Dr Peter Green, Senior Lecturer at the University of Liverpool and Director of Engineering Data Analytics Ltd, has put together a series of tutorial videos for the group. The videos focus on linear algebra, which is at the heart of a lot of machine learning approaches. The video series includes:
- An introduction to the power method, which can be used to estimate the dominant eigenvector of a matrix.
- A closer look at the power method, and considering the case where A is not symmetric, the impact of the initial estimate that is used in the power method, and looking at the ‘shifted power method’ which can be used to find different eigenvectors of A.
- Building on the previous videos, we look at The Gram-Schmidt Process which forms the base of many different approaches in linear algebra, doing some maths before thinking about a geometrical interpretation of the algorithm, and a definition of “span”.
- Applying the Gram-Schmidt process, specifically showing that it can be used to create a QR decomposition, and how that can be used to solve linear systems of equations.
- A first look at the Conjugate Gradients algorithm: a method for solving linear systems whose suitability for deployment on GPUs makes it a core part of many modern Machine Learning approaches.
- A deep dive into the “conjugate directions” algorithm, showing how it converges after n iterations, essentially motivating what will eventually become the conjugate gradients algorithm.
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