Scikit-Learn QuadraticDiscriminantAnalysis Model

Quadratic Discriminant Analysis (QDA) is used for classification tasks where the assumption of equal covariance matrices between classes does not hold. This example demonstrates the implementation of QDA for classification, including data preparation, model training, evaluation, and prediction.

QDA models the decision boundary as a quadratic curve. The key hyperparameters include reg_param (regularization parameter) and store_covariance (whether to store the covariance matrices). It is suitable for classification problems where classes are assumed to have different covariance matrices.

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
from sklearn.metrics import accuracy_score

# generate binary classification dataset
X, y = make_classification(n_samples=100, n_features=5, n_classes=2, n_clusters_per_class=1, random_state=1)

# split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)

# create model
model = QuadraticDiscriminantAnalysis()

# fit model
model.fit(X_train, y_train)

# evaluate model
yhat = model.predict(X_test)
acc = accuracy_score(y_test, yhat)
print('Accuracy: %.3f' % acc)

# make a prediction
row = [[-1.10325445, -0.49821356, -0.05962247, -0.89224592, -0.70158632]]
yhat = model.predict(row)
print('Predicted: %d' % yhat[0])

Running the example gives an output like:

Accuracy: 0.800
Predicted: 1

The steps are as follows:

1. A synthetic binary classification dataset is generated using the make_classification() function. This creates a dataset with a specified number of samples (n_samples), classes (n_classes), and a fixed random seed (random_state) for reproducibility. The dataset is split into training and test sets using train_test_split().

2. A QuadraticDiscriminantAnalysis model is instantiated with default hyperparameters. The model is then fit on the training data using the fit() method.

3. The performance of the model is evaluated by comparing the predictions (yhat) to the actual values (y_test) using the accuracy score metric.

4. A single prediction can be made by passing a new data sample to the predict() method.

This example demonstrates how to set up and use a QuadraticDiscriminantAnalysis model for binary classification tasks, showcasing the algorithm’s ability to handle cases with different covariance matrices for each class.