Often when we do principal component analysis we plot the principal components. Biplots are similar but in addition to the principal components we plot the low rank approximations of the variables.
Linux Commands
Philosophy of using command line is that input and output files are files. Basic Commands: Correct grammar of command is: verb adverb object where adverb is the flag you add to a command e.g -h...
Why do we need Measure Theory
In this post I describe the motivation for why we need to use measure theory in probability. In the ideal case, for some arbitrary sample space $\Omega$ we would like to be able to define a func...
Kernel PCA
In traditional PCA, as shown in my PCA post, we look for a linear subspace to project the data vectors onto orthogonally to provide a low dimensional representation of the data. However, restricti...
PCA - Solution
In a previous post we introduce PCA, and two equivalent objective definitions. In this post we now give the exact solutions to PCA. We saw that the objective can be written as: [\begin{align} \un...
linux aliases
To creata a Linux terminal alias you add the alias to the .bashrc file in your home directory. These are the aliases I am currently using: # custom aliases alias gs='git status' alias pers='cd /...
pandoc md file to pdf
On linux to install pandoc: $ sudo apt install \ pandoc \ texlive-latex-base \ texlive-fonts-recommended \ texlive-extra-utils \ texlive-latex-extra \ texlive-xetex Then ...
PCA - Definitions
In this post I will describe Principal Component Analysis (PCA), and in particular sample PCA. I show that the common definition of PCA can be formulated as finding the “best” low rank approximatio...
Duality
Duality In this document I give the main results for duality in standard optimisation problems. Main references: Convex Optimisation by Boyd and Vandenberghe - Chapter 5 Slides on KKT condit...