Quadratic Discriminant Analysis in Python (Step-by-Step)

Quadratic discriminant analysis is a method you can use when you have a set of predictor variables and you’d like to classify a response variable into two or more classes.

It is considered to be the non-linear equivalent to linear discriminant analysis.

This tutorial provides a step-by-step example of how to perform quadratic discriminant analysis in Python.

Step 1: Load Necessary Libraries

First, we’ll load the necessary functions and libraries for this example:

from sklearn.model_selection import train_test_split
from sklearn.model_selection import RepeatedStratifiedKFold
from sklearn.model_selection import cross_val_score
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis 
from sklearn import datasets
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

Step 2: Load the Data

For this example, we’ll use the iris dataset from the sklearn library. The following code shows how to load this dataset and convert it to a pandas DataFrame to make it easy to work with:

#load iris dataset
iris = datasets.load_iris()

#convert dataset to pandas DataFrame
df = pd.DataFrame(data = np.c_[iris['data'], iris['target']],
                 columns = iris['feature_names'] + ['target'])
df['species'] = pd.Categorical.from_codes(iris.target, iris.target_names)
df.columns = ['s_length', 's_width', 'p_length', 'p_width', 'target', 'species']

#view first six rows of DataFrame

   s_length  s_width  p_length  p_width  target species
0       5.1      3.5       1.4      0.2     0.0  setosa
1       4.9      3.0       1.4      0.2     0.0  setosa
2       4.7      3.2       1.3      0.2     0.0  setosa
3       4.6      3.1       1.5      0.2     0.0  setosa
4       5.0      3.6       1.4      0.2     0.0  setosa

#find how many total observations are in dataset


We can see that the dataset contains 150 total observations.

For this example we’ll build a quadratic discriminant analysis model to classify which species a given flower belongs to.

We’ll use the following predictor variables in the model:

  • Sepal length
  • Sepal width
  • Petal length
  • Petal width

And we’ll use them to predict the response variable Species, which takes on the following three potential classes:

  • setosa
  • versicolor
  • virginica

Step 3: Fit the QDA Model

Next, we’ll fit the QDA model to our data using the QuadraticDiscriminantAnalsyis function from sklearn:

#define predictor and response variables
X = df[['s_length', 's_width', 'p_length', 'p_width']]
y = df['species']

#Fit the QDA model
model = QuadraticDiscriminantAnalysis()
model.fit(X, y)

Step 4: Use the Model to Make Predictions

Once we’ve fit the model using our data, we can evaluate how well the model performed by using repeated stratified k-fold cross validation.

For this example, we’ll use 10 folds and 3 repeats:

#Define method to evaluate model
cv = RepeatedStratifiedKFold(n_splits=10, n_repeats=3, random_state=1)

#evaluate model
scores = cross_val_score(model, X, y, scoring='accuracy', cv=cv, n_jobs=-1)


We can see that the model performed a mean accuracy of 97.33%.

We can also use the model to predict which class a new flower belongs to, based on input values:

#define new observation
new = [5, 3, 1, .4]

#predict which class the new observation belongs to

array(['setosa'], dtype='<U10')

We can see that the model predicts this new observation to belong to the species called setosa.

You can find the complete Python code used in this tutorial here.

Featured Posts

Leave a Reply

Your email address will not be published. Required fields are marked *