Elements of linear algebra and algorithmics for data analytics

This course is aimed at training participants in conceptual and theoretical elements for addressing machine learning. Particularly, the area of pattern recognition studied from a linear algebra and functional analysis point of view. In addition, some recommendations are given for the typesetting and presentation of scientific articles in this area.

Find full course material here.

Lecture I: Elements of linear algebra

Vector and vector spaces

Notation of vectors and matrices

Euclidean and Hilbert spaces

Linear transformation, inner product, and norm

Base, linear independence, orthogonality, rank and vector space span

Eigenvalues ​​and eigenvectors

Lecture II: Data representation and classification

General scheme of pattern recognition

Outlier, relevance analysis and variable transformation

Feature extraction and selection

Classification and clustering

Optimization of quadratic forms: Application in PCA and SVM

Heuristics: K-means and generic center-based clustering

Lecture III: Equation interpetation and algorithm writing

Recommendations for writing and interpreting equations

Recommendations for the formulation of pseudocodes

Advanced topics of scientific text editors

Writing and translation of scientific articles: Practical example