More on Heatmap

A reader asks about this heatmap post on Flowing Data. Sure, we can do it easily with ArrayPlot. Grab the notebook here.

data = Import["ppg2008.csv"];

Grid[data]

 

numbers = data[[2 ;; All, 2 ;; All]]; (* this is the data for heatmap *)
playernames = data[[2 ;; All, 1]]; (* for the labels *)
statnames = data[[1, 2 ;; All]]; (* for the labels *)

Then we need to scale the each column separately to [0,1].

newnumber = Transpose[Rescale[#] & /@ (Transpose[numbers])];

Then you can generate a simple heatmap simply by ArrayPlot[newnumber].

Of course, we like to add the labels with FrameTicks option. FrameTicks->{{left,right},{bottom,top}}  mark options specified separately for each edge. 

Transpose[{Range[Length[playernames]], playernames}] generate the list {{1, “player1”} … {50, “player50”}} to label the player names.

Transpose[{Range[Length[statnames]], Map[Rotate[#, 60 Degree] &, statnames]}] with this line, we can rotate the labels at the same time.

Here is the final product, click to see the full graphic.

Charting time series as calendar heat maps

I haven’t updated this blog for a while. I am working on one Matlab project right now. It is kind of difficult for me to work with Matlab and Mathematica at the same time.

There is an interesting post Charting time series as calendar heat maps in R. The original idea from SAS Analysis of airline performance. I create a simple version in Mathematica. The tricky part is to generate the background grid.

The code I use is from an old tutorial of Making a Calendar. For each month, the boundary is defined by 8 points, marked out by darker line. The monthly grids are shifted to the right positions to form a yearly grid. Once you figure out this part, the rest is just straightforward.

I use the stock as the example, this  is actually not the best data set for this type of visualization.

Calendar heatmap:

Download the file calendarheatmap.nb for the detail.

By the way, you can do whatever you like with the materials posted on this blog, there is no copyright problem.

Make a US county thematic map using Mathematica

I read a blog entry How to Make a US County Thematic Map Using Free Tools. The idea is to use Python script to modify the style settings in SVG file to make the most recent unemployment map. Mathematica can’t import SVG file directly, however, SVG file is in XML format, it is very easy to extract the necessary data from SVG file. If you are not sure what’s going here, please refer to the original blog.

All the files are zipped together, just unzip it, run the notebook. Download it here.

User-defined color themes

With Blend function, it is quite simple to use user-defined color themes.

Blend[{col₁, col₂, col₃, ...}, x]: linearly interpolates between colors col_i as x varies from 0 to 1.

We like to use the following color theme:

c = {{37, 57, 175}, {40, 127, 251}, {50, 190, 255}, {106, 235,
    255}, {138, 236, 174}, {205, 255, 162}, {240, 236, 121}, {255,
    189, 87}, {255, 161, 68}, {255, 186, 133}, {255, 255, 255}};

colors = RGBColor[#/255] & /@ c;

This shows the each color in the theme:

Graphics[Table[{EdgeForm[Black], FaceForm[colors[[i]]],
   Rectangle[{i, 0}, {i + 1, 1}]}, {i, 1, Length[colors]}]]

Check the color theme with Blend function:

DensityPlot[x, {x, 0, Length[c]}, {y, 0, 1}, AspectRatio -> Automatic,
  FrameTicks -> None, ColorFunction -> (Blend[colors, #] &),
PlotRangePadding -> None]

Then you probably notice how to use it in your own plot,

ColorFunction -> (Blend[colors, #] &)

Test the color theme with the data:

ReliefPlot[data, ColorFunction -> (Blend[colors, #] &)]

Maybe the ligher color is better.

lightercolors = Lighter[#] & /@ colors;

Just for fun, let’s play the color theme with an existing image.

img=ImageData[ColorConvert[place_any_image_here, ”Grayscale”]];

ArrayPlot[img, ColorFunction -> (Blend[darkercolors, #] &)]

Wikipedia Page Analysis

Wikipedia has lots of scientific information, however, due to its nature, it is still not considered as a research resource.  This doesn’t mean it has to be ignored. I have checked some pages related with various topics in GIS field. Most of them are well-written, the information are actually quite accurate, several contributors are the professionals in the field. In this post, I like to check some metadata information of  “Mathematica” Page on Wikipedia, it may gives us some ideas about its quality.

Tools we need: Mediawiki API and Mathematica. There are plenty examples on how to use Mediawiki api. Basic procedure is to use Import[queryurl,”XML”], then parse xml to get the information we need.

Page revision history:

(* import  contributor and timestamp *)

url = "http://en.wikipedia.org/w/api.php?action=query&prop=revisions&\
titles=Mathematica&rvprop=user|timestamp&rvlimit=500&redirects$rvuser&\
format=xml";

xml = Import[url, "XML"];
rawdata= Cases[xml, XMLElement["rev", w_, _] :> w, Infinity];
data = {"user", "timestamp"} /. rawdata;

 

 

This page is constantly revised, we probably can assume the information on “Mathematica” page is up-to-date.

The information on the contributors is also interesting.

 

We can dig out more information on the contributors:

(* import paged edited by each user *)

userpages[usr_] :=
  Module[{url, uxml, udata, unicase},
   url = "http://en.wikipedia.org/w/api.php?action=query&list=\
usercontribs&uclimit=500&format=xml&ucuser=" <> usr;
   uxml = Import[url, "XML"];
   udata = Cases[uxml, XMLElement["item", w_, _] :> w, Infinity];
   unicase = DeleteCases[Union["title" /. udata ],
     x_ /; (StringMatchQ[x, "User talk:" ~~ __] || StringMatchQ[x, "Talk:" ~~ __] || StringMatchQ[x, "User:" ~~ __])]; Map[usr -> # &, unicase]];

 

The common pages edited by these top5 contributors:

  

From the pages they have edited, they have worked on several topics closely related with Mathematica. This looks good, we may say they probably know what they are doing.

Update:

Download Wikipedia Notebook for the details.