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liorpachter.wordpress.com | ||
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evelinag.com
This is day 15 of the F# Advent Calendar. Do you know who wrote the classic Christmas story, 'A Christmas Carol'? Are you sure it was Charles Dickens? In this blog post, I'm using Principal Component Analysis to compare and visualise similarity between classic works of literature. |
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leimao.github.io
Fundamentals to Principal Component Analysis |
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www.oranlooney.com
In the previous article in this series we distinguished between two kinds of unsupervised learning (cluster analysis and dimensionality reduction) and discussed the former in some detail. In this installment we turn our attention to the later. In dimensionality reduction we seek a function \(f : \mathbb{R}^n \mapsto \mathbb{R}^m\) where \(n\) is the dimension of the original data \(\mathbf{X}\) and \(m\) is less than or equal to \(n\). That is, we want to map some high dimensional space into some lower dimensional space. |
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mkatkov.wordpress.com
For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... |
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