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www.ethanepperly.com | ||
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nickhar.wordpress.com
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| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
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nhigham.com
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| | | | | A norm on $latex \mathbb{C}^{m \times n}$ is unitarily invariant if $LATEX \|UAV\| = \|A\|$ for all unitary $latex U\in\mathbb{C}^{m \times m}$ and $latex V\in\mathbb{C}^{n\times n}$ and for all $latex A\in\mathbb{C}^{m \times n}$. One can restrict the definition to real matrices, though the term unitarily invariant is still typically used. Two widely used matrix norms... | |
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blog.georgeshakan.com
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| | | | | In this post, I talk about the mathematical foundations of PCA | |
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www.jeremykun.com
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| | | This post is a sequel to Formulating the Support Vector Machine Optimization Problem. The Karush-Kuhn-Tucker theorem Generic optimization problems are hard to solve efficiently. However, optimization problems whose objective and constraints have special structure often succumb to analytic simplifications. For example, if you want to optimize a linear function subject to linear equality constraints, one can compute the Lagrangian of the system and find the zeros of its gradient. More generally, optimizing... | ||
