The Johnson-Lindenstrauss lemma is a mathematical result that states that a set of points in a high-dimensional space can be embedded into a space of much lower dimension while preserving distances between the points. It has applications in compressed sensing, manifold learning, dimensionality reduction, and graph embedding, and is useful for reducing the dimensionality of data while preserving its relevant structure. The lemma is tight up to a constant factor, meaning there exists a set of points that needs a certain dimension to preserve distances within a certain factor.
Stanford University
Spring 2022
CS 168 provides a comprehensive introduction to modern algorithm concepts, covering hashing, dimension reduction, programming, gradient descent, and regression. It emphasizes both theoretical understanding and practical application, with each topic complemented by a mini-project. It's suitable for those who have taken CS107 and CS161.
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