Master 2024/2025

Geometrical Methods of Machine Learning

Type: Elective course (Math of Machine Learning)

When: 1 year, 4 module

Open to: students of one campus

Language: English

Course Syllabus

Abstract

Many machine learning problems are fundamentally geometric in nature. The general goal of machine learning is to extract previously unknown information from data, which is reflected in the structure (underlying geometry) of the data. Thus, understanding the shape of the data plays an important role in modern learning theory and data analytics. Real-world data obtained from natural sources are usually non- uniform and concentrate along lower dimensional structures, and geometrical methods allow discovering the shape of these structures from given data. Originally being part of dimensionality reduction research, geometrical methods in machine learning has now become the central methodology for uncovering the semantics of information from the data. The aim of the course is to explain basic ideas and results in using the modern geometrical methods for solving main machine learning problems such as classification, regression, dimensionality reduction, representation learning, clustering, etc. A large part of the course addresses to most popular geometrical model of high- dimensional data called manifold model and introduces modern manifold learning methods. Necessary short information on differential geometry and topology will be given in the course. The course lets students to be involved in meaningful real-life machine learning projects, such as mobile robot navigation, neuroimaging, to cope with challenging problems.