The main goal of the course is to understand basic concepts of numerical linear algebra and where such computations arise in data science applications. The focus is on developing an understanding of the mathematical foundation of techniques in informatics and data science and informatics. The goal is also to gain practical experience via basic programming examples and to become familiar with recent research topics in the area.

Students will complete short assignments given periodically throughout the semester (possibly including, but not limited to, simple programming assignments and written summaries of research articles) as well as a final exam.

G. Strang, Linear Algebra and Learning From Data, 2019.

A. Blum, J. Hopcroft, and R. Kannan. Foundations of Data Science.

J. Grus. Data Science from Scratch: First Principles with Python, O’Reilly Media, 2015.

G. Strang, Linear Algebra and Its Applications, Thomson/Brooks Cole.

B. Steele, J. Chandler, S. Reddy. Algorithms for Data Science, Springer, 2016.

J. Brownlee. Basics of Linear Algebra for Machine Learning, 2018.

G. Strang, Linear Algebra and Learning From Data, 2019.

A. Blum, J. Hopcroft, and R. Kannan. Foundations of Data Science.

J. Grus. Data Science from Scratch: First Principles with Python, O’Reilly Media, 2015.

G. Strang, Linear Algebra and Its Applications, Thomson/Brooks Cole.

B. Steele, J. Chandler, S. Reddy. Algorithms for Data Science, Springer, 2016.

J. Brownlee. Basics of Linear Algebra for Machine Learning, 2018.

The final exam will consist of an oral exam given during the scheduled exam period. In case of distance learning, the exam will be adapted to a distance format.

1. Matrix representations and matrix decompositions

2. Eigenvalue decomposition, least squares regression, singular value decomposition

3. Numerical linear algebra in data science applications

a. principal component analysis, low-rank approximation and compression

b. clustering and classification

c. Pagerank and semantic indexing

d. non-negative matrix decomposition

4. Current research directions and applications

1. Matrix representations and matrix decompositions

2. Eigenvalue decomposition, least squares regression, singular value decomposition

3. Numerical linear algebra in data science applications

a. principal component analysis, low-rank approximation and compression

b. clustering and classification

c. Pagerank and semantic indexing

d. non-negative matrix decomposition

4. Current research directions and applications

As a preliminary we assume to have basic knowledge of linear algebra as, for example, from the course NMAG101 and experience in programming.