Syllabus
1. Numerical properties of the SVD and spectral decomposition.
2. PCA and the spectral decomposition.
3. (Multi)-linear regression and the SVD.
4. Dimension reduction in high-dimensional statistics.
5. Pattern recognition and other classification tasks.
6. Nonnegative matrix decompositions.
7. The page ranking problem.
Annotation
This course focuses on statistical methods based on matrix computations where the effective application of methods of numerical linear algebra is crucial. The main emphasis is on understanding and selecting methods that have low computational and memory requirements, and are if possible stable and reliable.
The first part of the course will concentrate on statistical tasks associated with the matrix decomposition SVD, like PCA, regression, dimension reduction and the small sample size problem (especially in the case of sparse data), pattern recognition and similar classification tasks or problems from the area of data mining. In the next part we will focus on non-negative matrix decompositions used for example in text mining and on computations of numerical linear algebra that are used to solve the page ranking problem for search engines.