Titanic survivors prediction with Machine Learning algorithms

This code is meant to predict the survivors of the Titanic tragedy in 1912 based on passenger data available on Kaggle

Loading Libraries required

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
sns.set()

Loading Datasets

titanic_train = pd.read_csv('train_data.csv')
titanic_test = pd.read_csv('test_data.csv')

Training dataset

titanic_train.head(10)

titanic_train.shape #Total rows and columns in Training dataset

We can see that there are 891 rows and 12 columns in our training dataset.

Describing training dataset

titanic_test.describe()

describe(include = ['O'])* will show the descriptive statistics of object data types.

titanic_train.describe(include=['O'])

We use info() method to see more information of our train dataset.

titanic_train.info()

We can see that Age value is missing for many rows. Out of 891 rows, the Age value is present only in 714 rows. Similarly, Cabin values are also missing in many rows. Only 204 out of 891 rows have Cabin values.

titanic_train.isnull().sum()

There are 177 rows with missing Age, 687 rows with missing Cabin and 2 rows with missing Embarked information.

Looking into the testing dataset

titanic_test.shape

Survived column is not present in Test data. We have to train our classifier using the Train data and generate predictions (Survived) on Test data.

titanic_test.head()

titanic_test.info()

There are missing entries for Age in Test dataset as well.

Out of 418 rows in Test dataset, only 332 rows have Age value. Cabin values are also missing in many rows. Only 91 rows out ot 418 have values for Cabin column.

titanic_test.isnull().sum()

There are 86 rows with missing Age, 327 rows with missing Cabin and 1 row with missing Fare information.

Relationship between Features and Survival

In this section, we analyze relationship between different features with respect to Survival. We see how different feature values show different survival chance. We also plot different kinds of diagrams to visualize our data and findings.

survived = titanic_train[titanic_train['Survived'] == 1]
not_survived = titanic_train[titanic_train['Survived'] == 0]

print ("Survived: %i (%.1f%%)"%(len(survived), float(len(survived))/len(titanic_train)*100.0))

print ("Not Survived: %i (%.1f%%)"%(len(not_survived), float(len(not_survived))/len(titanic_train)*100.0))
print ("Total: %i"%len(titanic_train))

Pclass vs. Survival

Higher class passengers have better survival chance.

titanic_train.Pclass.value_counts()
titanic_train.groupby('Pclass').Survived.value_counts()

sns.barplot(x='Pclass', y='Survived', data=titanic_train)

Sex vs. Survival

Females have better survival chance.

titanic_train.groupby('Sex').Survived.value_counts()

Sex     Survived
female  1           233
        0            81
male    0           468
        1           109
Name: Survived, dtype: int64

titanic_train[['Sex', 'Survived']].groupby(['Sex'], as_index=False).mean()


Sex	Survived

0	female	0.7420381	
1   male	0.188908

sns.barplot(x='Sex', y='Survived', data=titanic_train)

Pclass & Sex vs. Survival

Below, we just find out how many males and females are there in each Pclass. We then plot a stacked bar diagram with that information. We found that there are more males among the 3rd Pclass passengers.

tab = pd.crosstab(titanic_train['Pclass'], titanic_train['Sex'])
print (tab)


tab.div(tab.sum(1).astype(float), axis=0).plot(kind="bar", stacked=True)
plt.xlabel('Pclass')
plt.ylabel('Percentage')

Pclass, Sex & Embarked vs. Survival

sns.factorplot(x='Pclass', y='Survived', hue='Sex', col='Embarked', data=titanic_train)

From the above plot, it can be seen that:

• Almost all females from Pclass 1 and 2 survived.
• Females dying were mostly from 3rd Pclass.
• Males from Pclass 1 only have slightly higher survival chance than Pclass 2 and 3.

Embarked vs. Survived

titanic_train[['Embarked', 'Survived']].groupby(['Embarked'], as_index=False).mean()

sns.barplot(x='Embarked', y='Survived', data=titanic_train)

Parch vs. Survival

titanic_train[['Parch', 'Survived']].groupby(['Parch'], as_index=False).mean()

sns.barplot(x='Parch', y='Survived', ci=None, data=titanic_train) # ci=None will hide the error bar

Age vs. Survival

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(131)
ax2 = fig.add_subplot(132)
ax3 = fig.add_subplot(133)

sns.violinplot(x="Embarked", y="Age", hue="Survived", data=titanic_train, split=True, ax=ax1)
sns.violinplot(x="Pclass", y="Age", hue="Survived", data=titanic_train, split=True, ax=ax2)

sns.violinplot(x="Sex", y="Age", hue="Survived", data=titanic_train, split=True, ax=ax3)

From Pclass violinplot, we can see that:

• 1st Pclass has very few children as compared to other two classes.
• 1st Plcass has more old people as compared to other two classes.
• Almost all children (between age 0 to 10) of 2nd Pclass survived.
• Most children of 3rd Pclass survived.
• Younger people of 1st Pclass survived as compared to its older people.

From Sex violinplot, we can see that:

• Most male children (between age 0 to 14) survived.
• Females with age between 18 to 40 have better survival chance.

Correlating Features

Heatmap of Correlation between different features:

Positive numbers = Positive correlation, i.e. increase in one feature will increase the other feature & vice-versa.

Negative numbers = Negative correlation, i.e. increase in one feature will decrease the other feature & vice-versa.

In our case, we focus on which features have strong positive or negative correlation with the Survived feature

plt.figure(figsize=(15,6))

sns.heatmap(titanic_train.drop('PassengerId',axis=1).corr(), vmax=0.6, square=True, annot=True)

Feature Extraction

In this section, we select the appropriate features to train our classifier. Here, we create new features based on existing features. We also convert categorical features into numeric form.

Name Feature

Let's first extract titles from Name column.

titanic_combined_data = [titanic_train, titanic_test] # combining train and test dataset

for dataset in titanic_combined_data:

    dataset['Title'] = dataset.Name.str.extract(' ([A-Za-z]+)\.')

We have added a new column named Title in the Train dataset with the Title present in the particular passenger name. We now replace some less common titles with the name "Other".

for dataset in titanic_combined_data:
    dataset['Title'] = dataset['Title'].replace(['Lady', 'Countess','Capt', 'Col', \
    'Don', 'Dr', 'Major', 'Rev', 'Sir', 'Jonkheer', 'Dona'], 'Other')


    dataset['Title'] = dataset['Title'].replace('Mlle', 'Miss')
    dataset['Title'] = dataset['Title'].replace('Ms', 'Miss')
    dataset['Title'] = dataset['Title'].replace('Mme', 'Mrs')

titanic_train[['Title', 'Survived']].groupby(['Title'], as_index=False).mean()    

After that, we convert the categorical Title values into numeric form.

title_mapping = {"Mr": 1, "Miss": 2, "Mrs": 3, "Master": 4, "Other": 5}

for dataset in titanic_combined_data:
    dataset['Title'] = dataset['Title'].map(title_mapping)
    dataset['Title'] = dataset['Title'].fillna(0)

Sex Feature

We convert the categorical value of Sex into numeric. We represent 0 as female and 1 as male.

for dataset in titanic_combined_data:
    dataset['Sex'] = dataset['Sex'].map( {'female': 1, 'male': 0} ).astype(int)

011380353.1000C123S34503Allen, Mr. William Henry035.0003734508.0500NaNS1

Embarked Feature

There are empty values for some rows for Embarked column. The empty values are represented as "nan" in below list.

titanic_train.Embarked.unique()

array(['S', 'C', 'Q', nan], dtype=object)

Let's check the number of passengers for each Embarked category.

titanic_train.Embarked.value_counts()


S    644
C    168
Q     77
Name: Embarked, dtype: int64

We find that category "S" has maximum passengers. Hence, we replace "nan" values with "S".

for dataset in titanic_combined_data:
    dataset['Embarked'] = dataset['Embarked'].fillna('S')

We now convert the categorical value of Embarked into numeric. We represent 0 as S, 1 as C and 2 as Q.

for dataset in titanic_combined_data:
    #print(dataset.Embarked.unique())
    dataset['Embarked'] = dataset['Embarked'].map( {'S': 0, 'C': 1, 'Q': 2} ).astype(int)

Age Feature

We first fill the NULL values of Age with a random number between (mean_age - std_age) and (mean_age + std_age).

We then create a new column named AgeBand. This categorizes age into 5 different age range.

for dataset in titanic_combined_data:
    age_avg = dataset['Age'].mean()
    age_std = dataset['Age'].std()
    age_null_count = dataset['Age'].isnull().sum()
    
    age_null_random_list = np.random.randint(age_avg - age_std, age_avg + age_std, size=age_null_count)
    dataset['Age'][np.isnan(dataset['Age'])] = age_null_random_list
    dataset['Age'] = dataset['Age'].astype(int)
    
titanic_train['AgeBand'] = pd.cut(titanic_train['Age'], 5)


print (titanic_train[['AgeBand', 'Survived']].groupby(['AgeBand'], as_index=False).mean())



         AgeBand  Survived
0  (-0.08, 16.0]  0.500000
1   (16.0, 32.0]  0.357778
2   (32.0, 48.0]  0.377510
3   (48.0, 64.0]  0.434783
4   (64.0, 80.0]  0.090909

Now, we map Age according to AgeBand.

for dataset in titanic_combined_data:
    dataset.loc[ dataset['Age'] <= 16, 'Age'] = 0
    dataset.loc[(dataset['Age'] > 16) & (dataset['Age'] <= 32), 'Age'] = 1
    dataset.loc[(dataset['Age'] > 32) & (dataset['Age'] <= 48), 'Age'] = 2
    dataset.loc[(dataset['Age'] > 48) & (dataset['Age'] <= 64), 'Age'] = 3
    dataset.loc[ dataset['Age'] > 64, 'Age'] = 4

Fare Feature

Replace missing Fare values with the median of Fare.

for dataset in titanic_combined_data:
    dataset['Fare'] = dataset['Fare'].fillna(titanic_train['Fare'].median())

Create FareBand. We divide the Fare into 4 category range.

titanic_train['FareBand'] = pd.qcut(titanic_train['Fare'], 4)

print (titanic_train[['FareBand', 'Survived']].groupby(['FareBand'], as_index=False).mean())

          FareBand  Survived
0   (-0.001, 7.91]  0.197309
1   (7.91, 14.454]  0.303571
2   (14.454, 31.0]  0.454955
3  (31.0, 512.329]  0.581081

Map Fare according to FareBand

for dataset in titanic_combined_data:
    dataset.loc[ dataset['Fare'] <= 7.91, 'Fare'] = 0
    dataset.loc[(dataset['Fare'] > 7.91) & (dataset['Fare'] <= 14.454), 'Fare'] = 1
      
    dataset.loc[(dataset['Fare'] > 14.454) & (dataset['Fare'] <= 31), 'Fare']   = 2
    dataset.loc[ dataset['Fare'] > 31, 'Fare'] = 3
    dataset['Fare'] = dataset['Fare'].astype(int)

SibSp & Parch Feature

Combining SibSp & Parch feature, we create a new feature named FamilySize.

for dataset in titanic_combined_data:
    dataset['FamilySize'] = dataset['SibSp'] +  dataset['Parch'] + 1

print (titanic_train[['FamilySize', 'Survived']].groupby(['FamilySize'], as_index=False).mean())




   FamilySize  Survived
0           1  0.303538
1           2  0.552795
2           3  0.578431
3           4  0.724138
4           5  0.200000
5           6  0.136364
6           7  0.333333
7           8  0.000000
8          11  0.000000

About data shows that:

• Having FamilySize upto 4 (from 2 to 4) has better survival chance.
• FamilySize = 1, i.e. travelling alone has less survival chance.
• Large FamilySize (size of 5 and above) also have less survival chance.

Let's create a new feature named IsAlone. This feature is used to check how is the survival chance while travelling alone as compared to travelling with family.

for dataset in titanic_combined_data:
    dataset['IsAlone'] = 0
    dataset.loc[dataset['FamilySize'] == 1, 'IsAlone'] = 1
    
print (titanic_train[['IsAlone', 'Survived']].groupby(['IsAlone'], as_index=False).mean())



   IsAlone  Survived
0        0  0.505650
1        1  0.303538

This shows that travelling alone has only 30% survival chance.

Feature Selection

We drop unnecessary columns/features and keep only the useful ones for our experiment. Column PassengerId is only dropped from Train set because we need PassengerId in Test set.

features_drop = ['Name', 'SibSp', 'Parch', 'Ticket', 'Cabin', 'FamilySize']

titanic_train = titanic_train.drop(features_drop, axis=1)

titanic_test = titanic_test.drop(features_drop, axis=1)

titanic_train = titanic_train.drop(['PassengerId', 'AgeBand', 'FareBand'], axis=1)

titanic_train.head()

titanic_test.head()

We are done with Feature Selection/Engineering. Now, we are ready to train a classifier with our feature set.

Classification & Accuracy

Define training and testing set

X_train = titanic_train.drop('Survived', axis=1)
y_train = titanic_train['Survived']

X_test = titanic_test.drop("PassengerId", axis=1).copy()

X_train.shape, y_train.shape, X_test.shape

((891, 7), (891,), (418, 7))

There are many classifying algorithms present. Among them, we choose the following Classification algorithms for our problem:

• Logistic Regression
• Support Vector Machines (SVC)
• Linear SVC
• k-Nearest Neighbor (KNN)
• Decision Tree
• Random Forest
• Naive Bayes (GaussianNB)
• Perceptron
• Stochastic Gradient Descent (SGD)

Here's the training and testing procedure:

First, we train these classifiers with our training data.

After that, using the trained classifier, we predict the Survival outcome of test data.

Finally, we calculate the accuracy score (in percentange) of the trained classifier.

Please note: that the accuracy score is generated based on our training dataset.

# Importing Classifier Modules

from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC, LinearSVC
from sklearn.neighbors import KNeighborsClassifier
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier
from sklearn.naive_bayes import GaussianNB
from sklearn.linear_model import Perceptron
from sklearn.linear_model import SGDClassifier

Logistic Regression

Logistic regression, or logit regression, or logit model is a regression model where the dependent variable (DV) is categorical. This article covers the case of a binary dependent variable—that is, where it can take only two values, "0" and "1", which represent outcomes such as pass/fail, win/lose, alive/dead or healthy/sick.

clf = LogisticRegression()
clf.fit(X_train, y_train)
y_pred_log_reg = clf.predict(X_test)
acc_log_reg = round( clf.score(X_train, y_train) * 100, 2)



print (str(acc_log_reg) + ' percent')

80.13 percent

Support Vector Machine (SVM)

Support Vector Machine (SVM) model is a Supervised Learning model used for classification and regression analysis. It is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall.

In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces. Suppose some given data points each belong to one of two classes, and the goal is to decide which class a new data point will be in. In the case of support vector machines, a data point is viewed as a -dimensional vector (a list of  numbers), and we want to know whether we can separate such points with a -dimensional hyperplane.

When data are not labeled, supervised learning is not possible, and an unsupervised learning approach is required, which attempts to find natural clustering of the data to groups, and then map new data to these formed groups. The clustering algorithm which provides an improvement to the support vector machines is called support vector clustering and is often used in industrial applications either when data are not labeled or when only some data are labeled as a preprocessing for a classification pass.

In the below code, SVC stands for Support Vector Classification.

In [77]:

clf = SVC()
clf.fit(X_train, y_train)
y_pred_svc = clf.predict(X_test)
acc_svc = round(clf.score(X_train, y_train) * 100, 2)


print (acc_svc)
83.39

Linear SVM

Linear SVM is a SVM model

In the below code, LinearSVC stands for Linear Support Vector Classification.

clf = LinearSVC()
clf.fit(X_train, y_train)
y_pred_linear_svc = clf.predict(X_test)
acc_linear_svc = round(clf.score(X_train, y_train) * 100, 2)


print (acc_linear_svc)
79.01

k-Nearest Neighbors

k-nearest neighbors algorithm (k-NN) is one of the simplest machine learning algorithms and is used for classification and regression. In both cases, the input consists of the  closest training examples in the feature space. The output depends on whether -NN is used for classification or regression:

• In -NN classification, the output is a class membership. An object is classified by a majority vote of its neighbors, with the object being assigned to the class most common among its  nearest neighbors ( is a positive integer, typically small). If , then the object is simply assigned to the class of that single nearest neighbor.
• In -NN regression, the output is the property value for the object. This value is the average of the values of its  nearest neighbors.

clf = KNeighborsClassifier(n_neighbors = 3)
clf.fit(X_train, y_train)
y_pred_knn = clf.predict(X_test)
acc_knn = round(clf.score(X_train, y_train) * 100, 2)


print (acc_knn)
84.51

Decision Tree

A decision tree is a flowchart-like structure in which each internal node represents a "test" on an attribute (e.g. whether a coin flip comes up heads or tails), each branch represents the outcome of the test, and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represent classification rules.

clf = DecisionTreeClassifier()
clf.fit(X_train, y_train)
y_pred_decision_tree = clf.predict(X_test)
acc_decision_tree = round(clf.score(X_train, y_train) * 100, 2)


print (acc_decision_tree)
87.32

Random Forest

Random forests or random decision forests are an ensemble learning method for classification, regression and other tasks, that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees. Random decision forests correct for decision trees' habit of overfitting to their training set.

Ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone.

clf = RandomForestClassifier(n_estimators=100)
clf.fit(X_train, y_train)
y_pred_random_forest = clf.predict(X_test)
acc_random_forest = round(clf.score(X_train, y_train) * 100, 2)


print (acc_random_forest)
87.32

Gaussian Naive Bayes

Naive Bayes classifiers are a family of simple probabilistic classifiers based on applying Bayes' theorem with strong (naive) independence assumptions between the features.

Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if cancer is related to age, then, using Bayes' theorem, a person's age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person's age.

Naive Bayes is a simple technique for constructing classifiers: models that assign class labels to problem instances, represented as vectors of feature values, where the class labels are drawn from some finite set. It is not a single algorithm for training such classifiers, but a family of algorithms based on a common principle: all naive Bayes classifiers assume that the value of a particular feature is independent of the value of any other feature, given the class variable. For example, a fruit may be considered to be an apple if it is red, round, and about 10 cm in diameter. A naive Bayes classifier considers each of these features to contribute independently to the probability that this fruit is an apple, regardless of any possible correlations between the color, roundness, and diameter features.

clf = GaussianNB()
clf.fit(X_train, y_train)
y_pred_gnb = clf.predict(X_test)
acc_gnb = round(clf.score(X_train, y_train) * 100, 2)


print (acc_gnb)
77.78

Perceptron

Perceptron is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.

clf = Perceptron(max_iter=5, tol=None)
clf.fit(X_train, y_train)
y_pred_perceptron = clf.predict(X_test)
acc_perceptron = round(clf.score(X_train, y_train) * 100, 2)


print (acc_perceptron)
77.33

Stochastic Gradient Descent (SGD)

Stochastic gradient descent (often shortened in SGD), also known as incremental gradient descent, is a stochastic approximation of the gradient descent optimization method for minimizing an objective function that is written as a sum of differentiable functions. In other words, SGD tries to find minima or maxima by iteration.

clf = SGDClassifier(max_iter=5, tol=None)
clf.fit(X_train, y_train)
y_pred_sgd = clf.predict(X_test)
acc_sgd = round(clf.score(X_train, y_train) * 100, 2)

print (acc_sgd)
76.77

Confusion Matrix

A confusion matrix, also known as an error matrix, is a specific table layout that allows visualization of the performance of an algorithm. Each row of the matrix represents the instances in a predicted class while each column represents the instances in an actual class (or vice versa). The name stems from the fact that it makes it easy to see if the system is confusing two classes (i.e. commonly mislabelling one as another).

In predictive analytics, a table of confusion (sometimes also called a confusion matrix), is a table with two rows and two columns that reports the number of false positives, false negatives, true positives, and true negatives. This allows more detailed analysis than mere proportion of correct classifications (accuracy). Accuracy is not a reliable metric for the real performance of a classifier, because it will yield misleading results if the data set is unbalanced (that is, when the numbers of observations in different classes vary greatly). For example, if there were 95 cats and only 5 dogs in the data set, a particular classifier might classify all the observations as cats. The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate for the cat class but a 0% recognition rate for the dog class.

Here's another guide explaining Confusion Matrix with example.

In our (Titanic problem) case:

True Positive: The classifier predicted Survived and the passenger actually Survived.

True Negative: The classifier predicted Not Survived and the passenger actually Not Survived.

False Postiive: The classifier predicted Survived but the passenger actually Not Survived.

False Negative: The classifier predicted Not Survived but the passenger actually Survived.

In the example code below, we plot a confusion matrix for the prediction of Random Forest Classifier on our training dataset. This shows how many entries are correctly and incorrectly predicted by our classifer.

from sklearn.metrics import confusion_matrix
import itertools

clf = RandomForestClassifier(n_estimators=100)
clf.fit(X_train, y_train)

y_pred_random_forest_training_set = clf.predict(X_train)
acc_random_forest = round(clf.score(X_train, y_train) * 100, 2)


print ("Accuracy: %i %% \n"%acc_random_forest)

class_names = ['Survived', 'Not Survived']


# Compute confusion matrix
cnf_matrix = confusion_matrix(y_train, y_pred_random_forest_training_set)
np.set_printoptions(precision=2)


print ('Confusion Matrix in Numbers')
print (cnf_matrix)
print ('')

cnf_matrix_percent = cnf_matrix.astype('float') / cnf_matrix.sum(axis=1)[:, np.newaxis]

print ('Confusion Matrix in Percentage')
print (cnf_matrix_percent)
print ('')

true_class_names = ['True Survived', 'True Not Survived']
predicted_class_names = ['Predicted Survived', 'Predicted Not Survived']

df_cnf_matrix = pd.DataFrame(cnf_matrix, 
                             index = true_class_names,
                             columns = predicted_class_names)

df_cnf_matrix_percent = pd.DataFrame(cnf_matrix_percent, 
                                     index = true_class_names,
                                     columns = predicted_class_names)

plt.figure(figsize = (15,5))

plt.subplot(121)
sns.heatmap(df_cnf_matrix, annot=True, fmt='d')

plt.subplot(122)
sns.heatmap(df_cnf_matrix_percent, annot=True)

Comparing Models

Let's compare the accuracy score of all the classifier models used above.

models = pd.DataFrame({
    'Model': ['Logistic Regression', 'Support Vector Machines', 'Linear SVC', 
              'KNN', 'Decision Tree', 'Random Forest', 'Naive Bayes', 
              'Perceptron', 'Stochastic Gradient Decent'],
    
    'Score': [acc_log_reg, acc_svc, acc_linear_svc, 
              acc_knn,  acc_decision_tree, acc_random_forest, acc_gnb, 
              acc_perceptron, acc_sgd]
    })


models.sort_values(by='Score', ascending=False)

From the above table, we can see that Decision Tree and Random Forest classfiers have the highest accuracy score.

Among these two, we choose Random Forest classifier as it has the ability to limit overfitting as compared to Decision Tree classifier.