Linear discriminant analysis in Python

Linear discriminant analysis (LDA) is a dimensionality reduction technique for pattern recognition and classification. It transforms the data into a lower dimensional space, maximizing the separation between classes, thus facilitating the distinction of different data categories.

The following steps demonstrate the process of training and visualizing a LDA model using the provided dataset.

Step 1 - Importing the libraries

In the first step, we import the necessary libraries.

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Step 2 - Importing the dataset

After importing libraries, we load the dataset from a CSV file.

items = pd.read_csv('Data.csv')
label1 = items.iloc[:, 0:13].values
label2 = items.iloc[:, 13].values

Here, we use the iloc() function in Python to assign the variables label1 and label2 values of the feature variable and the target variable values from the dataset.

Step 3 - Splitting the dataset into training and test set

In this step, we split the data into training and test sets using the train_test_split function. 

from sklearn.model_selection import train_test_split
label1_train, label1_test, label2_train, label2_test = train_test_split(label1, label2, test_size = 0.2, random_state = 0)

Step 4 - Feature scaling

In this step, we scale the input features label1_train and label1_test to normalize the data.

from sklearn.preprocessing import StandardScaler
scaling = StandardScaler()
label1_train = scaling.fit_transform(label1_train)
label1_test = scaling.transform(label1_test)

Step 5 - Applying LDA

Here, we apply LDA with two components to transform the training and test data.

from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
analysis = LDA(n_components = 2)
label1_train = analysis.fit_transform(label1_train, label2_train)
label1_test = analysis.transform(label1_test)

Step 6 - Fitting the model to the training dataset

In this step, we create a logistic regression model and train it on the transformed training data.

from sklearn.linear_model import LogisticRegression
model = LogisticRegression(random_state = 0)
model.fit(label1_train, label2_train)

Step 7 - Predicting the test set results

Here, we predict the outcomes of the test set.

prediction = model.predict(label1_test)
from sklearn.metrics import confusion_matrix, accuracy_score
matrix = confusion_matrix(label2_test, prediction)
print(matrix)
score = accuracy_score(label2_test, prediction)
print(score)

We also calculate the confusion matrix and accuracy score to evaluate the model's performance.

Learn about the evaluation metrics.

Step 8 - The visualization of training set results

Then we create a scatter plot to visualize the linear discriminants of the model and observe its separation of the three different categories in the training dataset.

from matplotlib.colors import ListedColormap
seq1, seq2 = label1_train, label2_train
grid1, grid2 = np.meshgrid(np.arange(start = seq1[:, 0].min() - 1, stop = seq1[:, 0].max() + 1, step = 0.01),
                     np.arange(start = seq1[:, 1].min() - 1, stop = seq1[:, 1].max() + 1, step = 0.01))
plt.contourf(grid1, grid2, model.predict(np.array([grid1.ravel(), grid2.ravel()]).T).reshape(grid1.shape),
             alpha = 0.75, cmap = ListedColormap(('lightblue', 'peachpuff', 'mistyrose')))
plt.xlim(grid1.min(), grid1.max())
plt.ylim(grid2.min(), grid2.max())
for key, value in enumerate(np.unique(seq2)):
    plt.scatter(seq1[seq2 == value, 0], seq1[seq2 == value, 1],
                c = ListedColormap(('mediumturquoise', 'lightsalmon', 'lightcoral'))(key), label = value)
plt.title('Training set')
plt.xlabel('LDA1')
plt.ylabel('LDA2')
plt.legend()
plt.savefig('output/1_training.png')
plt.show()

Here we saved the visualization generated by the code as an image file named 1_training.png in the specified folder output using plt.savefig.

Step 9 - The visualization of test set results

Similarly, we create a scatter plot to visualize the linear discriminants of the model and observe its separation of the three different categories in the test dataset.

from matplotlib.colors import ListedColormap
seq1, seq2 = label1_test, label2_test
grid1, grid2 = np.meshgrid(np.arange(start = seq1[:, 0].min() - 1, stop = seq1[:, 0].max() + 1, step = 0.01),
                     np.arange(start = seq1[:, 1].min() - 1, stop = seq1[:, 1].max() + 1, step = 0.01))
plt.contourf(grid1, grid2, model.predict(np.array([grid1.ravel(), grid2.ravel()]).T).reshape(grid1.shape),
             alpha = 0.75, cmap = ListedColormap(('lightblue', 'peachpuff', 'mistyrose')))
plt.xlim(grid1.min(), grid1.max())
plt.ylim(grid2.min(), grid2.max())
for key, value in enumerate(np.unique(seq2)):
    plt.scatter(seq1[seq2 == value, 0], seq1[seq2 == value, 1],
                c = ListedColormap(('mediumturquoise', 'lightsalmon', 'lightcoral'))(key), label = value)
plt.title('Test set')
plt.xlabel('LDA1')
plt.ylabel('LDA2')
plt.legend()
plt.savefig('output/2_testing.png')
plt.show()

Here we saved the visualization generated by the code as an image file named 2_testing.png in the specified folder output using plt.savefig.

Code

main.py
Data.csv
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
items = pd.read_csv('Data.csv')
label1 = items.iloc[:, 0:13].values
label2 = items.iloc[:, 13].values
from sklearn.model_selection import train_test_split
label1_train, label1_test, label2_train, label2_test = train_test_split(label1, label2, test_size = 0.2, random_state = 0)
from sklearn.preprocessing import StandardScaler
scaling = StandardScaler()
label1_train = scaling.fit_transform(label1_train)
label1_test = scaling.transform(label1_test)
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
analysis = LDA(n_components = 2)
label1_train = analysis.fit_transform(label1_train, label2_train)
label1_test = analysis.transform(label1_test)
from sklearn.linear_model import LogisticRegression
model = LogisticRegression(random_state = 0)
model.fit(label1_train, label2_train)
prediction = model.predict(label1_test)
from sklearn.metrics import confusion_matrix, accuracy_score
matrix = confusion_matrix(label2_test, prediction)
print(matrix)
score = accuracy_score(label2_test, prediction)
print(score)
from matplotlib.colors import ListedColormap
seq1, seq2 = label1_train, label2_train
grid1, grid2 = np.meshgrid(np.arange(start = seq1[:, 0].min() - 1, stop = seq1[:, 0].max() + 1, step = 0.01),
                     np.arange(start = seq1[:, 1].min() - 1, stop = seq1[:, 1].max() + 1, step = 0.01))
plt.contourf(grid1, grid2, model.predict(np.array([grid1.ravel(), grid2.ravel()]).T).reshape(grid1.shape),
             alpha = 0.75, cmap = ListedColormap(('lightblue', 'peachpuff', 'mistyrose')))
plt.xlim(grid1.min(), grid1.max())
plt.ylim(grid2.min(), grid2.max())
for key, value in enumerate(np.unique(seq2)):
    plt.scatter(seq1[seq2 == value, 0], seq1[seq2 == value, 1],
                c = ListedColormap(('mediumturquoise', 'lightsalmon', 'lightcoral'))(key), label = value)
plt.title('Training set')
plt.xlabel('LDA1')
plt.ylabel('LDA2')
plt.legend()
plt.savefig('output/1_training.png')
plt.show()
plt.clf()
from matplotlib.colors import ListedColormap
seq1, seq2 = label1_test, label2_test
grid1, grid2 = np.meshgrid(np.arange(start = seq1[:, 0].min() - 1, stop = seq1[:, 0].max() + 1, step = 0.01),
                     np.arange(start = seq1[:, 1].min() - 1, stop = seq1[:, 1].max() + 1, step = 0.01))
plt.contourf(grid1, grid2, model.predict(np.array([grid1.ravel(), grid2.ravel()]).T).reshape(grid1.shape),
             alpha = 0.75, cmap = ListedColormap(('lightblue', 'peachpuff', 'mistyrose')))
plt.xlim(grid1.min(), grid1.max())
plt.ylim(grid2.min(), grid2.max())
for key, value in enumerate(np.unique(seq2)):
    plt.scatter(seq1[seq2 == value, 0], seq1[seq2 == value, 1],
                c = ListedColormap(('mediumturquoise', 'lightsalmon', 'lightcoral'))(key), label = value)
plt.title('Test set')
plt.xlabel('LDA1')
plt.ylabel('LDA2')
plt.legend()
plt.savefig('output/2_testing.png')
plt.show()

Conclusion

In conclusion, linear discriminant analysis (LDA) demonstrates the effective classification of data into distinct categories. The LDA plots visualize the separation achieved by the model, indicating its potential to distinguish between different data categories accurately.

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