pca code in python from scratch
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principal component analysis (pca) is a dimensionality reduction technique widely used in machine learning and data analysis. in this tutorial, we'll walk through the process of implementing pca from scratch in python. we'll use numpy for numerical operations and matplotlib for visualization.
let's create a sample dataset to demonstrate pca. for simplicity, we'll generate random data with two features.
standardizing the data ensures that each feature has a mean of 0 and a standard deviation of 1. this step is crucial for pca.
next, we calculate the covariance matrix for the standardized data.
now, we find the eigenvalues and eigenvectors of the covariance matrix.
sort the eigenvalues in descending order and select the top k eigenvectors.
project the standardized data onto the selected principal components.
plot the original data and the data after pca to visualize the dimensionality reduction.
this simple tutorial demonstrates the basic steps to implement pca from scratch in python. you can adapt this code to work with larger datasets and explore the benefits of dimensionality reduction in various machine learning applications.
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