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Showing posts from April, 2022

Principal Component Analysis - A Geometric Approach

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Overview Principal Component Analysis is a neat statistical trick, with a simple bit of linear algebra backing it up.  Imagine you've got a dependent, or response variable, $Y$ and a large number of independent, a.k.a. explanatory, variables $X_1, ... X_p$.  You also have $n$ measurements of each, giving you a matrix $$ \begin{align} X = & \begin{pmatrix} x_{11} & x_{12} & ... & x_{1n}\\ \vdots & & & \\ x_{p1} & x_{p2} & ... & x_{pn}\\ \end{pmatrix} \\ = & \begin{pmatrix} -\mathbb{x_1}- \\ \vdots \\ -\mathbb{x_p}- \\ \end{pmatrix} \\ \end{align} $$ You want to build a model explaining how $Y$ depends on the $X_i$, perhaps a linear model like $$ Y = \beta_0 + \sum_{i=1}^p \beta_i X_i $$ but first you need to check that the $X_i$ are more or less independent of each other, otherwise there's no way of uniquely setting the $\beta_i$ values and the stats package is likely to produce an unreliable output.  In general the $X_i$ are not inde

Ubuntu hack

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Getting the faffing auto-suspend feature working properly I use Ubuntu on all my computers and it always works 99% well.  But there's always one minor issue that I could live with, were it not for my pathological perfectionism.  On this one it's the auto-suspend, which just wasn't working at all.  This computer lives in the living room and I don't like any noise pollution there, or the idea of pointlessly consuming power.  I think the ethernet card was continuously keeping the machine awake, even if auto suspend was enabled in System Settings -> Power Management .  Eventually I found a solution Add a startup program via Preferences -> Startup Applications Disable auto suspend Log out and back in again (or reboot) For the disabling of auto-suspend I actually just removed the power manager altogether with sudo apt remove mate-power-manager .  If you're using gnome instead it's probably sudo apt remove gnome-power-manager .  The one-line startup program was