[Python] Linear Discriminant Analysis.ipynb

Kernel: Python 3

Linear Discriminant Analysis

Data preprocessing

# Importing the libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from sklearn.model_selection import train_test_split # for training and testing split
from sklearn.preprocessing import StandardScaler # for Feature scaling
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA # for applying LDA
from sklearn.linear_model import LogisticRegression # for classifier
from sklearn.metrics import confusion_matrix # for making confusion matrix
from matplotlib.colors import ListedColormap # for visualization

%matplotlib inline
plt.rcParams['figure.figsize'] = [14, 8]

# Importing the dataset
dataset = pd.read_csv('Wine.csv')
X = dataset.iloc[:, 0:13].values
y = dataset.iloc[:, 13].values

dataset.head(5)

dataset.tail(5)

np.set_printoptions(suppress=True, threshold=13)

X[0]

array([   14.23,     1.71,     2.43,    15.6 ,   127.  ,     2.8 ,
           3.06,     0.28,     2.29,     5.64,     1.04,     3.92,  1065.  ])

# Splitting the dataset into the Training set and Test set
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 42)

# Feature Scaling
sc_X = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)

Applying Linear Discriminant Analysis

lda = LDA(n_components = 2)
X_train = lda.fit_transform(X_train, y_train)
X_test = lda.transform(X_test)

X_test[0]

array([-3.17092336,  2.12434125])

X_train[0]

array([ 5.43777422,  2.52448581])

Fitting Logistic Regression to the Training Set

classifier = LogisticRegression(random_state = 42)
classifier.fit(X_train, y_train)

LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
          penalty='l2', random_state=42, solver='liblinear', tol=0.0001,
          verbose=0, warm_start=False)

Predicting Test set result

y_pred = classifier.predict(X_test)

y_pred[0:10]

array([1, 1, 3, 1, 2, 1, 2, 3, 2, 3])

y_test[0:10]

array([1, 1, 3, 1, 2, 1, 2, 3, 2, 3])

Making the Confusion Matrix

cm = confusion_matrix(y_test, y_pred)
cm

array([[14,  0,  0],
       [ 0, 14,  0],
       [ 0,  0,  8]])

Here we have almost no incorrect prediction at all.

Accuracy

(cm[0][0] + cm[1][1] + cm[2][2])/ np.sum(cm)

1.0

Visualizing the training set results

X_set, y_set = X_train, y_train
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1,
                              stop = X_set[:, 0].max() +1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1,
                              stop = X_set[:, 1].max() +1, step = 0.01))
# plot the contour
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
            alpha = 0.75,
            cmap = ListedColormap(('red', 'green', 'blue')))
# plot the points
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())

for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
               c = ListedColormap(('red', 'green', 'blue'))(i), label = j, edgecolors = 'white', linewidth = 0.7)
plt.title('Logistic Regression (Training set)')
plt.xlabel('1st Linear Discriminant Component')
plt.ylabel('2nd Linear Discriminant Component')
plt.legend()

<matplotlib.legend.Legend at 0x7f5a13940da0>

Visualizing the test set results

X_set, y_set = X_test, y_test
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1,
                              stop = X_set[:, 0].max() +1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1,
                              stop = X_set[:, 1].max() +1, step = 0.01))
# plot the contour
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
            alpha = 0.75,
            cmap = ListedColormap(('red', 'green', 'blue')))
# plot the points
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())

for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
               c = ListedColormap(('red', 'green', 'blue'))(i), label = j, edgecolors = 'white', linewidth = 0.7)
plt.title('Logistic Regression (Training set)')
plt.xlabel('1st Linear Discriminant Component')
plt.ylabel('2nd Linear Discriminant Component')
plt.legend()

<matplotlib.legend.Legend at 0x7f5a09f124e0>