syllabus_604_22.pdf
OUTLINE OF MATERIAL
The goal of this course is to present in detail the fundamental mathematical ideas
behind the data science concepts.
- Introduction to Data Science and Big Data.
- Review of elementary statistics and Exploratory Data Analysis.
- Some relevant concepts from geometry and topology.
- Overview of classi cation methods; Metric learning and nearest neighbor
search; voting. - Kernel methods, Mercer’s theorem, and Support Vector Machines.
- Multi-class classi cation methods.
- Training, testing, validation; Cross-validation.
- Clustering vs classi cation techniques; k-means.
- Frame theory and dictionaries.
- Elementary spectral graph theory, minimum and maximum graph cuts, graph
partitions. - Principal Component Analysis.
- Laplacian Eigenmaps, manifold learning and dimension reduction concepts.
