Mathematical Aspects of Data Analysis

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- Linear Algebra
- Choosing Hyperparameters

Examples

Computational examples and course demonstrations are listed below.

Python for Data Analysis

Approximate Carathéodory: averaging handwritten digits

The SVD of a collection of faces

PCA of the Iris Dataset

PCA of a collection of faces

The Ellipse Picture of the SVD

SVD: Linear vs. Nonlinear Relationships

Forecasting the Keeling Curve

The Geometry of Least Squares

Regression Is Not PCA

The Variance of Least Squares

k-Means on Handwritten Digits

k-Means: A Bad Fixed Point

k-Means vs. Spectral Clustering on Two Circles

Spectral Clustering: A Victory Lap

\(\lambda_2\) and Connectivity

\(k\)-Way Spectral Clustering as a Graph Comes Apart

The Swiss Roll: SVD vs. Spectral Embedding

Unshredding an Image with One Eigenvector

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