📚 Syllabus & Course Curriculum
Data Science & Analytics
Module-by-module breakdown of Topological Data Analysis (TDA): Persistent Homology for High-Dimensional Datasets, from foundations to a certified capstone project.
Motivation
• Structure that clustering and PCA miss, such as loops and voids
• Topological invariants and what stays true under continuous deformation
• Realistic expectations: TDA is a complement to, not a replacement for, statistics
Complexes
• Simplicial complexes, and the Vietoris-Rips and Cech constructions
• The scale parameter problem that persistence exists to solve
• Homology groups and Betti numbers as counts of connected components, loops and voids
Persistence
• Filtrations, persistence diagrams and barcodes
• Reading persistence as signal and short bars as noise, with care
• The stability theorem and why it makes the method trustworthy
Practice
• Ripser, GUDHI and giotto-tda, and the computational cost in higher dimensions
• Persistence images and landscapes to feed a machine learning model
• Bottleneck and Wasserstein distances for comparing diagrams
Application
• Case studies in transcriptomics, materials and time series via delay embedding
• Metric choice and normalisation, which change the result more than expected
• Statistical significance and avoiding topological signal read from noise
Earn government-registered certification in Topological Data Analysis (TDA): Persistent Homology for High-Dimensional Datasets
e-Certificate and e-Marksheet issued on successful completion.
