TILM3632 Introduction to Dimension Reduction (5 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Grading scale:
0-5
Description
Dimension reduction techniques are crucial for analyzing high-dimensional data in statistics and machine learning. These methods reduce data complexity while preserving its essential structure, enabling better visualization, interpretation, and computational efficiency.
This course introduces unsupervised and supervised linear dimension reduction techniques and provides a brief overview of nonlinear methods and approaches for complex data structures. Students will explore the mathematical foundations and practical applications of variety of such dimension reduction methods.
Learning outcomes
After the course, the student
- understands the role and importance of dimension reduction in high-dimensional data analysis,
- explains the mathematical principles of unsupervised dimension reduction techniques such as PCA,
- demonstrates a basic understanding of supervised dimension reduction methods,
- gains familiarity with nonlinear dimension reduction approaches,
- recognizes the challenges of applying dimension reduction to complex data structures,
- selects appropriate dimension reduction methods based on the characteristics of a given dataset,
- applies the studied dimension reduction methods in practice using R,
- is able to interpret and communicate the results of dimension reduction analyses effectively.
Additional information
This course replaces TILM3611 Multivariate Analysis, Advanced Course (TILM3611 Monimuuttujamenetelmien jatkokurssi). The course is organized jointly with the University of Helsinki (Statistics).
Description of prerequisites
TILM3704 Monimuuttujamenetelmät (TILM3704 Multivariate Analysis) and its prerequisites, or equivalent studies, and basic proficiency in R.