LDA linear discriminant analysis skills in Python

LDA (Linear Discriminant Analysis) is a classic linear discriminant analysis method. Its main purpose is to project the original data into a low-dimensional space and maximize the inter-class distance and minimize the intra-class distance. In Python, we can leverage the Scikit-learn package to implement the LDA trick.

LDA techniques can be applied to many practical problems, such as image classification, face recognition, text classification, etc. In this article, we will briefly introduce the principles of LDA and the steps to use it for classification in Python.

1. The principle of LDA

The goal of LDA is to maximize the distance between each category while minimizing the distance within each category. In classification problems, we want to find a low-dimensional representation that maximizes the distance between data in different categories and minimizes the distance between data within the same category.

Using LDA techniques to achieve this goal, we need to follow the following steps:

• Calculate the mean vector for each category.
• Calculate the dispersion matrix, including the scatter matrix within and between categories.
• Calculate the common scatter matrix of the data set.
• Calculate the projection vector and project the data.

In short, the goal of the LDA technique is to find a projection matrix that maps high-dimensional data into a low-dimensional space and preserves inter-category distances and intra-category distances.

2. Using LDA for classification in Python

In Python, we can use LDA techniques for classification through the Scikit-learn package.

First, we need to import the module:

from sklearn.discriminant_analysis import LinearDiscriminantAnalysis

Then, we need to prepare training data. Suppose we have an image classification problem, we can use the following code to load the training data:

from sklearn.datasets import fetch_olivetti_faces

data = fetch_olivetti_faces().data

targets = fetch_olivetti_faces().target

Next, we can use the following code to split the data into a training set and a test set:

from sklearn.model_selection import train_test_split

X_train , =2)

X_train_lda = lda.fit_transform(X_train, y_train)

Finally, we can use the following code to train the classifier and make predictions on the test data:

from sklearn.neighbors import KNeighborsClassifier

knn = KNeighborsClassifier()

knn.fit(X_train_lda, y_train)

X_test_lda = lda.transform(X_test)

accuracy = knn.score(X_test_lda, y_test)

print("Accuracy:", accuracy)

In this simple model, we use the KNN classifier for classification, and A fairly high accuracy rate was obtained on the test data.

Summary

LDA technique is a powerful linear discriminant analysis method that can be applied to many practical problems. In Python, we can implement the LDA trick through the Scikit-learn package and use it in classification problems. Whether you are doing image classification, face recognition, text classification, etc., LDA techniques can help you obtain better classification results.

The above is the detailed content of LDA linear discriminant analysis skills in Python. For more information, please follow other related articles on the PHP Chinese website!