The main goal of the course is to explain the main concepts of linear algebra that are used in data analysis and machine learning. Another goal is to improve the student’s practical skills of using linear algebra methods in machine learning and data analysis. 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 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.
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.
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.
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.
In this week we will apply the acquired knowledge about linear regression and SVM models in this final project.