Casey Cooper

A showcase of my personal projects as well as various data science techniques. My resume can be found on the About Me page.

Support Vector Machines in Python

Data Cleaning

The dataset being used is the classic titanic dataset from the seaborn library. The models will attempt to predict whether the passenger survived or not.

The initial uncleaned dataset can be viewed and downloaded below.

Unclean_Data_Titanic.csvDownload

The first step is removing duplicate columns.

  • survived is the same as alive
  • embarked is the same as embark_town
  • sex is the same as who
  • pclass is the same as class

So, alive, embark_town, who, and class were removed.

The second step is dealing with missing values for the deck column. Approximately 77% of the data for this column was missing, so the deck variable was removed alltogether.

The third step is dealing with missing values for the embarked column. There are only two missing values. Since, this is a categorical column, the missing values were replaced with the mode. The mode was ‘S’.

The fourth step is dealing with missing values for the age column. Since age may have a relationship with other columns, the missing values were imputed with the mean after grouping by pclass and sex.

The cleaned dataset can be viewed and downloaded below.

Clean_Data_Titanic.csvDownload

The code for the data cleaning can be viewed and downloaded below.

Titanic_Data_Prep.pyDownload
Copy Code
# -*- coding: utf-8 -*-
"""
Created on Mon May 15 16:37:51 2023

@author: casey
"""

## LOAD LIBRARIES
# Set seed for reproducibility
import random; 
random.seed(53)
import pandas as pd
import seaborn as sns

# ------------------------------------------------------------------------------------------------ #
## LOAD DATASET
df = sns.load_dataset('titanic')

# ------------------------------------------------------------------------------------------------ #
## DISPLAY DETAILS OF DATASET

# Number of rows and columns
df.shape

# General details (includes missing values)
df.info()

# Visual look at dataset
df.head(10)

# ------------------------------------------------------------------------------------------------ #
## REMOVE DUPLICATE COLUMNS
# 'survived' is same as 'alive', 
# 'embarked' is abbreviation of 'embark_town', 
# 'sex' is same as 'who' 
# 'pclass' is same as 'class'

df.drop(columns=['alive','embark_town','who','class'], axis = 1, inplace = True)

# ------------------------------------------------------------------------------------------------ #
## DEAL WITH MISSING VALUES
df.isnull().sum()

# 'deck' has 77% of values missing so that column will just be removed
df.drop(columns=['deck'], axis=1, inplace=True)

# `embarked` has 2 missing values, will replace with the mode
df.embarked.fillna('S', inplace=True)

# age may have a relationship with other columns, so try imputing after grouping
#df.age.fillna(df.age.median(), inplace = True)
df['age'] = df['age'].groupby([df['pclass'], df['sex']]).apply(lambda x: x.fillna(x.mean()))

# ------------------------------------------------------------------------------------------------ #
## WRITE CLEANED DATASET TO .CSV

df.to_csv('C:/Users/casey/OneDrive/Documents/Machine_Learning/Supervised_Learning/Data/Clean_Data_Titanic.csv',
          index = False)

The final cleaned dataset contains the following columns.

  • survived: whether the passenger survived or not (1=survived, 0=not survived)
  • pclass: the class the passenger stayed in (1, 2, or 3)
  • sex: the sex of the passenger
  • age: the age of the passenger
  • sibsp: number of siblings/spouses aboard for each passenger
  • parch: number of parents/children aboard for each passenger
  • fare: the fare for each passenger
  • embarked: port each passenger embarked from
  • adult_male: whether the passenger was an adult male or not
  • alone: whether the passenger was traveling alone or not

Modeling Prep

  • Numeric variables only
    • Use one hot encoding for categorical variables
  • Normalize the dataset
    • Necessary because SVMs use a distance metric
  • Split data into train and test sets

Creating Support Vector Machine models in python requires three key preparatory steps. The first, is that variables need to be numeric. So, any categorical variables need to be converted to numeric variables using one hot encoding. In this case, pclass, sex, embarked, alone, and adult_male were all converted to numeric variables. The second, is that the dataset needs to undergo normalization. A distance metric is used as part of the algorithm for Support Vector Machines. So, if data isn’t normalized, then larger values will be weighted greater than smaller values, when it is possible they shouldn’t be. The third, is that since, Support Vector Machines are a supervised machine learning model, it requires the prepped data to be split into training and testing sets. The training set is used to train the model. The testing set is used to test the accuracy of the model. In the following example, the training set is created by randomly selecting 80% of the data and the testing set is created by randomly selecting 20% of the data. These numbers are not the only option, just a popular one. The training and testing sets must be kept disjoint (separated) throughout the modeling process. Failure to do so, will most likely result in overfitting and poor performance on real data that is not from the training or testing set.

The code for the modeling prep, as well as the modeling and model evaluation can be viewed and downloaded below.

Titanic_SVM.pyDownload
Copy Code
# -*- coding: utf-8 -*-
"""
Created on Wed May 17 11:18:28 2023

@author: casey
"""

## LOAD LIBRARIES
# Set seed for reproducibility
import random; 
random.seed(53)
import pandas as pd

# Import all we need from sklearn
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report, confusion_matrix
from sklearn.preprocessing import MinMaxScaler
from sklearn import svm

# Import visualization
import scikitplot as skplt
import matplotlib.pyplot as plt
import seaborn as sns

# ------------------------------------------------------------------------------------------------ #
## LOAD DATA
svm_df = pd.read_csv('C:/Users/casey/OneDrive/Documents/Machine_Learning/Supervised_Learning/Data/Clean_Data_Titanic.csv')

# ------------------------------------------------------------------------------------------------ #
## CREATE DUMMY VARIABLES FOR CATEGORICAL VARIABLES
svm_onehot = svm_df.copy()
svm_onehot = pd.get_dummies(svm_onehot, columns = ['pclass', 'sex', 'embarked', 'alone', 'adult_male'])


# ------------------------------------------------------------------------------------------------ #
## NORMALIZE DATA 
# Min-Max Scaling used since varibles are not normally distributed
scaler = MinMaxScaler(feature_range=(0, 1))
svm_onehot_scaled = scaler.fit_transform(svm_onehot)
svm_onehot_scaled = pd.DataFrame(svm_onehot_scaled, columns=svm_onehot.columns)

# ------------------------------------------------------------------------------------------------ #
## CREATE TRAIN AND TEST SETS

# X will contain all variables except the labels (the labels are the first column 'survived')
X = svm_onehot_scaled.iloc[:,1:]
# y will contain the labels (the labels are the first column 'survived')
y = svm_onehot_scaled.iloc[:,:1]

# split the data vectors randomly into 80% train and 20% test
# X_train contains the quantitative variables for the training set
# X_test contains the quantitative variables for the testing set
# y_train contains the labels for training set
# y_test contains the lables for the testing set
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

# ------------------------------------------------------------------------------------------------ #
## CREATE MODEL WITH LINEAR KERNEL
# Look at below documentation for parameters
# https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html
SVM_Classifier = svm.SVC(kernel='linear', C=1)
SVM_Classifier.fit(X_train, y_train)

## EVALUATE MODEL
y_pred = SVM_Classifier.predict(X_test)
print(confusion_matrix(y_test, y_pred))
print(classification_report(y_test, y_pred))

# ------------------------------------------------------------------------------------------------ #
## PLOT CONFUSION MATRIX

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

ax1 = fig.add_subplot(121)
skplt.metrics.plot_confusion_matrix(y_pred, y_test,
                                    title="Confusion Matrix for SVM Model (Linear Kernel, C=1)",
                                    cmap="Oranges",
                                    ax=ax1)

# ------------------------------------------------------------------------------------------------ #
## CREATE MODEL WITH RBF KERNEL
# Look at below documentation for parameters
# https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html
SVM_Classifier = svm.SVC(kernel='rbf', C=0.5)
SVM_Classifier.fit(X_train, y_train)

## EVALUATE MODEL
y_pred = SVM_Classifier.predict(X_test)
print(confusion_matrix(y_test, y_pred))
print(classification_report(y_test, y_pred))

# ------------------------------------------------------------------------------------------------ #
## PLOT CONFUSION MATRIX

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

ax1 = fig.add_subplot(121)
skplt.metrics.plot_confusion_matrix(y_pred, y_test,
                                    title="Confusion Matrix for SVM Model (RBF Kernel, C=0.5)",
                                    cmap="Oranges",
                                    ax=ax1)

# ------------------------------------------------------------------------------------------------ #
## CREATE MODEL WITH SIGMOID KERNEL
# Look at below documentation for parameters
# https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html
SVM_Classifier = svm.SVC(kernel='sigmoid', C=0.5)
SVM_Classifier.fit(X_train, y_train)

## EVALUATE MODEL
y_pred = SVM_Classifier.predict(X_test)
print(confusion_matrix(y_test, y_pred))
print(classification_report(y_test, y_pred))

# ------------------------------------------------------------------------------------------------ #
## PLOT CONFUSION MATRIX

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

ax1 = fig.add_subplot(121)
skplt.metrics.plot_confusion_matrix(y_pred, y_test,
                                    title="Confusion Matrix for SVM Model (Sigmoid Kernel, C=0.5)",
                                    cmap="Oranges",
                                    ax=ax1)

# ------------------------------------------------------------------------------------------------ #
## CREATE MODEL WITH POLYNOMIAL KERNEL
# Look at below documentation for parameters
# https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html
SVM_Classifier = svm.SVC(kernel='poly', degree=2, C=0.5)
SVM_Classifier.fit(X_train, y_train)

## EVALUATE MODEL
y_pred = SVM_Classifier.predict(X_test)
print(confusion_matrix(y_test, y_pred))
print(classification_report(y_test, y_pred))

# ------------------------------------------------------------------------------------------------ #
## PLOT CONFUSION MATRIX

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

ax1 = fig.add_subplot(121)
skplt.metrics.plot_confusion_matrix(y_pred, y_test,
                                    title="Confusion Matrix for SVM Model (Sigmoid Kernel, C=0.5)",
                                    cmap="Oranges",
                                    ax=ax1)

Model Evaluation Key Ideas

  • Attempt to classify passengers of the titanic as survived or not, with high accuracy
  • The larger the regularization parameter, the higher the chance of overfitting (default is 1)

Modeling (Linear Kernel, C=1)

To begin, a model was created using the Linear kernel and a regularization parameter of 1.

The confusion matrix and evaluation metrics can be viewed below.

  • Accuracy: 0.83
  • Precision (0): 0.86
  • Precision (1): 0.76
  • Recall (0): 0.87
  • Recall (1): 0.75

Modeling (RBF Kernel, C=0.5)

Next, a model was created using the RBF kernel and a regularization parameter of 0.5.

The confusion matrix and evaluation metrics can be viewed below.

  • Accuracy: 0.82
  • Precision (0): 0.81
  • Precision (1): 0.84
  • Recall (0): 0.94
  • Recall (1): 0.59

Modeling (Sigmoid Kernel, C=0.5)

Next, a model was created using the Sigmoid kernel and a regularization parameter of 0.5.

The confusion matrix and evaluation metrics can be viewed below.

  • Accuracy: 0.77
  • Precision (0): 0.82
  • Precision (1): 0.68
  • Recall (0): 0.83
  • Recall (1): 0.67

Modeling (Polynomial Kernel, degree=2, C=0.5)

Next, a model was created using the Polynomial kernel, a degree of 2, and a regularization parameter of 0.5.

The confusion matrix and evaluation metrics can be viewed below.

  • Accuracy: 0.82
  • Precision (0): 0.81
  • Precision (1): 0.84
  • Recall (0): 0.94
  • Recall (1): 0.59