Principal Component Analysis - Lecture 8

Dive into the world of Principal Component Analysis in this 55-minute lecture from MIT's Computational Thinking course. Explore key concepts such as matrix rank, data cloud size measurement using statistics, and the Singular-Value Decomposition (SVD). Learn how to transform images into data, understand the effects of noise, and measure data set width. Discover techniques for rotating axes and data, and delve into higher dimensions. Gain insights into correlated data, standard deviation, and rotations in 300 dimensions. Follow along with timestamped sections for easy navigation through topics like understanding data, matrix rank, and the SVD. Enhance your computational thinking skills and grasp fundamental principles of data analysis in this comprehensive lecture from The Julia Programming Language.

Syllabus

Introduction: Understanding data.
Rank of a matrix.
Matrix rank.
Effect of noise.
From images to data.
Measuring data cloud "size" – using statistics.
Measuring a "width" of a data set.
Root-mean-square distance: Standard deviation.
Correlated data.
Rotating the axes.
Rotating the data.
Higher dimensions.
What is the Singular-Value Decomposition (SVD)?.
Rotations in 300 dimensions.