the prediction.

Step 3: Assign ‘Y’ with a return value of the predicted object.

Step 4: if Y = = 0 then return “Low Risk”

          else if Y = = 1 then return “Moderate Risk”

          else if Y = = 2 then return “High Risk”

          else return “Severe Risk”

Algorithm 4: Model Training

Step 1: Load the trained data.

Step 2: From the user data initialize the trained model object.

Step 3: Return the model object.

Algorithm 5: Stroke predictor (SPR)

Step 1: Load the required new data.

Step 2: Process the new record with the existing model object

Step 3: From the new record, initialize the predicted object.

Step 4: Return the model object with predicted stroke levels.

3.5 Dataset

The data set used in this research work includes a total of 4,799 subjects which contains 3,123 males and 1,676 females and the summary of primary attributes are available in the data set shown in Table 1 [23]. As a part of data pre-processing, from the above available dataset, we have excluded the ‘Gender’ attribute in this research work.

Table 1. Summary of dataset

3.6 Performance evaluation metrics

In the process of testing the Area Under Curve (AUC) and Receiver Operating Characteristics (ROC) is one of the standardized ways. It deals with the probability among the classifier of randomly picked positive sample to that of the randomly picked negative sample.

Accuracy (ACC) is evaluated to the number of all exact identifications separated to that of the sum of a number of the dataset.

Accuracy = $\frac{\text { True Positive }+\text { True } \text { Negative }}{\text { True Positive }+\text { True } \text { Negative }+\text { False Negative }+\text { False Positive }}$

The Sensitivity is evaluated to the number of identifications of correct positive divisions to that of the total positives number.

Sensitivity =$\frac{\text { True Positives }}{\text { True Positives + False Negative }}$

The Specificity is determined by the total amount of correct negative identifications separated by the total negative numbers.

Specificity =$\frac{\text { True Negative }}{\text { True Negative + False Positives }}$

The False Positive Rate is determined by the FP / (FP+TN) evaluation. It is determined to the ratio of negative points that are wrongly taken as positive when compared to that of all the negative points of the data.

False Positive Rate =$\frac{\text { False Positive }}{\text { True } \text { Negative }+\text { False Positive }}$

F1-Score determines how specific the classifier is and also how rigid it can be. The proportion of high precision and low recall draws out the most accurate possibilities, but it omits various examples that become complex while dividing. The mathematical expression is given by:

F1- Score = 2 $* \frac{1}{\frac{1}{\text { precision }}+\frac{1}{\text { recall }}}$

The Precision gives multiple positive outcomes when distinguished by a number of positive results identified by the classifiers.

Precision $=\frac{\text { True Positives }}{\text { True Positives + False Positives }}$

An improvised Random Forest ensemble technique with a stroke prediction algorithm is implemented in this research work to identify the risk factor. An accuracy of 96.97% is achieved through the stroke predictor (SPR) model with an error rate of 0.03%. Using an improvised Random Forest model, we obtained efficient results with improved prediction accuracy. As future research, we can derive methods for different types of strokes along with risk levels using an image data set.