Course Overview
This course introduces the student to a range of topics and concepts in unsupervised machine learning including the foundation of Topological Data Analysis, dimensionality reduction and clustering. The course covers a practical machine learning algorithms which are driven by geometric or topological concepts. The algorithmic and the practical are emphasized throughout the course in an inclusive manner.
- Clustering : K-means clustering, graph based clustering, graph clustering, Hierarchical Clustering, Laplacian-based clustering
- Topological Data Analysis: Persistent homology, Mapper, Reeb graphs, Contour trees, Merge trees.
- Dimensionality reduction: PCA, MDS, ISOMAP, T-SNE, Laplacian based methods.
| Lecture | Material | |
| An introduction to Clustering | Lecture 1 | |
| Graph Algorithms | Lecture_2 | |
| KNN-graphs KD-trees | Lecture_3 | |
| Nearest Neighbors-Based Clustering and Classification Methods | Lecture_4 | |
| Hierarchical clustering | Lecture_5 | |
| Graph Laplacian | Lecture_6 | |
| Spectral Clustering | Lecture_7 | |
| DBSCAN and Graph Clustering | Lecture_8 | |
| An Introduction to Topological Data Analysis | Lecture_9 | |
| The Mapper Algorithm | Lecture_11 | |
| Contour Trees and Persistence | Lecture_12 | |
| An Introduction to Persistent Homology | Lecture_13 |
An introduction to persistent homology-II
Application of Persistent Homology
MDS and ISOMAP
Locally Linear Embedding and Spectral Embedding
Due to a popular request, I finished the course with two lectures on introduction to Deep Learning.