Linear Algebra for Data Science

2021/2022

Academic Year

ENG

Instruction in English

5

ECTS credits

Delivered at:

Big Data and Information Retrieval School

Course type:

Elective course

When:

1 year, 1, 2 module

Instructors

Piontkovski, Dmitri

Chernyshev, Vsevolod L.

Course Syllabus

Abstract

In the lecture course, we consider some topics of linear algebra beyond the standard first year course which are extremely important for applications. Mostly, these are applications to data analysis and machine learning, as well as to economics and statistics. We begin with inversions of rectangle matrices, that is, we discuss pseudo-inverse matrices (and their connections to the linear regression model). Among others, we discuss iteration methods (and their using in models of random walk on a graph applied to Internet search such as PageRank algorithm), matrix decompositions (such as SVD) and methods of dimension decreasing (with their connection to some image compression algorithms), and the theory of matrix norms and perturbation theory (for error estimates in matrix computations). The course includes also symbolic methods in systems of algebraic equations, approximation problems, Chebyshev polynomials, matrix functions such as exponents etc. We plan to invite some external lecturers who successfully apply linear algebra in their work. The students are also be invited to give their own talks on additional topics of applied or theoretical linear algebra.