So far, we have learned about various techniques that help predict the class based on its features and their relationship. In this lesson, we will be addressing the concept of an algorithm based on Support Vectors that can be used for classifying data. Support-vector machines are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis.
An SVM model 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 the side of the gap on which they fall. The objective of the support vector machine algorithm is to find a hyperplane in N-dimensional space that distinctly classifies the data points. A Support Vector Classification model uses the following hyperparameters in its model that determine the performance of the model.
Now that we know the basic idea of support vectors, we will now discuss a step-wise Python implementation of the algorithm.
Before we begin to develop a model and understand it, let us import some essential Python libraries for mathematical calculations, data loading, preprocessing, and model development and prediction.
# Importing the libraries import numpy as np import pandas as pd import matplotlib.pyplot as plt %matplotlib inline # scikit-learn modules from sklearn.datasets import load_breast_cancer from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.svm import SVC from sklearn.metrics import confusion_matrix, accuracy_score, classification_report # For plotting the classification results from mlxtend.plotting import plot_decision_regions
For this problem, we will be loading the Breast Cancer dataset from scikit-learn. The dataset consists of data related to breast cancer patients and their diagnosis (malignant or benign).
# Importing the dataset dataset = load_breast_cancer() # Converting to pandas dataframe df = pd.DataFrame(dataset.data, columns = dataset.feature_names) df['target'] = pd.Series(dataset.target) df.head()
print("Total samples in our dataset is: {}".format(df.shape[0]))
Total samples in our dataset is: 569
dataset.describe()
After loading the data set, the independent variable ($x$) and the dependent variable ($y$) need to be separated. Our concern is to find the relationships between the features and the target variable from the above dataset.
For this implementation example, we will only be using the ‘mean perimeter’ and ‘mean texture’ features but you can certainly use all of them.
# Selecting the features features = ['mean perimeter', 'mean texture'] x = df[features] # Target Variable y = df['target']
After separating the independent variables ($x$) and dependent variable $(y)$, these values are split into train and test sets to train and evaluate the linear model. We use the train_test_split() module of scikit-learn for splitting the available data into an 80-20 split. We will be using twenty percent of the available data as the test set and the remaining data as the train set.
# Splitting the dataset into the training and test set x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.20, random_state = 25 )
After splitting the data into dependent and independent variables, the Support Vector Classifier model is fitted with the training data using the SVC() class from scikit-learn.
# Fitting SVC to the Training set model = SVC(kernel = 'linear', random_state = 0) model.fit(x_train, y_train)
SVC(kernel='linear', random_state=0)
Finally, the model is tested on the data to get the predictions.
# Predicting the results y_pred = model.predict(x_test)
Let us now evaluate the model using the confusion matrix and calculate its classification accuracy. Confusion matrix determines the performance of the predicted model. Other metrics such as the precision, recall and f1-score are given by the classification report module of scikit-learn.
Precision defines the ratio of correctly predicted positive observations of the total predicted positive observations. It defines how accurate the model is. Recall defines the ratio of correctly predicted positive observations to all observations in the actual class. F1 Score is the weighted average of Precision and Recall and is often used as a metric in place of accuracy for imbalanced datasets.
# Confusion matrix
print("Confusion Matrix")
matrix = confusion_matrix(y_test, y_pred)
print(matrix)
# Classification Report
print("\nClassification Report")
report = classification_report(y_test, y_pred)
print(report)
# Accuracy of the model
accuracy = accuracy_score(y_test, y_pred)
print('SVC Accuracy of the model: {:.2f}%'.format(accuracy*100))
Confusion Matrix
[[28 11]
[ 8 67]]
Classification Report
precision recall f1-score support
0 0.91 0.77 0.83 39
1 0.89 0.96 0.92 75
accuracy 0.89 114
macro avg 0.90 0.86 0.88 114
weighted avg 0.90 0.89 0.89 114
SVC Accuracy of the model: 89.47%
Hence, the model is working quite well with an accuracy of 89.47%.
We will now plot the decision boundary of the model on test data.
# Plotting the decision boundary
plot_decision_regions(x_test.values, y_test.values, clf = model, legend = 2)
plt.title("Decision boundary using SVC (Test)")
plt.xlabel("mean_perimeter")
plt.ylabel("mean_texture");
Hence, the plot shows the distinction between the two classes as classified by the Support Vector Classification algorithm in Python.
The final code for the implementation of Support Vector Classification in Python is as follows.
# Importing the libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
# scikit-learn modules
from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.svm import SVC
from sklearn.metrics import confusion_matrix, accuracy_score, classification_report
# Plotting the classification results
from mlxtend.plotting import plot_decision_regions
# Importing the dataset
dataset = load_breast_cancer()
# Converting to pandas DataFrame
df = pd.DataFrame(dataset.data, columns = dataset.feature_names)
df['target'] = pd.Series(dataset.target)
print("Total samples in our dataset is: {}".format(df.shape[0]))
# Describe the dataset
df.describe()
# Selecting the features
features = ['mean perimeter', 'mean texture']
x = df[features]
# Target variable
y = df['target']
# Splitting the dataset into the training and test set
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.20, random_state = 25 )
# Fitting SVC to the Training set
model = SVC(kernel = 'linear', random_state = 0)
model.fit(x_train, y_train)
# Predicting the results
y_pred = model.predict(x_test)
# Confusion matrix
print("Confusion Matrix")
matrix = confusion_matrix(y_test, y_pred)
print(matrix)
# Classification Report
print("\nClassification Report")
report = classification_report(y_test, y_pred)
print(report)
# Accuracy of the model
accuracy = accuracy_score(y_test, y_pred)
print('SVC Accuracy of the model: {:.2f}%'.format(accuracy*100))
# Plotting the decision boundary
plt.figure(figsize=(10,6))
plot_decision_regions(x_test.values, y_test.values, clf = model, legend = 2)
plt.title("Decision boundary using SVC (Test)")
plt.xlabel("mean_perimeter")
plt.ylabel("mean_texture")
In this lesson, we discussed the concept of Support Vector Classifier along with its implementation in Python. In the next lesson, we will discuss classifiers based on Stochastic Gradient Descent algorithm.
