MAT 6493 - Geometric Data Analysis - Fall 2022 UdeM
UdeM MAT 6493

MAT 6493

Geometric Data Analysis

Fall 2022

Guy Wolf (guy.wolf@umontreal.ca)


Modern data analysis methods are expected to handle massive amounts of high dimensional data that are being collected in a variety of domains. The high dimensionality of such data introduces numerous challenges, typically referred to as the "curse of dimensionality", which render traditional statistical learning approaches impractical or ineffective for their analysis. To cope with these challenges, significant effort has been focused on developing geometric data analysis approaches that model and capture the intrinsic geometry of processed data, rather than directly modeling their distribution. In this course we will explore such approaches and provide an analytical study of the models and algorithms they use. We will start by considering supervised learning and distinguish classifiers that are based on geometric principles from posterior and likelihood estimation approaches. Next, we will consider the unsupervised learning task of clustering data and contrast approaches based on density estimation from ones that rely on metric spaces or graph constructions. Finally, we will consider more fundamental tasks in intrinsic representation learning, with particular focus on dimensionality reduction and manifold learning, e.g., with diffusion maps, tSNE, and PHATE. Time permitting, we will include guest talks on research areas related to the course, and discuss recent developments in graph signal processing and geometric deep learning.

This is a graduate-level 4 credit course at UdeM, available also via the ISM. It is suitable for CS, statistics, and applied math students interested in data science and machine learning.


Meetings

Lectures:

Mondays, 4186 Pav. Andre-Aisenstadt, from 13h30 to 17h20 (officially, but possibly ending early depending on pace & covered materials)

Office Hours:

By request on MS Teams with possibility to set an in-person meeting if necessary.

Textbooks

No required textbook, but the following books were used when preparing some (although not all) of the course materials: Other course materials are based on research papers that will be cited in the course slides.

Topics:

Slides will be made available on MS Teams and are designed to be sufficient for studying the course even without regularly attending class.

Guest speakers (covering specialised topics of interest):


Final grade composition:

The final grade in this class will be based on three components:

Final projects:


Literature review:


Homework:

While discussion between students is not discouraged, homework are meant to be done & submitted individually.