Chapter 6: Searching for Structure in Point Data

This chapter covers high-dimensional point statistics, including density estimation, clustering, and correlation functions.

Histogram vs Kernel Density Estimation

Example Kernels

Great Wall KDE

Great Wall Density

Comparison of 1D Density Estimators

EM example: Gaussian Mixture Models

Mixture Model of SDSS Great Wall

Comparison of 1D Density Estimators

Number of Clusters for Gaussian Mixtures

Cloning a Distribution with Gaussian Mixtures

Extreme Deconvolution example

Extreme Deconvolution of Stellar Data

EM example: K-means

Mean Shift Example

Euclidean Minimum Spanning Tree

Diagramatic Description of n-point Correlations

Angular Two-point Correlation Function