Data analysis of large data sets is increasing in importance as a new tool in many fields in science and technology. This course gives an introduction to the use of many efficient numerical algorithms used in the analysis of large amounts of data. In particular we consider algorithms for low-rank approximations, clustering and fast manipulation of structured matrices. We use mathematical and numerical tools to study problems and algorithms.

Course overview

The course is divided into three blocks, with 4-5 lectures and one homework per block. In each block there is also a series of video quizzes which are mandatory to do. Details about lectures, video quizzes, reading material and recommended exercises are found under the links below.

Block 1: Low-rank data algorithms
Block 2: Numerical algorithms for clustering
Block 3: Structured matrices in data analysis

Before the course starts we recommend that you review the linear algebra summarized in Background material on linear algebra and also do the quiz: Background linear algebra.

Teachers

Olof Runborg, lectures, examiner
Vilhelm Peterson Lithell, teaching assistant

Homework

There are three homework assignments, one for each course block. They should be done in groups of one or two persons. The exercises involve both implementations of numerical methods and some analysis. The exercise texts will be available as PDF files below.

Homeworks should be handed in before the deadlines specified below. Each homework submitted by the deadline will give you one bonus point on the exam. (The point is added to your exam score.) Incorrect, or poorly written, homeworks have do be redone, and will not yield a bonus point.

The exercises are preferably done in Matlab. They are mostly designed with this in mind and occasionally require the use of certain Matlab built-in functions. However, you can also use e.g. Julia, if you prefer. Here is a link with some assistance using Julia in the course. KTH students can install Matlab on their own computers via KTHs programvarunedladdning.

Homeworks should be submitted in Canvas under Assignment/Homework X. Both a PDF with solutions to the problems and your Matlab/Julia code should be uploaded. Before submitting, you need to sign up to one of the Homework groups, together with your group partner if your work in pairs. You find the groups under the menu People. They are called "HWX group YY" where X is the homework number and YY is the group number. Even if you work on your own you need to submit as a Canvas group. (There is one group set per exercise, but by default you will be signed up with the same group members for later exercises as for the first one, so unless you want to change groups, you will only need to sign up once.)

Note: Please submit as a group even if Canvas allows you to submit without joining a group. Otherwise it will not be possible for the teacher to provide feedback.

The homework texts and data files are found below:

Homework 1 (deadline Feb 4)

Files and links for the homework (coming soon)

Homework 2 (deadline 16/2)

Files and links for the homework (coming soon)

Homework 3 (deadline 2/3)

Files and links for the homework (coming soon)

Note:

Bonus points expire after the re-exam and cannot be used next year.
If you have not completed the homework one week after the exam, you will have to do the non-completed homeworks next year/round

OBS! Each group should solve the problems independently. Both group members should contribute equally to the work and understand all parts of the submitted solution. Although you can discuss issues with other groups, all code and reports must be written by yourself, from scratch (and e.g. not based on a stub given to you). In particular, it is strictly forbidden to copy code from or to share code files with another group. Furthermore, see rules about generative AI below.

Note also the general ethical approach at KTH:

All members of a group are responsible for the group's work.
In any assessment, every student shall honestly disclose any help received and sources used.
Every student shall be able to present and answer questions about the entire assignment and solution.

Course literature

The literature consists of a number of lecture notes and extracts from books. For reading instructions, see the course overview links above.

Background material on linear algebra, by Elias Jarlebring
Block 1
- Lecture notes on low-rank data algorithms, by Elias Jarlebring
- Lecture notes on fast algorithms for big data, by Per-Gunnar Martinsson
- Extract about SVD, from the book Matrix Computations, by Gene Golub and Charles van Loan
Block 2
- Lecture notes on numerics for graphs and clustering, by Elias Jarlebring
- Tutorial on spectral clustering, by Ulrike von Luxburg
Block 3
- Lecture notes on structured algorithms for structured matrices, by Elias Jarlebring
- Extract about Toeplitz matrices, from the book Matrix Computations, by Gene Golub and Charles van Loan
- Extract about fast algorithms for rank-structured matrices, from the book Fast direct solvers for elliptic PDEs, by Per-Gunnar Martinsson
- Extract about the fast Fourier transform, from the book Numerical methods in matrix computations, by Åke Björck

Other material

Applications of low-rank approximations

Examination

To finish the course you need to:

Complete Homework 1,2,3 not later than one week after the exam (corresponds to ladok LABA).

Complete all video quizzes (see course overview links above) not later than one week after the exam (the CANVAS-deadlines are recommendations).
Pass the exam

Old exams

Generative AI

Generative AI is not allowed, with some exceptions in the programming part of the assignments.