pac.Rpres

Principal Component Analysis
========================================================
author: Kostis G.
date: 

What are the principal components?
==================================
* Dynamics with the largest variance. 
* Easy to see in low dimensional datasets, not so much when $d>2$.

Trying to generate an "Aha" moment.
========================================================

```{r echo=FALSE, fig.align="center"}
library(ggplot2);
N = 100;
width  <- seq(from = 5, to = 10, length=N);
height <- 5*width  + rnorm(N,1);

dat <- data.frame(width,height)
  
oplot <-qplot(width, height)
print(oplot)
``` 


Trying to generate an "Aha" moment.
========================================================
```{r fig.align="center", echo=FALSE}
print(oplot)
pca <- prcomp(dat, scale=TRUE)
summary(pca)
``` 

Result of PCA
=========================================================

```{r fig.align="center",echo=FALSE}
qplot(pca$x[,1],pca$x[,2])
```
* The dataset after doing PCA. 


Why do it?
=========================================================
* Allows us to see the important directions/dynamics of the dataset. 
* Sometimes suggests variables to drop because of not important interactions with the rest of the set! 




References
===========
* A tutorial on Principal Components Analysis, Jonathon Shlens
* Computing and visualizing PCA in R, R-bloggers.
* Principal Component Analysis, a how-to manual for R.