| Abstract: |
The aim of the subject is to learn and apply various mathematical and statistical methods related to the discovery of relevant patterns in data sets. Nowadays, huge amounts of data are being generated in many fields, and the goal is to understand what the data say. This process is often called learning from data. The first part of the course deals with the spectral and singular value decomposition of matrices from standpoints algebraic and geometric. These decompositions are the basis of the principal component analysis (PCA) and other factorial methods that could be applied to reduce the data dimension and visualize some patterns. A second part is devoted to classical clustering methods, a broad class of methods for discovering unknown subgroups in data. PCA and clustering are two particular types of unsupervised statistical learning. In a third step, we also focus in clustering methods but with a markedly different approach, using topology based methods to extract insights from the shape of complex data sets. The final part of the course will be devoted to supervised statistical learning: regression analysis, classification and regression trees and neural networks, among others. |
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