Extensions to Exchangeability: Statistical Analysis of Network Data

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 2 of 4

Excision: An Example

Covers the concept of excision in algebraic topology with a focus on simplicial and singular homology.

Homology Groups: Basics

Introduces reduced homology groups and explains their properties and applications in topology.

Natural Examples of Simplicial Sets

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

Network clustering

Explores network clustering, spectral clustering, k-means algorithm, eigenvalue properties, block model estimation, and structural similarity measurement.

Unsupervised Learning: Clustering Methods

Covers unsupervised learning focusing on clustering methods and the challenges faced in clustering algorithms like K-means and DBSCAN.

Nerves and Geometric Realization

Covers the explicit computations of nerves of categories and geometric realisations of simplicial sets.

Introduction to simplicial sets: Simplicial sets

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Clusters and Communities

Explores clustering, community detection, K-means, GMM, modularity, and the Louvain method.

Adjunction between Simplicial Sets and Enriched Categories

Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.