These are seminar materials for the Geometric Methods in Machine Learning course (Spring 2024) by Prof. A.V. Bernstein at Sk. Materials were prepared by Oleg Kachan.
| Seminar notebook | Theme(s) |
|---|---|
| Sem1 | Principal Component Analysis (PCA) |
| Sem2 | Independent Component Analysis (ICA) |
| Sem3 | Intrinsic dimension estimation Based on paper: Levina, Bickel (2004), Maximum Likelihood Estimation of Intrinsic Dimension |
| Sem4 | Nonlinear Dimensionality Reduction 1) Kernel PCA: Gaussian, polynomial, cosine, graph kernels 2) Metric Multidimensional Scaling (MDS) 3) Isomap 4) Locally Linear Embeddings (LLE) 5) Laplacian Eigenmaps (LE) 6) Local Tangent Space Alignment (LTSA) 7) non-Euclidean distance mods: p-Wasserstein |
| Sem5 | Topological Data Analysis (TDA) 1) Simplicial homology, Betti numbers 2) Persistent diagrams, Wasserstein distance on them and stability 3) Persistent homology (PH) of graphs 4) Vectorization of topological features: Persistent images, Betti curves 5) Persistent homology of digital images (Obayashi, Hiraoka – https://arxiv.org/abs/1706.10082) 6) Deep sets (Zaheer, Kottur, Ravanbakhsh, Poczos, Salakhutdinov, Smola – https://arxiv.org/abs/1703.06114) |