v Imbalanced Classes In SVM - Machine Learning

Imbalanced Classes In SVM

In support vector machines, $$C$$ is a hyperparameter determining the penalty for misclassifying an observation. One method for handling imbalanced classes in support vector machines is to weight $$C$$ by classes, so that

$$C_k = C * w_j$$

where $$C$$ is the penalty for misclassification, $$w_j$$ is a weight inversely proportional to class $$j$$'s frequency, and $$C_j$$ is the $$C$$ value for class $$j$$. The general idea is to increase the penalty for misclassifying minority classes to prevent them from being "overwhelmed" by the majority class.

In scikit-learn, when using SVC we can set the values for $$C_j$$ automatically by setting class_weight='balanced' The balanced argument automatically weighs classes such that:

$$w_j = \frac{n}{kn_{j}}$$

where $$w_j$$ is the weight to class $$j$$, $$n$$ is the number of observations, $$n_j$$ is the number of observations in class $$j$$, and $$k$$ is the total number of classes.

Preliminaries

# Load libraries
from sklearn.svm import SVC
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
import numpy as np


#Load data with only two classes
X = iris.data[:100,:]
y = iris.target[:100]


Imbalanced Iris Flower Classes

# Make class highly imbalanced by removing first 40 observations
X = X[40:,:]
y = y[40:]

# Create target vector indicating if class 0, otherwise 1
y = np.where((y == 0), 0, 1)


Standardize Features

# Standarize features
scaler = StandardScaler()
X_std = scaler.fit_transform(X)


Train Support Vector Classifier With Weighted Classes

# Create support vector classifier
svc = SVC(kernel='linear', class_weight='balanced', C=1.0, random_state=0)

# Train classifier
model = svc.fit(X_std, y)