
Course unit
MATHEMATICAL MODELS AND NUMERICAL METHODS FOR BIG DATA
SCP7079406, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/08 
Numerical Analysis 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

Background on Matrix Theory: Type of matrices: Diagonal, Symmetric, Normal, Positive De nite; Matrix canonical forms: Diagonal, Schur; Matrix spectrum: Kernel, Range, Eigenvalues, Eigenvectors and Eigenspaces Matrix Factorizations: LU, Cholesky, QR, SVD 
Target skills and knowledge:

Learning the mathematical and computational foundations of stateoftheart numerical algorithms that arise in the analysis of big data and in many machine learning applications. By using modern Matlab toolboxes for large and sparse data, the students will be guided trough the implementation of the methods on reallife problems arising in network analysis and machine learning. 
Examination methods:

Written exam 
Course unit contents:

Numerical methods for large linear systems
◦ Jacobi and GaussSeidel methods ◦ Subspace projection (Krylov) methods ◦ Arnoldi method for linear systems (FOM) ◦ (Optional) Sketches of GMRES ◦ Preconditioning: Sparse and incomplete matrix factorizations
Numerical methods for large eigenvalue problems
◦ The power method ◦ Subspace Iterations ◦ Krylovtype methods: Arnoldi (and sketches of Lanczos + NonHermitian Lanczos) ◦ (Optional) Sketches of their block implementation ◦ Singular values VS Eigenvalues ◦ Best rankk approximation
Large scale numerical optimization
◦ Steepest descent and Newton's methods ◦ Quasi Newton methods: BFGS ◦ Stochastic steepest descent ◦ Sketches of inexact Newton methods ◦ Sketches Limited memory quasi Newton method
Network centrality
◦ PerronFrobenius theorem ◦ Centrality based on eigenvectors (HITS and Pagerank) ◦ Centrality based on matrix functions
Data and network clustering
◦ KMeans algorithm ◦ Principal component analysis and dimensionality reduction ◦ Laplacian matrices, Cheeger constant, nodal domains ◦ Spectral embedding ◦ (Optional) Lovasz extension, exact relaxations, nonlinear power method (sketches)
Supervised learning
◦ Linear regression ◦ Logistic regression ◦ Multiclass classi cation ◦ (Optional) Neural networks (sketches) 
Planned learning activities and teaching methods:

Lectures supported by exercises and lab 
Textbooks (and optional supplementary readings) 

Lars Elden, Matrix Methods in Data Mining and Pattern Recognition, Second Edition. : SIAM, 2019.

Saad, Yousef, Numerical methods for large eigenvalue problemsYousef Saad. Philadelphia: SIAM, 2011. 2nd edition


