AniWiki: Animations in Statistics

K-Means Cluster Algorithm - [R code]

yihui — Wed, 09 Mar 2011 13:36:48 -0700

K-Means Cluster Algorithm

Move! Average! Cluster! Move! Average! Cluster! …

The k-Means cluster algorithm may be regarded as a series of iterations of: finding cluster centers, computing distances between sample points, and redefining cluster membership.

The data given by x is clustered by the k-means method, which aims to partition the points into k groups such that the sum of squares from points to the assigned cluster centers is minimized. At the minimum, all cluster centres are at the mean of their Voronoi sets (the set of data points which are nearest to the cluster centre).

Animation

R code

library(animation) 
saveHTML({ani.options(interval = 2, nmax = 50) 
par( mar = c(3, 3, 1, 1.5), mgp = c(1.5, 0.5, 0)) 
cent = 1.5 * c(1, 1, -1, -1, 1, -1, 1, -1) 
x = NULL
for (i in 1:8) x = c(x, rnorm(25, mean = cent[i])) 
x = matrix(x, ncol = 2) 
colnames(x) = c("X1", "X2") 
kmeans.ani(x, centers = 4, pch = 1:4, col = 1:4) 
},img.name = "kmeans_ani", htmlfile = "kmeans.html", ani.height = 500,    
ani.width = 600, title = "K-means Cluster Algorithm",      
description = c("Move! Average! Cluster! Move! Average! Cluster!...",          
"Which might be helpful in understanding the concept of K-means Culster Algorithm Analysis .")) 
## R version 2.12.1 (2010-12-16)
## Platform: i386-pc-mingw32/i386 (32-bit)
## Other packages: animation 2.0-0

df = cbind(x1 = c(rnorm(100, -2), rnorm(100, 2)), x2 = rnorm(200))
library(animation)
## 2 centers
saveHTML({
    kmeans.ani(df, centers = 2)
})

## 4 centers
saveHTML({
    kmeans.ani(df, centers = 4)
})

Dynamic Graphics - Chris Wild's inference research

yihui — Sun, 06 Feb 2011 13:53:11 -0700

Dynamic Graphics

This page is to gather some resources on dynamic graphics.

Software

name	description	image
GGobi	GGobi is a statistical software tool used for graphing various types of data. GGobi allows extensive exploration of the data with dynamic graphics. It is also a tool for looking at multivariate data. R (programming language) can be used in sync with GGobi. GGobi prides itself on its ability to link multiple graphs together. GGobi

Web-based Interactivity in Statistics

name	description	image
GASP	The Globally Accessible Statistical Procedures initiative is designed to make statistical routines easily available via the WWW. The routines currently available have been divided into two categories, data analysis and educational.

Teaching

name	description	image
Chris Wild's inference	http://www.stat.auckland.ac.nz/~wild/09.USCOTSTalk.html

Insert animations in ''AniWiki'' - update examples according to the new version of the plugin

yihui — Wed, 02 Feb 2011 16:34:40 -0700

Insert animations in ''AniWiki''

Please read the explanations in the plugin page to understand how animations work in AniWiki.

Always bear in mind that you have provided a correct url, i.e. your images can be accessed by such a series of addresses: url + i + type, where i is an integer giving the filename of each frame.

Rotation of a word ''Animation''

In the introduction page of the package ''animation'', I have used a rotating word as the beginning example. Now 30 images from that example are uploaded to this site, so here we are able to create an HTML animation page as follows:

<ani example http://animation.yihui.name/_media/wiki: png 30 0.1 autoplay true 400|'loopMode': 'sweep'>

The above code will generate the result below:

Buffon's Needle

Here is an example illustrating how to upload images to other websites and cite them here. I have generated 100 animation frames from the function buffon.needle() in package animation and uploaded them to Photobucket. You can view all the images in my album buffon's needle.

<ani buffon http://s288.photobucket.com/albums/ll181/xieyihui/buffon_s_needle/ png 100 0.1 autoplay|>

Here is the result (it can take one or two minutes to download all the images, depending on your internet connection):

Animation Plugin (for creating animations) - animation plugin update to the 3rd version

yihui — Wed, 02 Feb 2011 16:30:52 -0700

Animation Plugin (for creating animations)

The animation plugin can generate an animation from a sequence of images, e.g. 1.png, 2.png, 3.png, … The animation is driven by HTML & JS, and the JS library is from SciAnimator.

Download and Install

Plugin source: zip format (53K) (last updated on 2011-02-02)

For people who want to create animations in this wiki, the above file does not need to be downloaded (just follow the instructions below).

Updates

2011-02-02: the 3rd version
- the syntax has changed again, but this should not affect users; I've tried my best to maintain compatibility with old versions
2011-01-01: the plugin was rewritten using SciAnimator;
- the last version is not completely compatible with the new version
  - the width might not be correct
  - there might be a tag </ani> which is not parsed any more
- the description field in the last version was discarded
- the title field was replaced by opts
2008-06-20: the first version

Requirement

Any web browsers except the Microsoft Internet Explorer, e.g. Firefox, Safari, Google Chrome, Opera… The animations in the Internet Explorer might not be stable.

Usage

The syntax:

<ani id url type max interval autoplay navigator width | opts>

There are 9 parameters in total:

id: a unique identifer of each animation in the same page
url: the directory of the animation frames. NOT the actual URL of any animation frames; only a directory!
type: the image format. E.g. png, jpeg, etc
max: the maximum number of animation frames; an integer
interval: the time interval (duration) between animation frames in seconds; a non-negative real number
autoplay: (optional) if a string autoplay is provided here, the animation will start playing once the page is loaded; any other strings (including empty strings) means do not autoplay the animation
navigator: (optional) whether to include a navigator in the toolbar panel; default to omit the navigator because it is too wide; if a string true is provided here, the navigator will be included, but bear in mind that you should specify the width option as well in this case
width: (optional) the width of the animation frames in pixel; an integer
opts: additional JavaScript options, e.g. 'theme': 'dark' (note the single quotes are necessary in JS); see SciAnimator for more options

Please do note that the first 8 parameters are separated by spaces, while the 9th parameter is seperated by ”|”; besides, autoplay, navigator, width and opts can be left empty.

The animation interface

The interface just looks like a movie player, so perhaps you can figure out what these buttons do without any explanations.

Example

Suppose we have created a sequence of 30 images with height equal to 300px: 1.png, 2.png, 3.png, …, 30.png, and they are in this directory ”http://animation.yihui.name/_media/wiki:”. Now we wish to create an animation in this wiki specifying the initial time interval to be 0.1:

<ani example http://animation.yihui.name/_media/wiki: png 30 0.1 autoplay true 400|'utf8': false, 'theme': 'dark'>

which will produce:

Here is an example page, and you can find even more in this wiki.

Feedback

Please drop me an email if you have any suggestions. — Yihui Xie 2011/01/01 23:11

The Newton-Raphson Method for Root-finding - Fixed theory section, added further reading section.

nan.xiao — Mon, 31 Jan 2011 08:17:42 -0700

The Newton-Raphson Method for Root-finding

Newton's method (also known as the Newton-Raphson method or the Newton-Fourier method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function .

The iteration goes on in this way:

From the starting value , vertical lines and points are plotted to show the location of the sequence of iteration values , , …; tangent lines are drawn to illustrate the relationship between successive iterations; the iteration values are in the right margin of the plot.

Animation

Go along with the tangent lines and iterate. </ani>

R code

library(animation)
saveHTML({
    ani.options(nmax = 100, interval = 1)
    par(mar = c(3, 3, 1, 1.5), mgp = c(1.5, 0.5, 0), pch = 19)
    newton.method(function(x) 5 * x^3 - 7 * x^2 - 40 * x + 100, 
        7.15, c(-6.2, 7.1), main = "")
}, img.name = "newton_method", htmlfile = "newton_method.html", 
    ani.height = 500, ani.width = 500, outdir = getwd(), title = "Demonstration of the Newton-Raphson Method", 
    description = c("Go along with the tangent lines and iterate."))