CourseSpecifications
Valid as from the academic year 2024-2025

Analysis of High Dimensional Data (C003549)

Course size
Credits 5.0(nominal values; actual values may depend on programme)
Study time 150 h

Course offerings and teaching methods in academic year 2024-2025
A (semester 1)
EnglishGent

Lecturers in academic year 2024-2025
Clement, Lieven

lectureseminarindependent workgroup work

WE02

Offered in the following programmes in 2024-2025
Master of Science in Teaching in Science and Technology(main subject Mathematics)
Master of Science in Mathematics
Master of Science in Statistical Data Analysis
Exchange Programme in Mathematics (master's level)

lecturer-in-charge
crdts
5555

offeringAAAATeaching languages
EnglishKeywords
Statistics, multivariate data analysis, high dimensional data
Position of the course
Modern high throughput technologies easily generate data on thousands of variables; e.g.
genomics, chemometrics, environmental monitoring, ... Conventional statistical methods are nolonger suited for effectively analysing such high-dimensional data. Multivariate statisticalmethods may be used, but for often the dimensionality of the data set is much larger than thenumber of (biological) samples. Modern advances in statistical data analyses allow for theappropriate analysis of such data.
Methods for the analysis of high dimensional data rely heavilly on multivariate statisticalmethods. Therefore a large part of the course content is devoted to multivariate methods, butwith a focus on high dimensional settings and issues.
Multivariate statistical analysis covers many methods. In this course, only a few are discussed.
A selection of techniques is made based on our experience that they are frequently used inindustry and research institutes (e.g. principal component analysis, cluster analysis,classification methods). Central in the course are applications from different fields (analyticalchemistry, ecology, biotechnology, genomics, …).
Contents
1. Dimension reduction: Singular Value Decomposition (SVD), Principal Component Analysis(PCA), Multidimensional Scaling (MDS) and biplots for dimension-reduced data visualisation
2. Sparse SVD and sparse PCA
3. Prediction with high dimensional predictors: principal component regression; ridge, lasso andelastic net penalised regression methods
4. Classification (prediction of class membership): (penalised) logistic regression, linear andquadratic discriminant analysis, (sparse) Fisher discriminant analysis
5. Evaluation of prediction models: sensitivity, specificity, ROC curves, mean squared error,
cross validation
6. Feature selection
7. assocation versus prediction(Approved)

18. Large scale hypoptheses testing: FDR, FDR control methods, empirical Bayes (local) FDRcontrol
9. One of the following topics (depending on the interest of the students): functional dataanalysis, cannonical correlation analysis, correspondence analysis, biclustering, factor
analysis, model based clustering, …
Initial competences
Having successfully completed the course “analysis of continuous data”, or having acquired
otherwise the corresponding competences (knowledge of the theory and practice of linear
statistical models). A good knowledge in matrix algebra is also required.
Final competences
1 The student has knowledge of methods for analysing and exploring high-dimensional data
1 sets.
2 The student can see and quantify structures in large high dimensional/multivariate datasets,
1 using the software R.
3 The student can value and interpret the statistical data analyses of high-dimensional data
1 correctly.
4 The student can correctly report the results of the data analyses according to scientific
1 standards.
5 The student can comprehensively read scientific papers related to the course content.
6 The student can take responsibility and initiative in a group effort.
Conditions for credit contract
Access to this course unit via a credit contract is determined after successful competences assessment
Conditions for exam contract
This course unit cannot be taken via an exam contract
Teaching methods
Group work, Seminar, Lecture, Independent work
Extra information on the teaching methods
Theory: 15 hours lectures and 7,5 hours guided self study (discussion of papers)
Exercises: 15 hours PC room classes and 25 hours group or individual work (assignment)
Study material
Type: Handouts
Name: open-source e-course
Indicative price: Free or paid by faculty
Optional: noLanguage : English
Available on Ufora : No
Online Available : Yes
Usability and Lifetime within the Course Unit : intensiveReferences
Efron, B. (2010). Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing andPrediction. IMS Monographs.
Efron, B., and Hastie, T. (2016). Computer Age Statistical Inference. Cambridge UniversityPress.
Hastie T., Tibshirani R. and Friedman J. (2009). The Elements of Statistical Learning. Springer.
Johnson R. and Wichern D. (2008). Applied Multivariate Statistical Analysis (6th edition).
Prentice Hall.
Ramsay J. and Silverman B. (2005). Functional Data-analysis (second edition). SpringerVerlag.
Ramsay J. and Silverman B. (2002). Applied Functional Data-analysis: Methods and Case
Studies. Springer-Verlag.
Course content-related study coaching
In the practical sessions in the PC labs the students are coached by an assistant.
Students can make an appointment to ask questions to the lecturer. Questions and answers
can be exchanged in Ufora.
Assessment moments
end-of-term and continuous assessment
Examination methods in case of periodic assessment during the first examination period(Approved)

2

Written assessment with open-ended questions
Examination methods in case of periodic assessment during the second examination period
Written assessment with open-ended questions
Examination methods in case of permanent assessment
Peer and/or self assessment, Assignment
Possibilities of retake in case of permanent assessment
examination during the second examination period is possible in modified form
Extra information on the examination methods
Theory and exercises: periodical evaluation (open book, written exam with open-endedquestions) and non-periodical evaluation (2 homework assignments and 1 project assignment).
Calculation of the examination markTheory and exercises: periodical evaluation (50%) and non-periodical evaluation (1 homeworkassignment1 (12.5%) and 1 project assignment (37.5%)).
To pass for this course, the student must pass for both the periodical and the non-periodicalevaluation.
If the student fails for this course in the first examination period and if he/she wants a retake inthe second examination period, the non-periodical evaluation will be presented in a revised
form in the second examination period.
Peer assessment is used to correct the marks for the project assignment so as to provide amore representative score for the student’s individual contribution. A student’s individual score
for the project work will at most deviate 20% of average score for the group. 20% of the scoreof the project will be based on a report that is used to evaluate the process that student went
through to arrive at the result (focus on the skills to participate in a group effort).

(Approved)3