# Lecture 23 – Principal Components Analysis

Presented by Anthony D. Joseph

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

A reminder – the right column of the table below contains *Quick Checks*. These are **not** required but suggested to help you check your understanding.

Video | Quick Check | |
---|---|---|

23.0 Announcements. |
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23.1 Dimensionality. Visualizing high-dimensional data. |
23.1 | |

23.2 More visualizations of high-dimensional data. |
23.2 | |

23.3 Matrix decomposition, redundancy, and rank. Introduction to the singular value decomposition (SVD). |
23.3 | |

23.4 The theory behind the singular value decomposition. Orthogonality and orthonormality. |
23.4 | |

23.5 Definition and computation of principal components. Geometric interpretation of principal components and low rank approximations. Data centering. |
23.5 | |

23.6 Interpretation of singular values. The relationship between singular values and variance. Analyzing scree plots. |
23.6 | |

23.7 Introduction to principal Component analysis (PCA). PCA for exploratory data analysis. |
23.7 |