Mathematical Aspects of Data Analysis

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Lecture Notes

Lecture notes and accompanying material are listed below.

The Basics of CQC Data

Variances and Caratheodory

Finishing up Caratheodory, and then the SVD

Finishing the SVD Derivation, and Truncation

How Low Can You Go: Eckart-Young

Projections and the Principal Component Analysis

Linear Regression and Least Squares

The Statistics of Least Squares

Gauss-Markov and the Bias-Variance Tradeoff

Ridge Regression

PageRank

k-Means Clustering

Graphs and the graph Laplacian

Spectral embeddings and spectral clustering

Midterm Review

Normalized cuts

Nonlinear dimension reduction

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