Data Science and Machine Learning (Theory and Projects) A to Z - Feature Extraction: PCA Versus SVD

The video tutorial explores the relationship between Principal Component Analysis (PCA) and Singular Value Decomposition (SVD), explaining how SVD can be used to perform PCA. It covers the mathematical foundations of SVD, including the decomposition into matrices U, D, and V, and discusses eigenvectors and eigenvalues. The tutorial also demonstrates how SVD can be applied for dimensionality reduction, highlighting its practical implementation in software like MATLAB and Python. Finally, it introduces kernel PCA as a powerful dimensionality reduction technique.

What is the relationship between PCA and SVD?

Explain the process of centering a data matrix.

What does the matrix D represent in the context of SVD?

How are the eigenvectors of Xc and Xc transpose related to the matrix U?

What happens when you truncate the matrices U and V in SVD?

Describe the significance of the singular values in PCA.

What are the practical applications of SVD in PCA?

Discuss the importance of eigenvalues in the context of PCA.

How can PCA be achieved using SVD?

What is kernel PCA and how does it relate to traditional PCA?