Ndèye Gagnessiry Ndiaye and Christin Seifert
This notebook has been adapted from the nice example by Donne Martin http://nbviewer.jupyter.org/github/donnemartin/data-science-ipython-notebooks/blob/master/kaggle/titanic.ipynb. Here we only focus on preprocessing.
This work is licensed under the Apache License 2.0 http://www.apache.org/licenses/LICENSE-2.0
This notebook consists of following parts:
Description, Evaluation, and Data Set taken from the competition site.
The sinking of the RMS Titanic is one of the most infamous shipwrecks in history. On April 15, 1912, during her maiden voyage, the Titanic sank after colliding with an iceberg, killing 1502 out of 2224 passengers and crew. This sensational tragedy shocked the international community and led to better safety regulations for ships.
One of the reasons that the shipwreck led to such loss of life was that there were not enough lifeboats for the passengers and crew. Although there was some element of luck involved in surviving the sinking, some groups of people were more likely to survive than others, such as women, children, and the upper-class.
In this challenge, we ask you to complete the analysis of what sorts of people were likely to survive. In particular, we ask you to apply the tools of machine learning to predict which passengers survived the tragedy.
The historical data has been split into two groups, a 'training set' and a 'test set'. For the training set, we provide the outcome ( 'ground truth' ) for each passenger. You will use this set to build your model to generate predictions for the test set. For each passenger in the test set, you must predict whether or not they survived the sinking ( 0 for deceased, 1 for survived ). Your score is the percentage of passengers you correctly predict. The Kaggle leaderboard has a public and private component. 50% of your predictions for the test set have been randomly assigned to the public leaderboard ( the same 50% for all users ). Your score on this public portion is what will appear on the leaderboard. At the end of the contest, we will reveal your score on the private 50% of the data, which will determine the final winner. This method prevents users from 'overfitting' to the leaderboard.
VARIABLE DESCRIPTIONS:
survival Survival
(0 = No; 1 = Yes)
pclass Passenger Class
(1 = 1st; 2 = 2nd; 3 = 3rd)
name Name
sex Sex
age Age
sibsp Number of Siblings/Spouses Aboard
parch Number of Parents/Children Aboard
ticket Ticket Number
fare Passenger Fare
cabin Cabin
embarked Port of Embarkation
(C = Cherbourg; Q = Queenstown; S = Southampton)
SPECIAL NOTES:
Pclass is a proxy for socio-economic status (SES)
1st ~ Upper; 2nd ~ Middle; 3rd ~ Lower
Age is in Years; Fractional if Age less than One (1)
If the Age is Estimated, it is in the form xx.5
With respect to the family relation variables (i.e. sibsp and parch)
some relations were ignored. The following are the definitions used
for sibsp and parch.
Sibling: Brother, Sister, Stepbrother, or Stepsister of Passenger Aboard Titanic
Spouse: Husband or Wife of Passenger Aboard Titanic (Mistresses and Fiances Ignored)
Parent: Mother or Father of Passenger Aboard Titanic
Child: Son, Daughter, Stepson, or Stepdaughter of Passenger Aboard Titanic
Other family relatives excluded from this study include cousins,
nephews/nieces, aunts/uncles, and in-laws. Some children travelled
only with a nanny, therefore parch=0 for them. As well, some
travelled with very close friends or neighbors in a village, however,
the definitions do not support such relations.
In [1]:
import pandas as pd
import numpy as np
import pylab as plt
# Set the global default size of matplotlib figures
plt.rc('figure', figsize=(10, 5))
# Size of matplotlib figures that contain subplots
fizsize_with_subplots = (10, 10)
# Size of matplotlib histogram bins
bin_size = 10
In [2]:
df_train = pd.read_csv('material/Data-Preprocessing-Dataset.csv')
df_train.head()
Out[2]:
In [3]:
df_train.tail()
Out[3]:
View the data types of each column:
In [4]:
df_train.dtypes
Out[4]:
Type 'object' is a string for pandas, which poses problems with machine learning algorithms. If we want to use these as features, we'll need to convert these to number representations.
Get some basic information on the DataFrame
In [5]:
df_train.info()
Age, Cabin, and Embarked are missing values. Cabin has too many missing values, whereas we might be able to infer values for Age and Embarked.
Generate various descriptive statistics on the DataFrame:
In [6]:
df_train.describe()
#df_train.describe(include="all")
Out[6]:
Now that we have a general idea of the data set contents, we can dive deeper into each column. We'll be doing exploratory data analysis and cleaning data to setup 'features' we'll be using in our machine learning algorithms.
Plot a few features to get a better idea of each:
In [7]:
# Set up a grid of plots
fig = plt.figure(figsize=fizsize_with_subplots)
fig_dims = (3, 2)
# Plot death and survival counts
plt.subplot2grid(fig_dims, (0, 0))
df_train['Survived'].value_counts().plot(kind='bar',
title='Death and Survival Counts')
# Plot Pclass counts
plt.subplot2grid(fig_dims, (0, 1))
df_train['Pclass'].value_counts().plot(kind='bar',
title='Passenger Class Counts')
# Plot Sex counts
plt.subplot2grid(fig_dims, (1, 0))
df_train['Sex'].value_counts().plot(kind='bar',
title='Gender Counts')
plt.xticks(rotation=0)
# Plot Embarked counts
plt.subplot2grid(fig_dims, (1, 1))
df_train['Embarked'].value_counts().plot(kind='bar',
title='Ports of Embarkation Counts')
# Plot the Age histogram
plt.subplot2grid(fig_dims, (2, 0))
df_train['Age'].hist()
plt.title('Age Histogram')
plt.show()
Next we'll explore various features to view their impact on survival rates.
From our exploratory data analysis in the previous section, we see there are three passenger classes: First, Second, and Third class. We'll determine which proportion of passengers survived based on their passenger class.
Generate a cross tab of Pclass and Survived:
In [8]:
pclass_xt = pd.crosstab(df_train['Pclass'], df_train['Survived'])
pclass_xt
Out[8]:
Plot the cross tab:
In [9]:
# Normalize the cross tab to sum to 1:
pclass_xt_pct = pclass_xt.div(pclass_xt.sum(1).astype(float), axis=0)
pclass_xt_pct.plot(kind='bar',
stacked=True,
title='Survival Rate by Passenger Classes')
plt.xlabel('Passenger Class')
plt.ylabel('Survival Rate')
plt.show()
We can see that passenger class seems to have a significant impact on whether a passenger survived. Those in First Class the highest chance for survival.
Gender might have also played a role in determining a passenger's survival rate. We'll need to map Sex from a string to a number to prepare it for machine learning algorithms.
Generate a mapping of Sex from a string to a number representation:
In [10]:
sexes = sorted(df_train['Sex'].unique())
genders_mapping = dict(zip(sexes, range(0, len(sexes) + 1)))
genders_mapping
Out[10]:
Transform Sex from a string to a number representation:
In [11]:
df_train['Sex_Val'] = df_train['Sex'].map(genders_mapping).astype(int)
df_train.head()
Out[11]:
In [12]:
df_train.info()
Plot a normalized cross tab for Sex_Val and Survived:
In [13]:
sex_val_xt = pd.crosstab(df_train['Sex_Val'], df_train['Survived'])
sex_val_xt_pct = sex_val_xt.div(sex_val_xt.sum(1).astype(float), axis=0)
sex_val_xt_pct.plot(kind='bar', stacked=True, title='Survival Rate by Gender')
plt.show()
The majority of females survived, whereas the majority of males did not.
Next we'll determine whether we can gain any insights on survival rate by looking at both Sex and Pclass.
Count males and females in each Pclass:
In [14]:
# Get the unique values of Pclass:
passenger_classes = sorted(df_train['Pclass'].unique())
for p_class in passenger_classes:
print ('M: ', p_class, len(df_train[(df_train['Sex'] == 'male') &
(df_train['Pclass'] == p_class)]))
print ('F: ', p_class, len(df_train[(df_train['Sex'] == 'female') &
(df_train['Pclass'] == p_class)]))
Plot survival rate by Sex and Pclass:
In [15]:
# Plot survival rate by Sex
females_df = df_train[df_train['Sex'] == 'female']
females_xt = pd.crosstab(females_df['Pclass'], df_train['Survived'])
females_xt_pct = females_xt.div(females_xt.sum(1).astype(float), axis=0)
females_xt_pct.plot(kind='bar',
stacked=True,
title='Female Survival Rate by Passenger Class')
plt.xlabel('Passenger Class')
plt.ylabel('Survival Rate')
# Plot survival rate by Pclass
males_df = df_train[df_train['Sex'] == 'male']
males_xt = pd.crosstab(males_df['Pclass'], df_train['Survived'])
males_xt_pct = males_xt.div(males_xt.sum(1).astype(float), axis=0)
males_xt_pct.plot(kind='bar',
stacked=True,
title='Male Survival Rate by Passenger Class')
plt.xlabel('Passenger Class')
plt.ylabel('Survival Rate')
plt.show()
The vast majority of females in First and Second class survived. Males in First class had the highest chance for survival.
In [16]:
df_train[df_train['Embarked'].isnull()]
Out[16]:
Prepare to map Embarked from a string to a number representation:
In [17]:
# Get the unique values of Embarked
df_train['Embarked'] = df_train['Embarked'].astype(str)
embarked_locs = sorted(df_train['Embarked'].unique())
embarked_locs_mapping = dict(zip(embarked_locs,
range(0, len(embarked_locs) + 1)))
embarked_locs_mapping
Out[17]:
Transform Embarked from a string to a number representation to prepare it for machine learning algorithms:
In [18]:
df_train['Embarked_Val'] = df_train['Embarked'] \
.map(embarked_locs_mapping) \
.astype(int)
df_train.head()
Out[18]:
Plot the histogram for Embarked_Val:
In [19]:
df_train['Embarked_Val'].hist(bins=len(embarked_locs), range=(0, 3))
plt.title('Port of Embarkation Histogram')
plt.xlabel('Port of Embarkation')
plt.ylabel('Count')
plt.show()
In [22]:
df_train1 = pd.read_csv('material/Data-Preprocessing-Dataset.csv')
In [23]:
df_train1[df_train1['Embarked'].isnull()]
Out[23]:
Since the vast majority of passengers embarked in 'S': 2, we assign the missing values in Embarked to 'S':
In [24]:
if len(df_train1[df_train1['Embarked'].isnull()] > 0):
df_train.replace({'Embarked_Val' :
{ embarked_locs_mapping['nan'] : embarked_locs_mapping['S']
}
},
inplace=True)
embarked_locs_mapping
Out[24]:
Verify we do not have any more NaNs for Embarked_Val:
In [25]:
embarked_locs = sorted(df_train['Embarked_Val'].unique())
embarked_locs
Out[25]:
Plot a normalized cross tab for Embarked_Val and Survived:
In [26]:
embarked_val_xt = pd.crosstab(df_train['Embarked_Val'], df_train['Survived'])
embarked_val_xt_pct = \
embarked_val_xt.div(embarked_val_xt.sum(1).astype(float), axis=0)
embarked_val_xt_pct.plot(kind='bar', stacked=True)
plt.title('Survival Rate by Port of Embarkation')
plt.xlabel('Port of Embarkation')
plt.ylabel('Survival Rate')
plt.show()
It appears those that embarked in location 'C': 0 had the highest rate of survival. We'll dig in some more to see why this might be the case. Below we plot a graphs to determine gender and passenger class makeup for each port:
In [27]:
df_train.head()
Out[27]:
In [28]:
# Set up a grid of plots
fig = plt.figure(figsize=fizsize_with_subplots)
rows = 2
cols = 3
col_names = ('Sex_Val', 'Pclass')
col_names
for portIdx in embarked_locs:
for colIdx in range(0, len(col_names)):
plt.subplot2grid((rows, cols), (colIdx, portIdx))
df_train[df_train['Embarked_Val'] == portIdx][col_names[colIdx]] \
.value_counts().plot(kind='bar')
plt.show()
Leaving Embarked as integers implies ordering in the values, which does not exist. Another way to represent Embarked without ordering is to create dummy variables:
In [29]:
df_train = pd.concat([df_train, pd.get_dummies(df_train['Embarked_Val'], prefix='Embarked_Val')], axis=1)
In [30]:
df_train[df_train['Age'].isnull()][['Sex', 'Pclass', 'Age']].head()
Out[30]:
Determine the Age typical for each passenger class by Sex_Val. We'll use the median instead of the mean because the Age histogram seems to be right skewed.
In [31]:
# To keep Age in tact, make a copy of it called AgeFill
# that we will use to fill in the missing ages:
df_train['AgeFill'] = df_train['Age']
# Populate AgeFill
df_train['AgeFill'] = df_train['AgeFill'] \
.groupby([df_train['Sex_Val'], df_train['Pclass']]) \
.apply(lambda x: x.fillna(x.median()))
#df_train.AgeFill
Ensure AgeFill does not contain any missing values
In [32]:
len(df_train[df_train['AgeFill'].isnull()])
Out[32]:
Plot a normalized cross tab for AgeFill and Survived:
In [33]:
# Set up a grid of plots
fig, axes = plt.subplots(2, 1, figsize=fizsize_with_subplots)
# Histogram of AgeFill segmented by Survived
df1 = df_train[df_train['Survived'] == 0]['Age']
df2 = df_train[df_train['Survived'] == 1]['Age']
max_age = max(df_train['AgeFill'])
axes[0].hist([df1, df2],
bins= int(max_age / bin_size),
range=(1, max_age),
stacked=True)
axes[0].legend(('Died', 'Survived'), loc='best')
axes[0].set_title('Survivors by Age Groups Histogram')
axes[0].set_xlabel('Age')
axes[0].set_ylabel('Count')
# Scatter plot Survived and AgeFill
axes[1].scatter(df_train['Survived'], df_train['AgeFill'])
axes[1].set_title('Survivors by Age Plot')
axes[1].set_xlabel('Survived')
axes[1].set_ylabel('Age')
plt.show()
Unfortunately, the graphs above do not seem to clearly show any insights. We'll keep digging further.
Plot AgeFill density by Pclass:
In [34]:
for pclass in passenger_classes:
df_train.AgeFill[df_train.Pclass == pclass].plot(kind='kde')
plt.title('Age Density Plot by Passenger Class')
plt.xlabel('Age')
plt.legend(('1st Class', '2nd Class', '3rd Class'), loc='best')
plt.show()
When looking at AgeFill density by Pclass, we see the first class passengers were generally older then second class passengers, which in turn were older than third class passengers. We've determined that first class passengers had a higher survival rate than second class passengers, which in turn had a higher survival rate than third class passengers.
In [35]:
# Set up a grid of plots
fig = plt.figure(figsize=fizsize_with_subplots)
fig_dims = (3, 1)
# Plot the AgeFill histogram for Survivors
plt.subplot2grid(fig_dims, (0, 0))
survived_df = df_train[df_train['Survived'] == 1]
survived_df['AgeFill'].hist(bins=int(max_age / bin_size), range=(1, max_age))
# Plot the AgeFill histogram for Females
plt.subplot2grid(fig_dims, (1, 0))
females_df = df_train[(df_train['Sex_Val'] == 0) & (df_train['Survived'] == 1)]
females_df['AgeFill'].hist(bins= int( max_age / bin_size), range=(1, max_age))
# Plot the AgeFill histogram for first class passengers
plt.subplot2grid(fig_dims, (2, 0))
class1_df = df_train[(df_train['Pclass'] == 1) & (df_train['Survived'] == 1)]
class1_df['AgeFill'].hist(bins= int( max_age / bin_size), range=(1, max_age))
plt.show()
In the first graph, we see that most survivors come from the 20's to 30's age ranges and might be explained by the following two graphs. The second graph shows most females are within their 20's. The third graph shows most first class passengers are within their 30's.
Feature enginering involves creating new features or modifying existing features which might be advantageous to a machine learning algorithm.
Define a new feature FamilySize that is the sum of Parch (number of parents or children on board) and SibSp (number of siblings or spouses):
In [36]:
df_train['FamilySize'] = df_train['SibSp'] + df_train['Parch']
df_train.head()
Out[36]:
Plot a histogram of FamilySize:
In [37]:
df_train['FamilySize'].hist()
plt.title('Family Size Histogram')
plt.show()
Plot a histogram of AgeFill segmented by Survived:
In [38]:
# Get the unique values of Embarked and its maximum
family_sizes = sorted(df_train['FamilySize'].unique())
family_size_max = max(family_sizes)
df1 = df_train[df_train['Survived'] == 0]['FamilySize']
df2 = df_train[df_train['Survived'] == 1]['FamilySize']
plt.hist([df1, df2],
bins=family_size_max + 1,
range=(0, family_size_max),
stacked=True)
plt.legend(('Died', 'Survived'), loc='best')
plt.title('Survivors by Family Size')
plt.show()
Based on the histograms, it is not immediately obvious what impact FamilySize has on survival. The machine learning algorithms might benefit from this feature.
Additional features we might want to engineer might be related to the Name column, for example honorrary or pedestrian titles might give clues and better predictive power for a male's survival.
Many machine learning algorithms do not work on strings and they usually require the data to be in an array, not a DataFrame.
Show only the columns of type 'object' (strings):
In [39]:
df_train.dtypes[df_train.dtypes.map(lambda x: x == 'object')]
Out[39]:
Drop the columns we won't use:
In [40]:
df_train = df_train.drop(['Name', 'Sex', 'Ticket', 'Cabin', 'Embarked'],
axis=1)
Drop the following columns:
In [41]:
df_train = df_train.drop(['Age', 'SibSp', 'Parch', 'PassengerId', 'Embarked_Val'], axis=1)
df_train.dtypes
Out[41]:
Convert the DataFrame to a numpy array:
In [42]:
train_data = df_train.values
train_data
Out[42]:
In [43]:
def clean_data(df, drop_passenger_id):
# Get the unique values of Sex
sexes = sorted(df['Sex'].unique())
# Generate a mapping of Sex from a string to a number representation
genders_mapping = dict(zip(sexes, range(0, len(sexes) + 1)))
# Transform Sex from a string to a number representation
df['Sex_Val'] = df['Sex'].map(genders_mapping).astype(int)
# Get the unique values of Embarked
embarked_locs = sorted(df['Embarked'].unique())
# Generate a mapping of Embarked from a string to a number representation
embarked_locs_mapping = dict(zip(embarked_locs,
range(0, len(embarked_locs) + 1)))
# Transform Embarked from a string to dummy variables
df = pd.concat([df, pd.get_dummies(df['Embarked'], prefix='Embarked_Val')], axis=1)
# Fill in missing values of Embarked
# Since the vast majority of passengers embarked in 'S': 3,
# we assign the missing values in Embarked to 'S':
if len(df[df['Embarked'].isnull()] > 0):
df.replace({'Embarked_Val' :
{ embarked_locs_mapping[nan] : embarked_locs_mapping['S']
}
},
inplace=True)
# Fill in missing values of Fare with the average Fare
if len(df[df['Fare'].isnull()] > 0):
avg_fare = df['Fare'].mean()
df.replace({ None: avg_fare }, inplace=True)
# To keep Age in tact, make a copy of it called AgeFill
# that we will use to fill in the missing ages:
df['AgeFill'] = df['Age']
# Determine the Age typical for each passenger class by Sex_Val.
# We'll use the median instead of the mean because the Age
# histogram seems to be right skewed.
df['AgeFill'] = df['AgeFill'] \
.groupby([df['Sex_Val'], df['Pclass']]) \
.apply(lambda x: x.fillna(x.median()))
# Define a new feature FamilySize that is the sum of
# Parch (number of parents or children on board) and
# SibSp (number of siblings or spouses):
df['FamilySize'] = df['SibSp'] + df['Parch']
# Drop the columns we won't use:
df = df.drop(['Name', 'Sex', 'Ticket', 'Cabin', 'Embarked'], axis=1)
# Drop the Age column since we will be using the AgeFill column instead.
# Drop the SibSp and Parch columns since we will be using FamilySize.
# Drop the PassengerId column since it won't be used as a feature.
df = df.drop(['Age', 'SibSp', 'Parch'], axis=1)
if drop_passenger_id:
df = df.drop(['PassengerId'], axis=1)
return df