Parkinson's : Are you shaking?!

Parkinson's disease, or simply Parkinson's, is a long-term degenerative disorder of the central nervous system that mainly affects the motor system. As the disease worsens, non-motor symptoms become more common. The symptoms usually emerge slowly.

Early in the disease, the most obvious symptoms are shaking, rigidity, slowness of movement, and difficulty with walking.Thinking and behavioral problems may also occur.

Dementia becomes common in the advanced stages of the disease.Depression and anxiety are also common, occurring in more than a third of people with PD.

Other symptoms include sensory, sleep, and emotional problems. The main motor symptoms are collectively called "parkinsonism", or a "parkinsonian syndrome".

The cause of Parkinson's disease is unknown, but is believed to involve both genetic and environmental factors. Those with a family member affected are more likely to get the disease themselves.There is also an increased risk in people exposed to certain pesticides and among those who have had prior head injuries, while there is a reduced risk in tobacco smokers and those who drink coffee or tea.

The motor symptoms of the disease result from the death of cells in the substantia nigra, a region of the midbrain. This results in not enough dopamine in this region of the brain.The cause of this cell death is poorly understood, but it involves the build-up of proteins into Lewy bodies in the neurons. Diagnosis of typical cases is mainly based on symptoms, with tests such as neuroimaging used to rule out other diseases.

There is no cure for Parkinson's disease

After importing, cleaning, and merging data files -using pandas library- we started calculating some statistical inference to explore the data and its relationships.

Firstly, exploring the correlation between the data columns.We used the '.corr()' function using spearman correlation in the pandas library to explore that.

ax = sns.heatmap(df.corr(method='spearman'))
 plt.title('Correlation between features Using Spearman Method');

Where 'df' is the cleaned DataFrame.

General Observations:

Correlation rasied a few questions to explore during analysis.

Correlation diagram suggests thet PPE and MDVP:Fo and HNR are the most contributing features to status with either negative or positive correlation value.

Exploring PPE feature

PPE_1 = df[df.status == 1]['PPE']
 PPE_0 = df[df.status == 0]['PPE']
 
 ecdf_plot(PPE_0,PPE_1,'PPE for Negative Patients','PPE for Positive Patients')

 Observations:

Exploring MDVP:Fo feature

MDVP1 = df[df.status == 1]['MDVP:Fo(Hz)']
 MDVP0 = df[df.status == 0]['MDVP:Fo(Hz)']
 
 ecdf_plot(MDVP0,MDVP1,'MDVP:Fo(Hz) for Negative Patients','MDVP:Fo(Hz) for Positive Patients')

 Observations:

Exploring HNR feature

HNR1 = df[df.status == 1]['HNR']
 HNR0 = df[df.status == 0]['HNR']
 
 ecdf_plot(HNR0,HNR1,'HNR for Negative Patients','HNR for Positive Patients')

Observations:

Plotting a scatter plot matrix between all features to visually distinct which features could produce the most clear differentiable statuses.

Also taking into account correlation matrix as deduced above and their EDA.

Deduced from the above figure that MDVP:Fo(HZ) has the most differentiable measurement more over when correlated with HNR and PPE results are very interesting.

MDVP :Fo(Hz) Vs HNR

px.scatter(df, x ='HNR',y = 'MDVP:Fo(Hz)', color = 'status', title = 'Relationship between MDVP:Fo & HNR wrt Status')

Observations:¶

MDVP :Fo(Hz) Vs PPE

px.scatter(df, x ='PPE',y = 'MDVP:Fo(Hz)', color = 'status', title = 'Relationship between MDVP:Fo & PPE wrt Status')

Observations:

from sklearn.model_selection import train_test_split
 from sklearn import preprocessing
 from sklearn.preprocessing import MinMaxScaler
 from sklearn.model_selection import cross_val_score
 from sklearn.linear_model import LogisticRegression
 from sklearn.svm import SVC
 from sklearn.tree import DecisionTreeClassifier
 from sklearn.ensemble import RandomForestClassifier
 from sklearn.ensemble import AdaBoostClassifier
 from sklearn.model_selection import StratifiedKFold
 from sklearn.metrics import confusion_matrix, accuracy_score, recall_score, roc_curve, auc
 import xgboost as xgb

Preprocessing Data

Defining Target for the model and features

Y = df['status'].values # Target for the model
 X = df[['MDVP:Fo(Hz)', 'MDVP:Fhi(Hz)', 'MDVP:Flo(Hz)', 'MDVP:Jitter(%)','MDVP:Jitter(Abs)', 'MDVP:RAP', 'MDVP:PPQ', 'Jitter:DDP','MDVP:Shimmer', 'MDVP:Shimmer(dB)', 'Shimmer:APQ3', 'Shimmer:APQ5','MDVP:APQ', 'Shimmer:DDA', 'NHR', 'HNR', 'RPDE', 'DFA','spread1', 'spread2', 'D2', 'PPE']]

Spliting data to test and train sets

# Spliting data to test and train sets
 X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.25 ,random_state=42)

Normalizing Data using MinMaxScaler

scaler = MinMaxScaler().fit(X_train)
 
 X_train_scaled = scaler.transform(X_train)
 X_test_scaled = scaler.transform(X_test)

Defining list to store Performance Metrics

performance = [] # list to store all performance metric

Logistic Regression Model

Logistic Regression (aka logit, MaxEnt) classifier.

In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross-entropy loss if the ‘multi_class’ option is set to ‘multinomial’. (Currently the ‘multinomial’ option is supported only by the ‘lbfgs’, ‘sag’, ‘saga’ and ‘newton-cg’ solvers.)

This class implements regularized logistic regression using the ‘liblinear’ library, ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers. Note that regularization is applied by default. It can handle both dense and sparse input.

Model Implementation:

lr_best_score = 0
 lr_kfolds = 5 # set the number of folds
 
 
 # Finding the Best lr Model
 for c in [0.001, 0.1, 1, 4, 10, 100]:
  logRegModel = LogisticRegression(C=c)
 
  # perform cross-validation
  scores = cross_val_score(logRegModel, X_train, Y_train, cv = lr_kfolds, scoring = 'accuracy') # Get recall for each parameter setting
 
  # compute mean cross-validation accuracy
  score = np.mean(scores)
 
  # Find the best parameters and score
  if score > lr_best_score:
  lr_best_score = score
  lr_best_parameters = c
 
 # rebuild a model on the combined training and validation set
 SelectedLogRegModel = LogisticRegression(C = lr_best_parameters).fit(X_train_scaled, Y_train)
 
 # Model Test
 lr_test_score = SelectedLogRegModel.score(X_test_scaled, Y_test)
 
 # Predicted Output of Model
 PredictedOutput = SelectedLogRegModel.predict(X_test_scaled)
 
 # Extracting sensitivity & specificity from ROC curve to measure Performance of the model
 lr_fpr, lr_tpr, lr_thresholds = roc_curve(Y_test, PredictedOutput, pos_label=1)
 
 # Using AUC of ROC to validate models based on a single score
 lr_test_auc = auc(lr_fpr, lr_tpr)
 
 
 # Output Printing Scores
 print("Best accuracy on validation set is:", lr_best_score)
 
 print("Best parameter for regularization (C) is: ", lr_best_parameters)
 
 print("Test accuracy with best C parameter is", lr_test_score)
 print("Test AUC with the best C parameter is", lr_test_auc)
 
 # Appending results to performance list
 m = 'Logistic Regression'
 performance.append([m, lr_test_score, lr_test_auc, lr_fpr, lr_tpr, lr_thresholds])

Best accuracy on validation set is: 0.8427586206896553

Best parameter for regularization (C) is: 4

Test accuracy with best C parameter is 0.8979591836734694

Test AUC with the best C parameter is 0.7727272727272727

SVM Model

C-Support Vector Classification.

The implementation is based on libsvm. The fit time scales at least quadratically with the number of samples and may be impractical beyond tens of thousands of samples.

Model Implementation:

svm_best_score = 0
 svm_kfolds = 5
 
 
 for c_paramter in [0.001, 0.01, 0.1,6, 10, 100, 1000]: #iterate over the values we need to try for the parameter C
  for gamma_paramter in [0.001, 0.01, 0.1,5, 10, 100, 1000]: #iterate over the values we need to try for the parameter gamma
  for k_parameter in ['rbf', 'linear', 'poly', 'sigmoid']: # iterate over the values we need to try for the kernel parameter
 
  svmModel = SVC(kernel=k_parameter, C=c_paramter, gamma=gamma_paramter) #define the model
  # perform cross-validation
 
  scores = cross_val_score(svmModel, X_train_scaled, Y_train, cv = svm_kfolds, scoring='accuracy')
  # the training set will be split internally into training and cross validation
 
  # compute mean cross-validation accuracy
  score = np.mean(scores)
 
  # if we got a better score, store the score and parameters
  if score > svm_best_score:
  svm_best_score = score #store the score
  svm_best_parameter_c = c_paramter #store the parameter c
  svm_best_parameter_gamma = gamma_paramter #store the parameter gamma
  svm_best_parameter_k = k_parameter
 
 
 # rebuild a model with best parameters to get score
 SelectedSVMmodel = SVC(C = svm_best_parameter_c, gamma = svm_best_parameter_gamma, kernel = svm_best_parameter_k).fit(X_train_scaled, Y_train)
 
 # Model Test
 svm_test_score = SelectedSVMmodel.score(X_test_scaled, Y_test)
 
 # Predicted Output of Model
 PredictedOutput = SelectedSVMmodel.predict(X_test_scaled)
 
 # Extracting sensitivity & specificity from ROC curve to measure Performance of the model
 svm_fpr, svm_tpr, svm_thresholds = roc_curve(Y_test, PredictedOutput, pos_label=1)
 
 # Using AUC of ROC to validate models based on a single score
 svm_test_auc = auc(svm_fpr, svm_tpr)
 
 
 # Output Printing Scores
 print("Best accuracy on cross validation set is:", svm_best_score)
 
 print("Best parameter for c is: ", svm_best_parameter_c)
 print("Best parameter for gamma is: ", svm_best_parameter_gamma)
 print("Best parameter for kernel is: ", svm_best_parameter_k)
 
 print("Test accuracy with the best parameters is", svm_test_score)
 print("Test AUC with the best parameter is", svm_test_auc)
 
 
 
 # Appending results to performance list
 m = 'SVM'
 performance.append([m, svm_test_score, svm_test_auc, svm_fpr, svm_tpr, svm_thresholds])

Best accuracy on cross validation set is: 0.9448275862068967

Best parameter for c is: 6

Best parameter for gamma is: 5

Best parameter for kernel is: rbf

Test accuracy with the best parameters is 0.9387755102040817

Test AUC with the best parameter is 0.8636363636363636

DecisionTreeClassifier Model

Model Implementation:

dt_best_score = 0
 dt_kfolds = 10
 
 
 for md in range(1, 9): # iterate different maximum depth values
  # train the model
  treeModel = DecisionTreeClassifier(random_state=0, max_depth=md, criterion='gini')
 
  # perform cross-validation
  scores = cross_val_score(treeModel, X_train_scaled, Y_train, cv = dt_kfolds, scoring='accuracy')
 
  # compute mean cross-validation accuracy
  score = np.mean(scores)
 
  # if we got a better score, store the score and parameters
  if score > dt_best_score:
  dt_best_score = score
  dt_best_parameter = md
 
 
 # Rebuild a model on the combined training and validation set
 SelectedDTModel = DecisionTreeClassifier(max_depth = dt_best_parameter).fit(X_train_scaled, Y_train )
 
 # Model Test
 dt_test_score = SelectedDTModel.score(X_test_scaled, Y_test)
 
 # Predicted Output of Model
 PredictedOutput = SelectedDTModel.predict(X_test_scaled)
 
 # Extracting sensitivity & specificity from ROC curve to measure Performance of the model
 dt_fpr, dt_tpr, dt_thresholds = roc_curve(Y_test, PredictedOutput, pos_label=1)
 
 # Using AUC of ROC to validate models based on a single score
 dt_test_auc = auc(dt_fpr, dt_tpr)
 
 
 # Output Printing Scores
 print("Best accuracy on validation set is:", dt_best_score)
 
 print("Best parameter for the maximum depth is: ", dt_best_parameter)
 
 print("Test accuracy with best parameter is ", dt_test_score)
 print("Test AUC with the best parameter is ", dt_test_auc)
 
 
 # Appending results to performance list
 m = 'Decision Tree'
 performance.append([m, dt_test_score, dt_test_auc, dt_fpr, dt_tpr, dt_thresholds])

Best accuracy on validation set is: 0.8642857142857144
 Best parameter for the maximum depth is: 5
 Test accuracy with best parameter is 0.8979591836734694
 Test AUC with the best parameter is 0.8050239234449762

Features Importance

print("Feature importance: ")
 features = np.array([X.columns.values.tolist(), list(SelectedDTModel.feature_importances_)]).T
 
 for i in features:
  print(f'{i[0]} : {i[1]}')

Feature importance:

MDVP:Fo(Hz) : 0.2789793597522502

MDVP:Fhi(Hz) : 0.0

MDVP:Flo(Hz) : 0.0

MDVP:Jitter(%) : 0.0

MDVP:Jitter(Abs) : 0.06478134339071083

MDVP:RAP : 0.07963422307864516

MDVP:PPQ : 0.0

Jitter:DDP : 0.0

MDVP:Shimmer : 0.0

MDVP:Shimmer(dB) : 0.0

Shimmer:APQ3 : 0.0

Shimmer:APQ5 : 0.0

MDVP:APQ : 0.0

Shimmer:DDA : 0.0

NHR : 0.0

HNR : 0.13032482023307707

RPDE : 0.05792214232581203

DFA : 0.0

spread1 : 0.03439127200595089

spread2 : 0.0

D2 : 0.0

PPE : 0.3539668392135539

Random Forest Classifier Model

A random forest is a meta estimator that fits a number of decision tree classifiers on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting. The sub-sample size is controlled with the max_samples parameter if bootstrap=True (default), otherwise the whole dataset is used to build each tree.

Model Implementation:

rf_best_score = 0
 rf_kfolds = 5
 
 
 for M in range(2, 15, 2): # combines M trees
  for d in range(1, 9): # maximum number of features considered at each split
  for m in range(1, 9): # maximum depth of the tree
  # train the model
  # n_jobs(4) is the number of parallel computing
  forestModel = RandomForestClassifier(n_estimators = M, max_features = d, n_jobs = 4,max_depth = m, random_state = 0)
 
  # perform cross-validation
  scores = cross_val_score(forestModel, X_train_scaled, Y_train, cv = rf_kfolds, scoring = 'accuracy')
 
  # compute mean cross-validation accuracy
  score = np.mean(scores)
 
  # if we got a better score, store the score and parameters
  if score > rf_best_score:
  rf_best_score = score
  rf_best_M = M
  rf_best_d = d
  rf_best_m = m
 
 # Rebuild a model on the combined training and validation set
 SelectedRFModel = RandomForestClassifier(n_estimators=rf_best_M, max_features=rf_best_d,max_depth=rf_best_m, random_state=0).fit(X_train_scaled, Y_train )
 
 
 # Model Test
 rf_test_score = SelectedRFModel.score(X_test_scaled, Y_test)
 
 # Predicted Output of Model
 PredictedOutput = SelectedRFModel.predict(X_test_scaled)
 
 # Extracting sensitivity & specificity from ROC curve to measure Performance of the model
 rf_fpr, rf_tpr, rf_thresholds = roc_curve(Y_test, PredictedOutput, pos_label=1)
 
 # Using AUC of ROC to validate models based on a single score
 rf_test_auc = auc(rf_fpr, rf_tpr)
 
 
 # Output Printing Scores
 print("Best accuracy on validation set is:", rf_best_score)
 
 print("Best parameters of M, d, m are: ", rf_best_M, rf_best_d, rf_best_m)
 
 print("Test accuracy with the best parameters is", rf_test_score)
 print("Test AUC with the best parameters is:", rf_test_auc)
 
 
 
 # Appending results to performance list
 m = 'Random Forest'
 performance.append([m, rf_test_score, rf_test_auc, rf_fpr, rf_tpr, rf_thresholds])

Best accuracy on validation set is: 0.9317241379310346
 Best parameters of M, d, m are: 10, 7, 7
 Test accuracy with the best parameters is 0.8775510204081632
 Test AUC with the best parameters is: 0.7918660287081339

AdaBoost Classifier Model

An AdaBoost classifier is a meta-estimator that begins by fitting a classifier on the original dataset and then fits additional copies of the classifier on the same dataset but where the weights of incorrectly classified instances are adjusted such that subsequent classifiers focus more on difficult cases.

This class implements the algorithm known as AdaBoost-SAMME .

Model Implementation:

ada_best_score = 0
 ada_kfolds = 5
 
 
 for M in range(2, 15, 2): # combines M trees
  for lr in [0.0001, 0.001, 0.01, 0.1, 1,2,3]:
  # train the model
  boostModel = AdaBoostClassifier(n_estimators=M, learning_rate=lr, random_state=0)
 
  # perform cross-validation
  scores = cross_val_score(boostModel, X_train_scaled, Y_train, cv = ada_kfolds, scoring = 'accuracy')
 
  # compute mean cross-validation accuracy
  score = np.mean(scores)
 
  # if we got a better score, store the score and parameters
  if score > ada_best_score:
  ada_best_score = score
  ada_best_M = M
  ada_best_lr = lr
 
 # Rebuild a model on the combined training and validation set
 SelectedBoostModel = AdaBoostClassifier(n_estimators=ada_best_M, learning_rate=ada_best_lr, random_state=0).fit(X_train_scaled, Y_train )
 
 
 
 
 # Model Test
 ada_test_score = SelectedRFModel.score(X_test_scaled, Y_test)
 
 # Predicted Output of Model
 PredictedOutput = SelectedBoostModel.predict(X_test_scaled)
 
 # Extracting sensitivity & specificity from ROC curve to measure Performance of the model
 ada_fpr, ada_tpr, ada_thresholds = roc_curve(Y_test, PredictedOutput, pos_label=1)
 
 # Using AUC of ROC to validate models based on a single score
 ada_test_auc = auc(ada_fpr, ada_tpr)
 
 
 # Output Printing Scores
 print("Best accuracy on validation set is:", ada_best_score)
 
 print("Best parameter of M is: ", ada_best_M)
 print("best parameter of LR is: ", ada_best_lr)
 
 print("Test accuracy with the best parameter is", ada_test_score)
 print("Test AUC with the best parameters is:", ada_test_auc)
 
 
 # Appending results to performance list
 m = 'AdaBoost'
 performance.append([m, ada_test_score, ada_test_auc, ada_fpr, ada_tpr, ada_thresholds])

Best accuracy on validation set is: 0.9039080459770116
 Best parameter of M is: 10
 best parameter of LR is: 1
 Test accuracy with the best parameter is 0.8775510204081632
 Test AUC with the best parameters is: 0.7595693779904306

XGBoost Classifier Model

XGBoost is an optimized distributed gradient boosting library designed to be highly efficient, flexible and portable. It implements machine learning algorithms under the Gradient Boosting framework. XGBoost provides a parallel tree boosting (also known as GBDT, GBM) that solve many data science problems in a fast and accurate way. The same code runs on major distributed environment (Hadoop, SGE, MPI) and can solve problems beyond billions of examples.

Model Implementation:

xgb_best_score = 0
 xgb_kfolds = 5
 
 for n in [2,4,6,8,10]: #iterate over the values we need to try for the parameter n_estimators
  for lr in [1.1,1.2,1.22,1.23,1.3]: #iterate over the values we need to try for the learning rate parameter
  for depth in [2,4,6,8,10]: # iterate over the values we need to try for the depth parameter
  XGB = xgb.XGBClassifier(objective = 'binary:logistic', max_depth=depth, n_estimators=n, learning_rate = lr) #define the model
 
  # perform cross-validation
  scores = cross_val_score(XGB, X_train_scaled, Y_train, cv = xgb_kfolds, scoring='accuracy')
  # the training set will be split internally into training and cross validation
 
  # compute mean cross-validation accuracy
  score = np.mean(scores)
 
  # if we got a better score, store the score and parameters
  if score > xgb_best_score:
  xgb_best_score = score #store the score
  xgb_best_md = depth #store the parameter maximum depth
  xgb_best_ne = n #store the parameter n_estimators
  xgb_best_lr = lr #store the parameter learning rate
 
 
 # rebuild a model with best parameters to get score
 XGB_selected = xgb.XGBClassifier(objective = 'binary:logistic',max_depth=xgb_best_md, n_estimators=xgb_best_ne, learning_rate = xgb_best_lr).fit(X_train_scaled, Y_train)
 
 
 # Model Test
 xgb_test_score = XGB_selected.score(X_test_scaled, Y_test)
 
 # Predicted Output of Model
 PredictedOutput = XGB_selected.predict(X_test_scaled)
 
 # Extracting sensitivity & specificity from ROC curve to measure Performance of the model
 xgb_fpr, xgb_tpr, xgb_thresholds = roc_curve(Y_test, PredictedOutput, pos_label=1)
 
 # Using AUC of ROC to validate models based on a single score
 xgb_test_auc = auc(xgb_fpr, xgb_tpr)
 
 
 
 # Output Printing Scores
 print("Best accuracy on cross validation set is:", xgb_best_score)
 
 print("Best parameter for maximum depth is: ", xgb_best_md)
 print("Best parameter for n_estimators is: ", xgb_best_ne)
 print("Best parameter for learning rate is: ", xgb_best_lr)
 
 print("Test accuracy with the best parameters is", xgb_test_score)
 print("Test AUC with the best parameters is:", xgb_test_auc)
 
 
 # Appending results to performance list
 m = 'XGB'
 performance.append([m, xgb_test_score, xgb_test_auc, xgb_fpr, xgb_tpr, xgb_thresholds])

Best accuracy on cross validation set is: 0.93816091954023
 Best parameter for maximum depth is: 2
 Best parameter for n_estimators is: 10
 Best parameter for learning rate is: 1.2
 Test accuracy with the best parameters is 0.8979591836734694
 Test AUC with the best parameters is: 0.8050239234449762

Ensemble Voting Classifier Model

Model Implementation:

from sklearn.ensemble import VotingClassifier
 
 # Logistic regression model
 clf1 = LogisticRegression(C=lr_best_parameters).fit(X_train_scaled, Y_train)
 
 # SVC Model
 clf2 = SVC(C=svm_best_parameter_c, gamma=svm_best_parameter_gamma, kernel=svm_best_parameter_k,probability=True)
 
 # DecisionTreeClassifier model
 clf3 = DecisionTreeClassifier(max_depth=dt_best_parameter)
 
 # Random Forest Classifier Model
 clf4 = RandomForestClassifier(n_estimators=rf_best_M, max_features=rf_best_d,max_depth=rf_best_m, random_state=42)
 
 # AdaBoostClassifier Model
 clf5 = AdaBoostClassifier(n_estimators=ada_best_M, learning_rate=ada_best_lr, random_state=42)
 
 # XGBoost Classifier Model
 clf6 = xgb.XGBClassifier(objective = 'binary:logistic',max_depth=xgb_best_md, n_estimators=xgb_best_ne ,learning_rate = xgb_best_lr)
 
 
 
 # Defining VotingClassifier
 eclf1 = VotingClassifier(estimators=[ ('LogisticRegression', clf1), ('SVC', clf2),('DecisionTree',clf3),('Random Forest', clf4),('ADABoost',clf5),('XGBoost',clf6)], voting='hard')
 
 
 # Fitting VotingClassifier
 eclf1 = eclf1.fit(X_train_scaled, Y_train)
 
 
 # Model Test
 eclf_test_score = eclf1.score(X_test_scaled, Y_test)
 
 # Predicted Output of Model
 PredictedOutput = eclf1.predict(X_test_scaled)
 
 # Extracting sensitivity & specificity from ROC curve to measure Performance of the model
 eclf_fpr, eclf_tpr, eclf_thresholds = roc_curve(Y_test, PredictedOutput, pos_label=1)
 
 # Using AUC of ROC to validate models based on a single score
 eclf_test_auc = auc(eclf_fpr, eclf_tpr)
 
 
 
 # Output Printing Scores
 print("Test accuracy with the best parameters is", eclf_test_score)
 print("Test AUC with the best parameters is:", eclf_test_auc)
 
 
 # Appending results to performance list
 m = 'ECLF'
 performance.append([m, eclf_test_score, eclf_test_auc, eclf_fpr, eclf_tpr, eclf_thresholds])

Test accuracy with the best parameters is 0.9183673469387755

Test AUC with the best parameters is: 0.8181818181818181

result = pd.DataFrame(performance, columns=['Model', 'Accuracy', 'AUC', 'FPR', 'TPR', 'TH'])
 df = result[['Model', 'Accuracy', 'AUC']]
 results = df.sort_values('Accuracy',ascending = False)
 display(results)

After a lengthy analysis of the mentioned data, and several conclusions from various sections of this project, we could safely assume the following:-

And Finally, Thank you for reading.

Please feel free to check the full analysis here.