Programme Parameters
Graduate / Intermediate
3 Days (4.5 Hrs)
Online (e-LMS)
• A basic understanding of the subject area and fundamental programming or scientific concepts.
• A laptop or desktop with a stable internet connection.
• Willingness to complete assignments and the capstone project.
About This Course
Topological Data Analysis (TDA) teaches a powerful, mathematically grounded lens on data: studying its shape. You build intuition for the core idea of persistent homology — tracking how connected components, loops and voids appear and disappear across scales — and learn to compute and read persistence diagrams and barcodes. The course connects the theory to practice with tools such as GUDHI, Ripser and Giotto-TDA, and applications where TDA reveals structure that traditional methods miss, from biology to sensor data. You finish able to apply TDA to a high-dimensional dataset. A verified e-Certificate of competency and e-Marksheet from the Deep Science & Technology Consortium.
🎯 Program Aim
This course covers topological data analysis — using persistent homology and related methods to uncover shape, structure and features in complex, high-dimensional datasets.
📋 Course Objectives
1. Explain simplicial complexes and persistent homology.
2. Compute and interpret persistence diagrams and barcodes.
3. Use TDA tools such as GUDHI, Ripser and Giotto-TDA.
4. Combine TDA features with machine learning.
5. Apply TDA to a high-dimensional dataset.
👥 Who Should Enroll?
• Data scientists and applied mathematicians
• Researchers with complex, high-dimensional data
• ML practitioners seeking new features
• Students of computational topology
🚀 Key Learning Outcomes
• The ability to apply topological data analysis.
• A TDA project on real data.
• A new lens on high-dimensional structure.
• A verified e-Certificate of competency and e-Marksheet from the Deep Science & Technology Consortium.
💎 What You'll Gain
Live & Recorded Sessions
Lifetime access to class recordingse-Certificate on Completion
Cryptographically verified credentialPost-Programme Support
Direct access to mentors & councilHands-On Experience
Notebooks, real-world code & datasetsCurriculum Outline
Why Shape
• 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
From Point Cloud to Topology
• 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
The Central Construction
• 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
Computation and Vectorisation
• 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
Using It on Real Data
• 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
Technical Specifications
| Parameter | Requirement |
|---|---|
| Covered Tool / Platform | Python |
| Covered Tool / Platform | Pandas |
| Covered Tool / Platform | NumPy |
| Covered Tool / Platform | Matplotlib |
| Covered Tool / Platform | Seaborn |
| Covered Tool / Platform | Tableau |
| Covered Tool / Platform | SQL |
Frequently Asked Questions
Scholar Feedback & Reviews
Based on 0 scholar submissions
Rating Breakdown
No verified reviews published yet. Be the first to share your academic experience.
Leave Scholar Feedback
Your rating will help prospective scholars. Ratings below 3 stars are routed privately to the faculty mentor for immediate response.
