Understanding POD: the Proper Orthogonal Decomposition

This was a lot of fun to make! 3blue1brown has inspired me a lot to make a math video with cool animations! This is my take on the Proper Orthogonal Decomposition, an incredibly powerful and useful algorithm for data analysis ! I'm a fluid dynamicist by trade, so my examples come from there. Hope you found this useful! This was produced with Manim, a python library developed by 3blue1brown and maintained by the community to make mathematical animation videos! Thanks to all contributors for making this possible! 0:00 Intro 0:29 2D Measurements 1:34 Optimal basis vectors 3:14 Basis vectors in 3D 3:55 Higher dimensional data 4:44 Building the data matrix A 5:10 Formal definition of POD 6:34 The spatial mode matrix U 7:18 The energy matrix Sigma 7:45 The temporal mode matrix V 8:06 A simple traveling wave example 10:06 My take on interpretation of POD modes