Extensions to Exchangeability: Statistical Analysis of Network Data

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Homology and the fundamental group

Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.

Simplicial Sets: Introduction and Products

Introduces simplicial sets and explores the construction of products with a geometric interpretation.

Clustering: Unsupervised Learning

Covers clustering algorithms, evaluation methods, and practical applications in machine learning.

Dimensionality Reduction: PCA and LDA

Covers dimensionality reduction techniques like PCA and LDA, clustering methods, density estimation, and data representation.

Clustering: Unsupervised Learning

Explores clustering in high-dimensional space, covering methods like hierarchical clustering, K-means, and DBSCAN.

Supervised Learning Overview

Covers CNNs, RNNs, SVMs, and supervised learning methods, emphasizing the importance of tuning regularization and making informed decisions in machine learning.

Simplicial Homology: Examples

Explores examples of simplicial homology by equipping known topological spaces with delta complex structures.

Clustering Algorithms: K-Means vs Spectral Clustering

Compares K-Means and Spectral Clustering algorithms, highlighting their differences and practical applications in clustering student behaviors.

Simplices

Covers the concept of simplices in delta complexes and explains the standard n-simplex and the ordering of vertices.

Graph Statistics: Random Graphs, Graph Homomorphisms, and Network Analysis

Explores graph statistics, random graph generation, network analysis, centrality measures, and clustering coefficients.