# 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)