Matrix Methods for AI

Aim

The course aims to provide practical and theoretical knowledge about matrix methods used to solve problems in artificial intelligence applications. An important aspect of the course is to address a number of specific application problems in project form and thereby motivate, elucidate and introduce mathematical theory related to matrices and matrix computations. After completing the course, the course participant will achieve the following objectives.

• Have knowledge about how vectors and matrices are used in AI applications,
• Have knowledge of important concepts when solving systems of linear equations and least squares problems.
• Use different matrix decompositions (LU, QR, and SVD decomposition) to solve practical and theoretical problems.
• Know the principles of clustering and graph partitioning, and use such methods to solve practical problems.
• Have knowledge about tensors and tensor decompositions, and use such methods to solve practical problems.
• Have knowledge about non-negative matrix factorizations, and use such methods to solve practical problems.
• Have knowledge about sources of error in computer arithmetic, how errors propagate in computations.
• Know about cancellation and how it can be avoided.
• Be able to reason about, interpret and perform basic sensitivity analysis.
• Have knowledge about computer arithmetic and how hardware and memory hierarchy affect the efficiency of computer programs.

Content

Vectors and matrices in AI applications, matrix theory and matrix computations, solution of systems of linear equations and least squares problems, matrix decompositions, LU decomposition, QR decomposition, eigenvalues ​​and eigenvectors, singular value decomposition (SVD), singular values ​​and singular vectors, tensors, clustering and graph partitioning, non-negative matrix factorizaitons. Project work in a group where method and theory are used to solve an application problem in information technology, for example, classification of handwritten digits, text mining for document search, Page Rank for searching web pages, automatic extraction of keywords and key phrases, face recognition. The course also introduces error analysis, sensitivity analysis, condition number, memory hierarchy, design of software for computations.