How does Quadratic Discriminant Analysis work?
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# How does Quadratic Discriminant Analysis work?

This recipe explains how Quadratic Discriminant Analysis work

## Recipe Objective

Quadratic Discriminant Analysis is a classifier with a quadratic decision boundary, generated by fitting class conditional densities to the data and using Bayes’ rule. It fits a Gaussian density to each class.

So this recipe is a short example on how does Quadratic Discriminant Analysis work. Let's get started.

## Step 1 - Import the library

``` from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.datasets import load_iris from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis ```

Let's pause and look at these imports. We have exported train_test_split which helps in randomly breaking the datset in two parts. Here sklearn.dataset is used to import one classification based model dataset. Also, we have exported QuadraticDiscriminantAnalysis to build our model.

## Step 2 - Setup the Data

``` X,y=load_iris(return_X_y=True) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25) ```

Here, we have used load_iris function to import our dataset in two list form (X and y) and therefore kept return_X_y to be True. Further with have broken down the dataset into 2 parts, train and test with ratio 3:4.

## Step 3 - Building the model

``` model = QuadraticDiscriminantAnalysis() ```

We have simply built a classification model with QuadraticDiscriminantAnalysis with default values.

## Step 4 - Fit the model and predict for test set

``` model.fit(X_train, y_train) y_pred= model.predict(X_test) ```

Here we have simply fit used fit function to fit our model on X_train and y_train. Now, we are predicting the values of X_test using our built model.

## Step 5 - Printing the accuracy

``` print(model.score(X_train,y_train)) print(model.score(X_test,y_test)) ```

Here we have calculated accuracy score using score function for both our train and test set.

## Step 6 - Lets look at our dataset now

Once we run the above code snippet, we will see:

```0.9910714285714286
0.9736842105263158
```

Clearly, the model built for the given datset is highly efficient on any unknown set. It might be best model to fit on iris Dataset.

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