First Steps in Linear Algebra for Machine Learning

You will learn the fundamentals of working with data in vector and matrix form, acquire skills for solving systems of linear algebraic equations and finding the basic matrix decompositions and general understanding of their applicability.

This online course is suitable for you if you are not an absolute beginner in Matrix Analysis or Linear Algebra (for example, have studied it a long time ago, but now want to take the first steps in the direction of those aspects of Linear Algebra that are used in Machine Learning). Certainly, if you are highly motivated in study of Linear Algebra for Data Sciences this course could be suitable for you as well.

This Course is part of HSE University Master of Data Science degree program.

The course takes place on the platform of the Higher School of Economics. 

The course consists of 4 weeks. Each week contains video lectures, tests and materials for independent study. At the end of the course the practical project awaits you.

1. Systems of linear equations and linear classifier

In the first week we provide an introduction to multi-dimensional geometry and matrix algebra. After that, we study methods for finding linear system solutions based on Gaussian eliminations and LU-decompositions. We illustrate the methods with Python code examples of matrix calculations.

2. Full rank decomposition and systems of linear equations

The second week is devoted to getting to know some fundamental notions of linear algebra, namely: vector spaces, linear independence, and basis. Next, we will discuss what a rank of a matrix is, and how it could help us decompose a matrix. In addition, we will talk about the properties of a set of solutions for a system of linear equations. At the end of this week we will apply this theory to a scanned document processing.

3. Euclidean spaces

In the third week, we firstly introduce coordinates in an abstract vector space. This allows us to apply the usual matrix arithmetic to abstract vectors. Next, we discuss the concept of Euclidean space which allows us to measure distances and angles in vector spaces. Then we use these measures in the least squares method to find approximate solutions of linear systems and in the linear regression model based on it. Finally, we describe the core of the most common linear classifier called Support Vector Machine.

4. Final Project

In this week we will apply the acquired knowledge about linear regression and SVM models in this final project.

• main concepts of linear algebra that are used in data analysis and machine learning
• practical skills of using linear algebra methods in machine learning and data analysis.