Principle factor analysis examples in Python

In the fields of data analysis and machine learning, Principal Component Analysis (PCA) is a commonly used linear dimensionality reduction algorithm. PCA reduces the dimensionality of the data by finding the principal components of the data, thereby improving the interpretability and computational efficiency of the data. This article will illustrate the principles and applications of PCA through a Python example.

First, we need to import Python related libraries, such as numpy, matplotlib, pandas, sklearn, etc.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA

Next, we load the data. Here we use the Iris data set, which is a standard classification and clustering data set, including three varieties of iris. We use the read_csv() function in the pandas library to read this data set:

data = pd.read_csv('iris.csv')

Now, we need to normalize the data. Since PCA is calculated based on the covariance matrix of the data, the size and order of the covariance matrix are determined by the amount of variation in the data. Therefore, we need to normalize the range of all features to the same size before performing PCA analysis. We can use sklearn's StandardScaler to achieve standardization.

scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)

Next, we can use the cov() method in numpy to calculate the covariance matrix of the data, which will serve as the input to the PCA algorithm.

cov_matrix = np.cov(data_scaled.T)

Now, we can use the PCA class to find the principal components of the data. We can set the number of principal components to retain. Typically, we choose to retain a smaller number of principal components than the number of original features. In this example we will keep 2 principal components.

pca = PCA(n_components=2)
principal_components = pca.fit_transform(data_scaled)

Now, we can use matplotlib to plot the results of PCA. The resulting graph is displayed in a two-dimensional coordinate system, where the different color of each iris indicates the species to which it belongs. In this graphic, we can see different types of iris flowers spread in different directions.

plt.figure(figsize=(8,6))
plt.scatter(principal_components[:,0], principal_components[:,1], c=data['species'])
plt.xlabel('Principal Component 1')
plt.ylabel('Principal Component 2')
plt.show()

Through this example, we can see the working principle and application of principle factor analysis. PCA is a very useful technique that can be used in many fields such as data visualization, noise filtering, feature extraction, and data compression. Therefore, PCA is an indispensable tool in the field of data analysis and machine learning.

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