Exploring the Titanic Dataset (Python version)

Anton Fefilov 17 september 2016

1 Introduction

This is my first attempt to make ML research myself after awesome Andrew Ng's Coursera course on Machine Learning. As a basis for this work I took the awesome kernel Exploring the Titanic Dataset authored by Megan Risdal and replicated it with Python. Also I took a lot of useful information for this work in A Journey through Titanic kernel by Omar El Gabry.

There are three parts to my script as follows:

• Feature engineering
• Missing value imputation
• Prediction!

1.1 Load and check data

# Load packages

# pandas
import pandas as pd
from pandas import Series, DataFrame

# numpy, matplotlib, seaborn
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.graphics.mosaicplot import mosaic
import seaborn as sns

# configure seaborn
sns.set_style('whitegrid')

# draw graphics inline
%matplotlib inline

# machine learning
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC, LinearSVC
from sklearn.ensemble import RandomForestClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.naive_bayes import GaussianNB

# imputation
from fancyimpute import MICE

Now that our packages are loaded, let’s read in and take a peek at the data.

# get titanic & test csv files as a DataFrame
train_df = pd.read_csv("input/train.csv")
test_df = pd.read_csv("input/test.csv")

# preview the data structure
train_df.head()

	PassengerId	Survived	Pclass	Name	Sex	Age	SibSp	Parch	Ticket	Fare	Cabin	Embarked
0	1	0	3	Braund, Mr. Owen Harris	male	22.0	1	0	A/5 21171	7.2500	NaN	S
1	2	1	1	Cumings, Mrs. John Bradley (Florence Briggs Th...	female	38.0	1	0	PC 17599	71.2833	C85	C
2	3	1	3	Heikkinen, Miss. Laina	female	26.0	0	0	STON/O2. 3101282	7.9250	NaN	S
3	4	1	1	Futrelle, Mrs. Jacques Heath (Lily May Peel)	female	35.0	1	0	113803	53.1000	C123	S
4	5	0	3	Allen, Mr. William Henry	male	35.0	0	0	373450	8.0500	NaN	S

# bind train and test data
titanic_df = train_df.append(test_df, ignore_index=True)

# get sense of variables and datatypes
titanic_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1309 entries, 0 to 1308
Data columns (total 12 columns):
Age            1046 non-null float64
Cabin          295 non-null object
Embarked       1307 non-null object
Fare           1308 non-null float64
Name           1309 non-null object
Parch          1309 non-null int64
PassengerId    1309 non-null int64
Pclass         1309 non-null int64
Sex            1309 non-null object
SibSp          1309 non-null int64
Survived       891 non-null float64
Ticket         1309 non-null object
dtypes: float64(3), int64(4), object(5)
memory usage: 122.8+ KB

We’ve got a sense of our variables, their class type, and the first few observations of each. We know we’re working with 1309 observations of 12 variables. To make things a bit more explicit since a couple of the variable names aren’t 100% illuminating, here’s what we’ve got to deal with:

Variable Name	Description
PassengerId	Passenger's id
Survived	Survived (1) or died (0)
Pclass	Passenger’s class
Name	Passenger’s name
Sex	Passenger’s sex
Age	Passenger’s age
SibSp	Number of siblings/spouses aboard
Parch	Number of parents/children aboard
Ticket	Ticket number
Fare	Fare
Cabin	Cabin
Embarked	Port of embarkation

2. Feature engineering

2.1 What's in a name?

The first variable which catches my attention is passenger name because we can break it down into additional meaningful variables which can feed predictions or be used in the creation of additional new variables. For instance, passenger title is contained within the passenger name variable and we can use surname to represent families. Let’s do some feature engineering!

# Make a copy of the titanic data frame
title_df = titanic_df.copy()

# Grab title from passenger names
title_df["Name"].replace(to_replace='(.*, )|(\\..*)', value='', inplace=True, regex=True)

title_df.head()

	Age	Cabin	Embarked	Fare	Name	Parch	PassengerId	Pclass	Sex	SibSp	Survived	Ticket
0	22.0	NaN	S	7.2500	Mr	0	1	3	male	1	0.0	A/5 21171
1	38.0	C85	C	71.2833	Mrs	0	2	1	female	1	1.0	PC 17599
2	26.0	NaN	S	7.9250	Miss	0	3	3	female	0	1.0	STON/O2. 3101282
3	35.0	C123	S	53.1000	Mrs	0	4	1	female	1	1.0	113803
4	35.0	NaN	S	8.0500	Mr	0	5	3	male	0	0.0	373450

# Show title counts by sex
title_df.groupby(["Sex", "Name"]).size().unstack(fill_value=0)

Name	Capt	Col	Don	Dona	Dr	Jonkheer	Lady	Major	Master	Miss	Mlle	Mme	Mr	Mrs	Ms	Rev	Sir	the Countess
Sex
female	0	0	0	1	1	0	1	0	0	260	2	1	0	197	2	0	0	1
male	1	4	1	0	7	1	0	2	61	0	0	0	757	0	0	8	1	0

# Titles with very low cell counts to be combined to "rare" level
rare_titles = ['Dona', 'Lady', 'the Countess','Capt', 'Col', 'Don', 'Dr', 'Major', 'Rev', 'Sir', 'Jonkheer']
title_df.replace(rare_titles, "Rare title", inplace=True)

# Also reassign mlle, ms, and mme accordingly
title_df.replace(["Mlle","Ms", "Mme"], ["Miss", "Miss", "Mrs"], inplace=True)

# Show title counts by sex
title_df.groupby(["Sex", "Name"]).size().unstack(fill_value=0)

Name	Master	Miss	Mr	Mrs	Rare title
Sex
female	0	264	0	198	4
male	61	0	757	0	25

# Finally, grab surname from passenger name
uniq_surname_size = titanic_df["Name"].str.split(',').str.get(0).unique().size

print("We have %(uniq_surname_size)s unique surnames. I would be interested to infer ethnicity based on surname --- another time." % locals())

We have 875 unique surnames. I would be interested to infer ethnicity based on surname --- another time.

2.2 Do families sink or swim together?

Now that we’ve taken care of splitting passenger name into some new variables, we can take it a step further and make some new family variables. First we’re going to make a family size variable based on number of siblings/spouse(s) (maybe someone has more than one spouse?) and number of children/parents.

# Make a copy of the titanic data frame
family_df = titanic_df.loc[:,["Parch", "SibSp", "Survived"]]

# Create a family size variable including the passenger themselves
family_df["Fsize"] = family_df.SibSp + family_df.Parch + 1

family_df.head()

	Parch	SibSp	Survived	Fsize
0	0	1	0.0	2
1	0	1	1.0	2
2	0	0	1.0	1
3	0	1	1.0	2
4	0	0	0.0	1

# make figure wider
plt.figure(figsize=(15,5))

# visualize the relationship between family size & survival
sns.countplot(x='Fsize', hue="Survived", data=family_df)

<matplotlib.axes._subplots.AxesSubplot at 0x7f77dad54f10>

Ah hah. We can see that there’s a survival penalty to singletons and those with family sizes above 4. We can collapse this variable into three levels which will be helpful since there are comparatively fewer large families. Let’s create a discretized family size variable.

# Discretize family size
family_df.ix[family_df.Fsize > 4, "Fsize"] = "large"
family_df.ix[family_df.Fsize == 1, "Fsize"] = 'singleton'
family_df.ix[(family_df.Fsize < 5) & (family_df.Fsize > 1), "Fsize"] = "small"


family_df.head(10)

	Parch	SibSp	Survived	Fsize
0	0	1	0.0	small
1	0	1	1.0	small
2	0	0	1.0	singleton
3	0	1	1.0	small
4	0	0	0.0	singleton
5	0	0	0.0	singleton
6	0	0	0.0	singleton
7	1	3	0.0	large
8	2	0	1.0	small
9	0	1	1.0	small

# Show family size by survival using a mosaic plot
mosaic(family_df, ['Fsize', 'Survived'], title="Family size by survival")

(<matplotlib.figure.Figure at 0x7f77dc09fb50>,
 OrderedDict([(('small', '0.0'), (0.0, 0.0, 0.3244768921336578, 0.41983343193919809)), (('small', '1.0'), (0.0, 0.42315569107541073, 0.3244768921336578, 0.57684430892458916)), (('singleton', '0.0'), (0.3294273871831628, 0.0, 0.5967263393005967, 0.6941479982924702)), (('singleton', '1.0'), (0.3294273871831628, 0.69747025742868274, 0.5967263393005967, 0.30252974257131715)), (('large', '0.0'), (0.9311042215332644, 0.0, 0.06889577846673557, 0.83592326653091842)), (('large', '1.0'), (0.9311042215332644, 0.83924552566713095, 0.06889577846673557, 0.16075447433286888))]))

The mosaic plot shows that we preserve our rule that there’s a survival penalty among singletons and large families, but a benefit for passengers in small families. I want to do something further with our age variable, but 263 rows have missing age values, so we will have to wait until after we address missingness.

2.3 Treat a few more variables …

What’s left? There’s probably some potentially useful information in the passenger cabin variable including about their deck. Let’s take a look.

# This variable appears to have a lot of missing values
titanic_df["Cabin"].head(28)

0             NaN
1             C85
2             NaN
3            C123
4             NaN
5             NaN
6             E46
7             NaN
8             NaN
9             NaN
10             G6
11           C103
12            NaN
13            NaN
14            NaN
15            NaN
16            NaN
17            NaN
18            NaN
19            NaN
20            NaN
21            D56
22            NaN
23             A6
24            NaN
25            NaN
26            NaN
27    C23 C25 C27
Name: Cabin, dtype: object

# The first character is the deck. For example:
list(titanic_df["Cabin"][1])

['C', '8', '5']

# The number of not-null Cabin values
titanic_df["Cabin"].count()

295

There’s more that likely could be done here including looking into cabins with multiple rooms listed (e.g., row 28: “C23 C25 C27”), but given the sparseness of the column we’ll stop here.

3 Missingness

Now we’re ready to start exploring missing data and rectifying it through imputation. There are a number of different ways we could go about doing this. Given the small size of the dataset, we probably should not opt for deleting either entire observations (rows) or variables (columns) containing missing values. We’re left with the option of either replacing missing values with a sensible values given the distribution of the data, e.g., the mean, median or mode. Finally, we could go with prediction. We’ll use both of the two latter methods and I’ll rely on some data visualization to guide our decisions.

3.1 Sensible value imputation

# Let's find passengers with missing Embarked feature
np.where(titanic_df["Embarked"].isnull())[0]

array([ 61, 829])

titanic_df.ix[[61,829]]

	Age	Cabin	Embarked	Fare	Name	Parch	PassengerId	Pclass	Sex	SibSp	Survived	Ticket
61	38.0	B28	NaN	80.0	Icard, Miss. Amelie	0	62	1	female	0	1.0	113572
829	62.0	B28	NaN	80.0	Stone, Mrs. George Nelson (Martha Evelyn)	0	830	1	female	0	1.0	113572

We will infer their values for embarkment based on present data that we can imagine may be relevant: passenger class and fare. We see that they paid $80 and $80 respectively and their classes are 1 and 1 . So from where did they embark?

# Get rid of our missing passenger IDs
embark_fare_df = titanic_df.drop([61,829], axis=0)

# Let's visualize embarkment, passenger class ...
sns.factorplot(x='Embarked',y='Fare', hue='Pclass', kind="box",order=['C', 'Q', 'S'],data=embark_fare_df, size=7,aspect=2)

# ... and median fare
plt.axhline(y=80, color='r', ls='--')

<matplotlib.lines.Line2D at 0x7f77daa9d590>

Voilà! The median fare for a first class passenger departing from Charbourg (‘C’) coincides nicely with the $80 paid by our embarkment-deficient passengers. I think we can safely replace the NA values with ‘C’.

# Since their fare was $80 for 1st class, they most likely embarked from 'C'
titanic_df.loc[[61,829],"Embarked"] = 'C'

We’re close to fixing the handful of NA values here and there. Passenger on row 1044 has an NA Fare value.

# Let's find passengers with missing Fare feature
np.where(titanic_df["Fare"].isnull())[0]

array([1043])

titanic_df.ix[[1043]]

	Age	Cabin	Embarked	Fare	Name	Parch	PassengerId	Pclass	Sex	SibSp	Survived	Ticket
1043	60.5	NaN	S	NaN	Storey, Mr. Thomas	0	1044	3	male	0	NaN	3701

This is a third class passenger who departed from Southampton (‘S’). Let’s visualize Fares among all others sharing their class and embarkment (n = 494).

facet = sns.FacetGrid(titanic_df[(titanic_df['Pclass'] == 3) & (titanic_df['Embarked'] == 'S')], aspect=4)
facet.map(sns.kdeplot,'Fare',shade= True)
facet.set(xlim=(0, 80))

fare_median = titanic_df[(titanic_df['Pclass'] == 3) & (titanic_df['Embarked'] == 'S')]['Fare'].median()
plt.axvline(x=fare_median, color='r', ls='--')

<matplotlib.lines.Line2D at 0x7f77dc958bd0>

From this visualization, it seems quite reasonable to replace the NA Fare value with median for their class and embarkment which is $8.05.

# Replace missing fare value with median fare for class/embarkment
titanic_df.loc[[1043],'Fare'] = fare_median

3.2 Predictive imputation

Finally, as we noted earlier, there are quite a few missing Age values in our data. We are going to get a bit more fancy in imputing missing age values. Why? Because we can. We will create a model predicting ages based on other variables.

# Show number of missing Age values
titanic_df["Age"].isnull().sum()

263

fig, (axis1,axis2) = plt.subplots(1,2,figsize=(15,4))
axis1.set_title('Original Age values - Titanic')
axis2.set_title('New Age values - Titanic')

# plot original Age values
# NOTE: drop all null values, and convert to int
titanic_df['Age'].dropna().astype(int).hist(bins=70, ax=axis1)

# get average, std, and number of NaN values
average_age = titanic_df["Age"].mean()
std_age = titanic_df["Age"].std()
count_nan_age = titanic_df["Age"].isnull().sum()

# generate random numbers between (mean - std) & (mean + std)
rand_age = np.random.randint(average_age - std_age, average_age + std_age, size = count_nan_age)

# fill NaN values in Age column with random values generated
age_slice = titanic_df["Age"].copy()
age_slice[np.isnan(age_slice)] = rand_age

# plot imputed Age values
age_slice.astype(int).hist(bins=70, ax=axis2)

<matplotlib.axes._subplots.AxesSubplot at 0x7f77d9938fd0>

Things look good, so let’s replace our Age vector in the original data with the new values

titanic_df["Age"] = age_slice

# Show number of missing Age values
titanic_df["Age"].isnull().sum()

0

We’ve finished imputing values for all variables that we care about for now! Now that we have a complete Age variable, there are just a few finishing touches I’d like to make. We can use Age to do just a bit more feature engineering …