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.

Mikhail Kuznetsov contributed some awesome course notes one can use to prepare for the exam.

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)