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

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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
df.head()

   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
len(df.index)

150

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)
print(np.mean(scores))   

0.97333333333334

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
model.predict([new])

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.