Numerical Methods for Data Mining

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/08 Numerical Analysis.

Examination method

Assessment of a project developed on topics introduced in the course, discussion and oral exam.

Learning
objectives

The course aims to provide numerical tools and methodologies for the analysis of large volumes of data (Big data analytics) and the extraction of information from them (data mining). A central aspect of the course is the study of mathematical models and numerical algorithms for data processing, classification and clustering.

Syllabus

Data analysis through the SVD factorisation of the covariance matrix (Principal Component Analysis – PCA) and the PCA algorithm. Clustering and the main clustering algorithms: k-means and k-medoids. Numerical methods for data mining and machine learning; the linear discriminant analysis methodology. Outline of artificial neural networks: self-organising maps. Numerical classification algorithms, Support Vector Machines, the Nearest Neighbours method, the Learning Vector Quantization algorithm. Numerical methods for identification problems. Data representation in the case of static linear and dynamic linear regression problems and in the nonlinear case of neural networks. The Kalman filter. Outline of algorithms based on Monte Carlo methods (particle filter).

Expected learning
outcomes

By the end of the course, students must demonstrate that they

know and understand the main techniques for the analysis of large databases and for knowledge inference;
are able to apply the knowledge acquired to the predictive analysis of phenomena and to improving the effectiveness and efficiency of models;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem relating to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the subject matter, clarity of exposition, rigour in the use of language, familiarity with the notions acquired.

Numerical Methods for Data Mining