PCA Derivation | Unsupervised Learning for Big Data

Principal Component Analysis features so prominently in the world of data analysis that it's been re-discovered several times under different names in different fields. Here, we present one derivation which begins with the motivation of maintaining the maximal information in a small number of dimensions and uses Lagrange multipliers to solve a linear optimization problem. This is a part of a series of lectures from the Yale class "Unsupervised Learning for Big Data", taught by Professor Smita Krishnaswamy. Unsupervised learning is perhaps the most beautiful and most frequently astonishing area of machine learning. It doesn't need to guzzle tons of labeled data to solve problems by brute force. Instead, it uses elegant mathematical principles to understand (in some sense) the data itself and the patterns underlying it. Because this is a young field, there's no established textbook. The field of unsupervised learning is a collection of methods, and this course is an introduction to several of the most useful techniques, grounded in an intuitive understanding of the principles underlying them. The tools from this class have been applied to an incredible range of problems, from molecular biology, to financial modeling, to medicine and even astrophysics. We're making these lectures publicly available in an effort to make it easier for anyone to make use of these powerful and elegant techniques in their own research. To learn more about the Krishnaswamy Lab's work, visit krishnaswamylab.org