# Lecture 22 – Principal Components Analysis

Presented by Anthony D. Joseph

Content by Josh Hug, John DeNero, Sam Lau, and Suraj Rampure

The Quick Check for this lecture is due **Monday, November 23rd at 11:59PM.** A random one of the following Google Forms will give you an alphanumeric code once you submit; you should take this code and enter it into the “Lecture 22” question in the “Quick Check Codes” assignment on Gradescope to get credit for submitting this Quick Check.

Video | Quick Check | |
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22.1 Dimensionality. Visualizing high-dimensional data. |
22.1 | |

22.2 More visualizations of high-dimensional data. |
22.2 | |

22.3 Matrix decomposition, redundancy, and rank. Introduction to the singular value decomposition (SVD). |
22.3 | |

22.4 The theory behind the singular value decomposition. Orthogonality and orthonormality. |
22.4 | |

22.5 Definition and computation of principal components. Geometric interpretation of principal components and low rank approximations. Data centering. |
22.5 | |

22.6 Interpretation of singular values. The relationship between singular values and variance. Analyzing scree plots. |
22.6 | |

22.7 Introduction to principal Component analysis (PCA). PCA for exploratory data analysis. |
22.7 |