Oracle:Linear regression through a SQL Query

I want to have a linear approximation directly in an SQL query.

To make it easy: having a generic function f, I want to approximate it with the function:

Being sure that I found the A and B which minimize the global error between f and f' (where f' is the linear approximation of f). 

Let's generate some data: 

 create table zzz_some_data as   
  SELECT    
    'X' groupid,   
    level x,    
    exp(level/10) + sin(level/10 *3.14) + dbms_random.value(0,1) y   
   FROM DUAL   
   CONNECT BY LEVEL <= 20   
 union all   
  SELECT    
    'Y' groupid,   
    level x,    
    exp(level/10) + Cos(level/10 *3.14) + dbms_random.value(0,1) y  
   FROM DUAL   
   CONNECT BY LEVEL <= 20;  

As you can see there is a random factor. At the bottom of the tutorial, you can find the exact data generated. 

Plotting these numbers the functions look like this: 

Running the following query, I can get the value of A and B for the two functions:

 WITH mean_estimates AS  
 (  SELECT GroupID  
      ,AVG(x) AS xmean  
      ,AVG(y) AS ymean  
      ,min(y) as first_seq  
      ,max(y) as last_seq  
   FROM zzz_some_data  
   GROUP BY GroupID  
 ),  
 stdev_estimates AS  
 (  SELECT pd.GroupID  
      ,CASE     
        WHEN SUM(POWER(x - xmean, 2)) = 0 THEN 1   
        when COUNT(*) = 1 then 10000000  
        ELSE SQRT(SUM(POWER(x - xmean, 2)) / (COUNT(*) - 1))   
       END AS xstdev  
      ,CASE  
        when count(*) = 1 then 10000000   
        else SQRT(SUM(POWER(y - ymean, 2)) / (COUNT(*) - 1))     
       end AS ystdev  
   FROM zzz_some_data pd  
   INNER JOIN mean_estimates pm ON pm.GroupID = pd.GroupID  
   GROUP BY pd.GroupID, pm.xmean, pm.ymean  
 ),  
 standardized_data AS          -- increases numerical stability  
 (  SELECT pd.GroupID  
      ,(x - xmean) / xstdev                  AS xstd  
      ,CASE ystdev WHEN 0 THEN 0 ELSE (y - ymean) / ystdev END AS ystd  
   FROM zzz_some_data pd  
   INNER JOIN stdev_estimates ps ON ps.GroupID = pd.GroupID  
   INNER JOIN mean_estimates pm ON pm.GroupID = pd.GroupID  
 ),  
 standardized_beta_estimates AS  
 (  SELECT GroupID  
      ,CASE WHEN SUM(xstd * xstd) = 0 THEN 0  
         ELSE SUM(xstd * ystd) / (COUNT(*) - 1) END     AS betastd  
   FROM standardized_data pd  
   GROUP BY GroupID  
 ),   
 linear_model as   
 (  
 SELECT   
    pb.GroupID,     
    ymean - xmean * betastd * ystdev / xstdev AS BETA,   
    betastd * ystdev / xstdev         AS ALPHA,   
    first_seq,   
    last_seq  
 FROM standardized_beta_estimates pb  
 INNER JOIN stdev_estimates ps ON ps.GroupID = pb.GroupID  
 INNER JOIN mean_estimates pm ON pm.GroupID = pb.GroupID  
 )  
 select   
  GroupID,   
  alpha,   
  Beta  
 from linear_model  
 order by GroupID desc;  

This query generate the following output: 

 GROUPID   ALPHA    BETA  
 ------- ---------- ----------  
 Y    ,341603277 ,27926809   
 X    ,221725267 1,66190364   

Let's see now the results: 

Here the plot of the approximation of X:

Here the plot of the approximation of Y:

 CREATE TABLE "ZZZ_SOME_DATA"  
  (  
   "GROUPID" CHAR(1 BYTE),  
   "X"    NUMBER,  
   "Y"    NUMBER  
  );  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','1','1,61932317662496064883408392432113402523');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','2','2,77694913213341470441940320202765814948');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','3','2,91090102987016066482064043800309804071');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','4','3,13678897398740391101470575963142792902');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','5','3,31605237538417176477155850638842190865');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','6','3,13667075089211953539069065645455345878');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','7','3,47488861159608290867160313703997232386');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','8','3,42251149078741711848240969510483689103');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','9','3,70603465587716541507204559098228342981');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','10','3,49314419776404379007856528151793653642');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','11','3,24172315449369167895615169724235970383');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','12','2,96881260394832309096782780931487864967');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','13','3,07513520161764733445750922412894102533');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','14','3,81479688098856311171457385615269516843');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','15','4,32475565056326473828436305142365381565');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','16','4,85233459222270714560038164481370508461');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','17','5,61989845355259006300115338181868398089');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','18','6,31700004318003808435939347557223237057');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','19','6,76689263318576069778969371993663187878');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('X','20','7,82576523994149918219695417536412769495');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','1','2,53714598427679136859871205905510695503');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','2','2,3110817502573158903868891890087776345');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','3','1,94494243937675278618005281210530984129');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','4','2,25982980116506374957923410951751088925');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','5','1,86603427812480463944739874768807857366');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','6','2,05505938632236899572636979590661767446');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','7','2,3258999982985244735180126549118494278');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','8','1,83188925742276377791489099175111599133');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','9','2,41166969667358720655946060775919042819');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','10','1,8104604598253185583746180090281519982');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','11','2,87738150798966416515834453685956594055');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','12','3,43069799388754748665140656518089681805');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','13','3,54673238603787598200769925226968142282');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','14','4,43614682007291136740320048898865794443');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','15','4,87577441430844397983546298110499857896');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','16','6,00804958270558010522626027655493241713');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','17','6,3755271699704708032463599263767041073');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','18','7,12510967938699587673395044064905861434');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','19','8,17916759972655812255130821868093121265');  
 Insert into ZZZ_SOME_DATA (GROUPID,X,Y) values ('Y','20','9,11344975307640059368329002839752407251');  
 COMMIT;  

Tutorial: neural network in R by examples (using the package neuralnet)

Tutorial: Create a neural network in R

Let's start with the basics. 

If you want to start learning how does it work a NN in R, start searching for some packages supporting you. 

Googling a bit you will wee that there are two main packages: 

• Neuralnet: specific for neural networks
• Caret: generic machine learning package, containing a lot of machine learning algorithm, supporting very well the neural networks.

In this post I will show some investigation I made on the package "Neuralnet".
In this next post I show the investigation I made on the package "Caret".

Basic AND and OR functions

If you go on the help of R, typing: 

 ?neuralnet  

You can get the complete documentation.
Going quickly to the example, you find the following code:

 AND <- c(rep(0,7),1)  
 OR <- c(0,rep(1,7))  
 binary.data <- data.frame(expand.grid(c(0,1), c(0,1), c(0,1)), AND, OR)  
 net <- neuralnet(AND+OR~Var1+Var2+Var3, binary.data, hidden=0,   
             rep=10, err.fct="ce", linear.output=FALSE)  

Let's have a look inside to the returned object "net":

 > typeof(net)  
 [1] "list"  

 > summary(net)  
                   Length   Class      Mode    
 call                  7    -none-     call    
 response             16    -none-     numeric   
 covariate            24    -none-     numeric   
 model.list            2    -none-     list    
 err.fct               1    -none-     function  
 act.fct               1    -none-     function  
 linear.output         1    -none-     logical   
 data                  5    data.frame list    
 net.result           10    -none-     list    
 weights              10    -none-     list    
 startweights         10    -none-     list    
 generalized.weights  10    -none-     list    
 result.matrix       110    -none-     numeric   
 

> head(net)  
 $call  
 neuralnet(formula = AND + OR ~ Var1 + Var2 + Var3, data = binary.data,   
   hidden = 0, rep = 10, err.fct = "ce", linear.output = FALSE)  
 $response  
  AND OR  
 1  0 0  
 2  0 1  
 3  0 1  
 4  0 1  
 5  0 1  
 6  0 1  
 7  0 1  
 8  1 1  
 $covariate  
    [,1] [,2] [,3]  
 [1,]  0  0  0  
 [2,]  1  0  0  
 [3,]  0  1  0  
 [4,]  1  1  0  
 [5,]  0  0  1  
 [6,]  1  0  1  
 [7,]  0  1  1  
 [8,]  1  1  1  
 $model.list  
 $model.list$response  
 [1] "AND" "OR"   
 $model.list$variables  
 [1] "Var1" "Var2" "Var3"  
 $err.fct  
 function (x, y)   
 {  
   -(y * log(x) + (1 - y) * log(1 - x))  
 }  
 <environment: 0x00000000174034c8>  
 attr(,"type")  
 [1] "ce"  
 $act.fct  
 function (x)   
 {  
   1/(1 + exp(-x))  
 }  
 <environment: 0x00000000174034c8>  
 attr(,"type")  
 [1] "logistic"  

> print(net)
10 repetitions were calculated.

           Error Reached Threshold Steps
7  0.07270325501    0.007209205002   237
2  0.08361412743    0.008216337601   210
1  0.08425544114    0.008840366736   228
4  0.08667354432    0.009692218237   226
6  0.08736308608    0.009046804494   236
10 0.08767067498    0.009009176337   240
3  0.08817255652    0.009546552076   214
8  0.09165608530    0.009676470949   221
5  0.09170859687    0.008872336865   213
9  0.09517374836    0.009993935991   223

How can I use the NN once I have trained it?

 > test <- data.frame(expand.grid(c(0,1), c(0,1), c(0,1)))  
 > predicted <- compute(net, test) #Run them through the neural network  
 > print(predicted$net.result)  
            [,1]       [,2]  
 [1,] 0.000000005510800906 0.00003437586348  
 [2,] 0.000008322603907184 0.99999887725263  
 [3,] 0.000010232856460365 0.99999418995760  
 [4,] 0.015219103082846375 1.00000000000000  
 [5,] 0.000009115152595497 0.99998044588564  
 [6,] 0.013579325087889940 1.00000000000000  
 [7,] 0.016644285280624567 1.00000000000000  
 [8,] 0.962352882489281747 1.00000000000000  
 >   

What is very cool about this package is the graphical representation:

 > plot(net)

generate this plot:

Square root function

There is a great tutorial in this page: 

http://gekkoquant.com/2012/05/26/neural-networks-with-r-simple-example/

Let's have a look at the code: 

 install.packages('neuralnet')  
 library("neuralnet")  

 #Going to create a neural network to perform sqare rooting  
 #Type ?neuralnet for more information on the neuralnet library  
 #Generate 50 random numbers uniformly distributed between 0 and 100  
 #And store them as a dataframe  
 traininginput <- as.data.frame(runif(50, min=0, max=100))  
 trainingoutput <- sqrt(traininginput)  

 #Column bind the data into one variable  
 trainingdata <- cbind(traininginput,trainingoutput)  
 colnames(trainingdata) <- c("Input","Output")  

 #Train the neural network  
 #Going to have 10 hidden layers  
 #Threshold is a numeric value specifying the threshold for the partial  
 #derivatives of the error function as stopping criteria.  
 net.sqrt <- neuralnet(Output~Input,trainingdata, hidden=10, threshold=0.01)  

 #Test the neural network on some training data  
 testdata <- as.data.frame((1:10)^2) #Generate some squared numbers  
 net.results <- compute(net.sqrt, testdata) #Run them through the neural network  

Let's have a look at the reuslt:

 > cleanoutput <- cbind(testdata,sqrt(testdata),  
 +           as.data.frame(net.results$net.result))  
 > colnames(cleanoutput) <- c("Input","Expected Output","Neural Net Output")  
 > print(cleanoutput)  
   Input Expected Output Neural Net Output  
 1   1                 1       1.292537723  
 2   4                 2       2.004110690  
 3   9                 3       3.004860581  
 4   16                4       4.001313250  
 5   25                5       4.996608428  
 6   36                6       6.003918278  
 7   49                7       6.997395208  
 8   64                8       7.995504751  
 9   81                9       9.009677415  
 10  100              10       9.959406366  
 >   

Having a look at the graphical representation:

Square root function with more nodes in the hidden layer

And what if I wanted to increase the number of nodes in the hidden layer?
Please consider that this is only to see how to tune the network. Use an hidden layer for the Sqrt function is totally useless, and I will show it later with the results.

Anyway, to add more layers, it is simply needed to use the value:    "hidden = c(x, y, z)"
where:
- x: number of perceptrons in the first hidden layer
- y: number of perceptrons in the second hidden layer

- z: number of perceptrons in the third hidden layer

 traininginput <- as.data.frame(runif(50, min=0, max=100))  
 trainingoutput <- sqrt(traininginput)  
 trainingdata <- cbind(traininginput,trainingoutput)  
 colnames(trainingdata) <- c("Input","Output")  
 net.sqrt <- neuralnet(Output~Input,trainingdata, hidden=c(10, 10, 10), threshold=0.01)  

Let's plot now the network:

Let's check now the results (you will see, adding these hidden layer did not improve the results at all):

 > cleanoutput <- cbind(testdata,sqrt(testdata),  
 +           as.data.frame(net.results$net.result))  
 > colnames(cleanoutput) <- c("Input","Expected Output","Neural Net Output")  
 > print(cleanoutput)  
   Input Expected Output Neural Net Output  
 1   1                1    0.591036793  
 2   4                2    2.070495859  
 3   9                3    3.000115410  
 4   16               4    3.999594071  
 5   25               5    4.997643979  
 6   36               6    6.034835331  
 7   49               7    6.997600383  
 8   64               8    7.997306744  
 9   81               9    8.999801209  
 10  100             10    9.982023499  
 >   

Oracle: SQL for list of numbers or list of dates

For numbers:

I want to have a query which returns the list of the dates from today, for the next 10 years:

   SELECT   
     level seq,   
     _starting_ + _delta_ * level as ddate,   
   FROM DUAL  
   CONNECT BY LEVEL <= _occurrences_  

The "parameters" needed by this query are:

• Starting: the value where to start
• Delta: the number of days between each occurrence of the list
• Occurrences: How many occurrences in the list (how long is the list)

For example, given the following query:

SELECT
   level seq,
   100 + 5 * level as value
FROM DUAL
CONNECT BY LEVEL <= 10

I will have this output

     SEQ   VALUE  
 ---------- ----------  
      1    105   
      2    110   
      3    115   
      4    120   
      5    125   
      6    130   
      7    135   
      8    140   
      9    145   
     10    150   
  10 Zeilen gewählt  

For dates:

I want to have a query which returns the list of the dates from today, for the next 10 years:

   SELECT   
     level seq,   
     to_date(_starting_date_, 'yyyymmdd') + _delta_ * level as ddate,   
     to_char(to_date(_starting_date_, 'yyyymmdd') + _delta_ * level, 'yyyy-ww') as week,   
     to_char(to_date(_starting_date_, 'yyyymmdd') + _delta_ * level, 'yyyy-mm') as month  
   FROM DUAL  
   CONNECT BY LEVEL <= _occurrences_  

The "parameters" needed by this query are:

• Starting_date: the date where to start
• Delta: the number of days between each occurrence of the list
• Occurrences: How many occurrences in the list (how long is the list)

For example, given the following query:

   SELECT   
     level seq,   
     to_date('20140101', 'yyyymmdd') + 7 * level as ddate,   
     to_char(to_date('20140101', 'yyyymmdd') + 7 * level, 'yyyy-ww') as week,   
     to_char(to_date('20140101', 'yyyymmdd') + 7 * level, 'yyyy-mm') as month  
   FROM DUAL  
   CONNECT BY LEVEL <= 10  

I will have this output

     SEQ DDATE  WEEK  MONTH   
 ---------- -------- ------- -------  
      1 08.01.14 2014-02 2014-01   
      2 15.01.14 2014-03 2014-01   
      3 22.01.14 2014-04 2014-01   
      4 29.01.14 2014-05 2014-01   
      5 05.02.14 2014-06 2014-02   
      6 12.02.14 2014-07 2014-02   
      7 19.02.14 2014-08 2014-02   
      8 26.02.14 2014-09 2014-02   
      9 05.03.14 2014-10 2014-03   
     10 12.03.14 2014-11 2014-03   
  10 Zeilen gewählt  

Tutorial: Canvas in HTML5

Let's play a bit with the graphic & Canvas...
You can find the code here:
http://jsbin.com/umaDEvu/5/edit?html,output

 <!DOCTYPE HTML>  
 <html>  
   <head>  
     <style>  
       body {  
         margin: 0px;  
         padding: 0px;  
       }  
       #myCanvas {  
         border: 1px solid #9C9898;  
       }  
     </style>  
     <script>     
       var clicked = 0;  
       var loopMouth = 0;  
       var lastMouseX = 300;  
       var lastMouseY = 300;  
       var colorSetIndex = 2;  
       var colorSet = [["limegreen", "forestgreen", "darkgreen", "olive"],   
               ["mediumblue", "blue", "darkblue", "indigo"],   
               ["darkorange", "peru", "sienna", "darkgoldenrod"]];  
      function setColorSetIndex(colorIndex){  
       colorSetIndex = colorIndex;  
      }  
       function getMousePos(canvas, evt) {  
         // get canvas position  
         var obj = canvas;  
         var top = 0;  
         var left = 0;  
         while (obj && obj.tagName != 'BODY') {  
           top += obj.offsetTop;  
           left += obj.offsetLeft;  
           obj = obj.offsetParent;  
         }  
         lastMouseX = evt.clientX - left + window.pageXOffset;  
         lastMouseY = evt.clientY - top + window.pageYOffset;  
       }  
      function drawFace(context) {  
         //left ear  
         context.beginPath();  
         var grd = context.createRadialGradient(125, 130, 10, 175, 130, 100);  
         grd.addColorStop(0.01, colorSet[colorSetIndex][0]);  
         grd.addColorStop(0.5, colorSet[colorSetIndex][1]);  
         grd.addColorStop(0.7, colorSet[colorSetIndex][2]);  
         grd.addColorStop(0.95, colorSet[colorSetIndex][3]);  
         context.arc(175, 150, 75, 0, 2*Math.PI, false);  
         context.fillStyle = grd;  
         context.fill();  
         // right ear  
         context.beginPath();  
         var grd = context.createRadialGradient(450, 95, 10, 425, 130, 100);  
         grd.addColorStop(0.01, colorSet[colorSetIndex][0]);  
         grd.addColorStop(0.5, colorSet[colorSetIndex][1]);  
         grd.addColorStop(0.7, colorSet[colorSetIndex][2]);  
         grd.addColorStop(0.95, colorSet[colorSetIndex][3]);  
         context.arc(425, 125, 75, 0, 2*Math.PI, false);  
         context.fillStyle = grd;  
         context.fill();  
         //face  
         context.beginPath();  
         var grd = context.createRadialGradient(300, 140, 50, 300, 170, 175);  
         grd.addColorStop(0.01, colorSet[colorSetIndex][0]);  
         grd.addColorStop(0.5, colorSet[colorSetIndex][1]);  
         grd.addColorStop(0.7, colorSet[colorSetIndex][2]);  
         grd.addColorStop(0.95, colorSet[colorSetIndex][3]);  
         context.arc(300, 200, 150, 0, 2*Math.PI, false);  
         context.fillStyle = grd;  
         context.fill();  
      }  
      function drawEyes(context, mx, my) {  
         var cx = [300, 220, 200, 250, 380, 350, 400];  
         var cy = [100, 130, 170, 160, 130, 150, 185];  
         var ray = [ 30, 20, 10, 10, 20, 10, 10];  
         for (var i = 0; i < cx.length; i++) {  
          //compute the multiplier for the mouse position  
          var mmx = ((mx-300)/300*ray[i]);  
          var mmy = ((my-200)/200*ray[i]);  
          context.beginPath();  
          var grd = context.createRadialGradient(cx[i]+mmx, cy[i]+mmy, 1, cx[i]+mmx, cy[i]+mmy, ray[i]*3);  
          grd.addColorStop(0.01, "black");  
          grd.addColorStop(0.1, "white");  
          grd.addColorStop(0.99, "gray");  
          context.arc(cx[i], cy[i], ray[i], 0, 2*Math.PI, false);  
          context.fillStyle = grd;  
          context.fill();    
         }  
      }  
      function drawMouth(context) {  
         var grd_m = context.createRadialGradient(300, 300, 10, 300, 300, 100);  
         grd_m.addColorStop(0.1, "red");  
         grd_m.addColorStop(0.6, "black");  
       //for closing the mouth  
       var diffLeft;  
       var diffRight;   
       //loopMouth goes from 0-100  
       // from 0-50 it close the mouth  
       //from 50-100 it reopen the mouth  
       if(loopMouth < 50)  
       {  
        tempLoopMouth = loopMouth;  
        diffLeft=((380-230)/50)*(tempLoopMouth+1);  
        diffRight=((330-250)/50)*(tempLoopMouth+1);  
       }  
       else   
       {  
        tempLoopMouth = (100-loopMouth);  
        diffLeft=((380-230)/50)*(tempLoopMouth+1);  
        diffRight=((330-250)/50)*(tempLoopMouth+1);  
       }   
         context.beginPath();  
         context.moveTo(220, 230);  
         context.bezierCurveTo(220, 380 - diffLeft, 380, 330 - diffRight, 380, 250);  
         context.closePath(); // complete custom shape  
         context.fillStyle = grd_m;  
         context.fill();  
      }       
      function drawBackground(context){  
         //set the background  
         var grd = context.createRadialGradient(300, 200, 50, 300, 200, 600);  
         grd.addColorStop(0.01, "white");  
         grd.addColorStop(0.5, "black");  
         context.arc(300, 200, 600, 0, 2*Math.PI, false);  
         context.fillStyle = grd;  
         context.fill();  
      }  
      function drawAll(context){  
           drawBackground(context);  
           drawFace(context);  
           drawEyes(context, lastMouseX, lastMouseY);  
           drawMouth(context);  
      }        
      // requestAnim shim layer by Paul Irish    
      window.requestAnimFrame = (function(){    
      return window.requestAnimationFrame ||    
       window.webkitRequestAnimationFrame ||    
       window.mozRequestAnimationFrame ||    
       window.oRequestAnimationFrame ||    
       window.msRequestAnimationFrame ||    
       function(/* function */ callback, /* DOMElement */ element){    
       window.setTimeout(callback, 1000 / 60);    
       };    
      })();     
      function animationLoop(){  
       var canvas = document.getElementById("myCanvas");  
       var context = canvas.getContext("2d");  
       if(clicked == 1)  
         loopMouth++;  
       if(loopMouth==100)  
       {  
         loopMouth = 0;  
         clicked = 0;  
       }  
       drawAll(context);  
       requestAnimFrame(animationLoop);        
      }  
       window.onload = function(){  
         var canvas = document.getElementById("myCanvas");  
         var context = canvas.getContext("2d");  
         canvas.addEventListener('mousemove', function (evt) {  
           var mousePos = getMousePos(canvas, evt);  
           drawAll(context);  
         }, false);  
         canvas.addEventListener('click', function (evt) {  
           var mousePos = getMousePos(canvas, evt);  
           if(clicked == 0)   
            clicked = 1;   
         }, false);  
         drawAll(context, 300, 200);  
         // Start animation  
         animationLoop();  
       };  
     </script>  
   </head>  
   <body onmousedown="return false;">  
     <canvas id="myCanvas" width="600" height="400">  
     </canvas>  
    <button onclick="setColorSetIndex(0)"> green </button>  
    <button onclick="setColorSetIndex(1)"> blue </button>  
    <button onclick="setColorSetIndex(2)"> orange </button>  
    <div id="help">  
     Animations are:   
     <ul>  
      <li> moving mouse on the canvas = move eyes; </li>  
      <li> click on the canvas = close mouth; </li>  
      <li> click on the buttons = change monster color; </li>  
     </ul>  
    </div>  
     </body>  
 </html>  

As you can see, there is basically no HTML. It is a pure drawing made in Javascript...