Data Analysis

Teacher(s)

Segers Johan;

Language

French

Main themes

The course presents an overview of the main tools of exploratory multivariate data analysis via factorial methods. The data is projected onto a low-dimensional subspace while retaining maximum information. This reduction in dimension facilitates visualization and aids in the discovery of information and patterns in a data table.

• Reminders of algebra and geometry useful for data analysis
• Basic principles of factorial methods
• Principal component analysis
• Classification: moving averages and hierarchical classification
• Linear discriminant analysis
• Simple and multiple correspondence analysis
• Principal component regression
• Partial least squares regression

Learning outcomes

At the end of this learning unit, the student is able to :
1	General objectives. Presentation of the modern techniques for the analysis of huge multivariate data sets. Developing the basic tools for " data mining ". Specific objectives. At the end of this course, the students should be able to: - Manipulate and describe the information contained in huge data sets; - Understand why such or such method is appropriate; - Give a correct interpretation of the resulting pictures and of the output of the software; - Solve problems with real data sets.

Content

• Data matrices
• Principal component analysis
• Classification: k-means clustering and hierarchical clustering
• Linear discriminant analysis
• Simple and multiple correspondence analysis
• Principal component regression
• Partial least squares regression

Implementation of the methods is done in the R language using the RStudio integrated development environment, and the R Markdown framework is used to combine text, mathematical formulas, R code and R output (tables, graphs).

Teaching methods

During the lectures, the teacher presents the various statistical methods, covering the questions and data-sets to which they apply, the underlying mathematical theory, and how to program them in R. Homework assignments are given, the solution of which is discussed in the lectures too.
The tutorials take place in computer rooms and have as primary objective to allow the students to train themselves in applying the method on real data-sets in R.

Evaluation methods

Exam (12/20):

• written, closed book, with the help of a formula list and a pocket calculator
• exercises and questions involving (small) calculcations, interpretation of computer output, and understanding of the main results and formulas

Tests during the lectures:

• Test 1: Data matrices and principal component analysis
• Test 2: Clustering and linear discriminant analysis

Participation is optional. At the discretion of the student, each test can replace the part of the exam on the same topic.
Project (8/20):

• individually or in pairs
• data application, the data being sought by the students themselves
• written report, to be submitted at a date or at dates specified during the semester
• detailed instructions will be provided in the exercise sessions and on the MoodleUCL course page

Submitting a projet is a necessary requirement in order to participate at the exam and obtain an exam result. At a second exam inscription, a new project can be resubmitted.

Other information

Prerequisities:

• vector and matrix calculus
• Euclidean geometry: points, spaces, orthogonality, distances, angles
• basic notions in statistiques: sample mean, (co)variance, correlation, covariance matrix, conditional probabilities, normal distribution, chi-square distribution

Online resources

All teaching material is made available through the MoodleUCL cours page: slides, exercises, software scripts. In addition, links to interesting external material are given too: on-line courses, videos, software documentation.

Bibliography

• Escofier, B. et Pagès, J. (2016): Analyses factorielles simples et multiples, 5e édition, Dunod, Paris.
• Lebart, L., Piron, M. et Morineau, A. (2006): Statistique exploratoire multidimensionnelle, 4e édition, Dunod, Paris.
• Saporta, G. (2011): Probabilités, analyse des données et statistique, 3e édition révisée, Editions TECHNIP, Paris.

Teaching materials

• matériel sur moodle

Faculty or entity

LSBA