In my last post I outlined some “homework” that I had set myself – to write a script that would create linearly separable data. I want the ability to create it in an interactive environment. But before I create the interactivity I want to get the foundations correct. So in this post I will build the code but with the interactive elements.

In the last post I identified these four key elements to the script:

- Data
- Graph
- Line
- Response

Let’s take a look at each of these in turn.

## 1. Data

The start point is to create a data table containing columns for two input variables (X1 and X2) and a binary response (Y).

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Names Default To Here(1); // create X1 and X2 data and set colour // properties for binary response nDataPoints = 100; dt = New Table("Linearly Separable Data", Add Rows(nDataPoints), New Column("X1", Numeric, Continuous, Format( "Fixed Dec", 10, 2 ), Set Formula( Random Uniform() ) ), New Column("X2", Numeric, Continuous, Format( "Fixed Dec", 10, 2 ), Set Formula( Random Uniform() ) ), New column("Y", Numeric, Nominal, Set Property( "Value Colors", {-1 = 3, 1 = 4) ) ); |

**Lines 5 & 7
**The number of data points in the table have been set as a variable so that this can be easily changed (and ultimately specified by the user.

**Lines 6 to 25
**This is the

*New Table*function. If it looks like a lot of code that’s just because I have put each

*New Column*field on a separate line. It could have been written like this:

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dt = New Table("Linearly Separable Data", Add Rows(nDataPoints), New Column("X1", Numeric, Continuous, Format( "Fixed Dec", 10, 2 ),Set Formula( Random Uniform() ) ), New Column("X2", Numeric, Continuous, Format( "Fixed Dec", 10, 2 ),Set Formula( Random Uniform() ) ), New column("Y",Numeric, Nominal, Set Property( "Value Colors", {-1 = 3, 1 = 4} )) ); |

– more compact but ultimately less readable.

**Lines 12 & 18
**The function

*Random Uniform*generates random numbers uniformly from the range 0 to 1.

**Lines 11 & 17
**The numbers have been formatted so that they display with two decimal places. This is purely cosmetic.

**Lines 20 to 24
**This is the definition of the response column. The response is binary. Setting the modelling type to

*Nominal*will assist when I want to colour the data points based on the binary value (it will prevent JMP trying to use a continuous scale for the colour).

**Line 23
**The

*Value Colors*property of the column can be used to pre-assign colours to the binary levels (-1 and +1) of the response. To figure out the syntax for this property you can refer to the documentation or get JMP to do it for you:

## 2. Graph

The above code can be used to create a data table containing 100 rows of X1 and X2 data. Using *Graph Builder* a scatterplot of X2 versus X1 can be produced. Y can be applied to the *Color* role (even though it doesn’t yet have any data). The range of the axes can be modified to be from 0 to 1 and the marker sizes can be made as large as possible. With all of these edits JMP will create the following code (with a couple of exceptions listed below):

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// create graph of X1 versus X2 with Y assigned as colour gb = dt << Graph Builder( Size( 500, 500 ), Show Control Panel( 0 ), Variables( X( :X1 ), Y( :X2 ), Color( :Y ) ), Elements( Points( X, Y, Legend( 17 ) ) ), SendToReport( Dispatch( {}, "X1", ScaleBox, {Min(0),Max(1),Inc(1)} ), Dispatch( {}, "X2", ScaleBox, {Min(0),Max(1),Inc(1)} ), Dispatch( {}, "graph title", TextEditBox, {Set Text( "" )} ), Dispatch( {}, "Graph Builder", FrameBox, {Marker Size( 6 )} ) ) ); |

– line numbers are based on the full script, so this block of code follows on from the data creation.

**Line 26**

I have added an explicit reference to the table (dt) and added a reference to the *Graph Builder* object, gb.

## 3. Line

Here is the code followed by an explanation:

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// draw line: y=mx+c m = -0.4; c = 0.7; p1 = {0,c}; p2 = {1,m+c}; rep = gb << Report; fb = rep[FrameBox(1)]; fb << Add Graphics Script( Line(p1,p2) ); |

**Lines 41 to 44
**The equation of a line can be written as:

Drawing the line only requires the line to be evaluated at two points (p1 and p2) corresponding to X1=0 and X1 = 1 respectively.

p1 = {0,c} and p2 = {1, m+c}

**Line 45
**A reference to the

*Graph Builder*window is obtained by sending the

*Report*messsage to the

*Graph Builder*object.

**Line 46
**This line obtains a reference to the

*FrameBox*, which is the graphical region of the graph (where the markers are plotted).

**Lines 47 to 49
**The contents of the

*FrameBox*can be customised by adding graphics scripts. The code uses the

*Line*function to plot a line between the points p1 and p2.

## 4. Response

The line defines a boundary. Data points above the boundary need to be assigned a Y value of +1. Those points satisfy the criteria:

The data points below the line are set to -1.

Ultimately the definition of the line will be interactive (next post!) and so it is helpful if the response if defined as a formula, and the formula is based on externally defined variables. So I am going to use table variables to store the values of m and c:

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// binary response // 1 if above line, -1 if below dt << Set Table Variable("m",m); dt << Set Table Variable("c",c); Column(dt,"Y") << Set Formula( If ( :X2 > m*:X1+c, 1 , -1 ) ); |

The Y column has already been assigned as a *Color* role on the graph so this formula also results in the markers being colour-coded:

I now have a script which generates a Y column containing binary values that are separated by a straight line of abitrary orientation. In my next blog I will add “grab-handles” to the line so that the orientation can be defined interactively by the user.

Finally, here is a full listing of the code:

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Names Default To Here(1); // create X1 and X2 data and set colour properties for binary response nDataPoints = 100; dt = New Table("Linearly Separable Data", Add Rows(nDataPoints), New Column("X1", Numeric, Continuous, Format( "Fixed Dec", 10, 2 ), Set Formula( Random Uniform() ) ), New Column("X2", Numeric, Continuous, Format( "Fixed Dec", 10, 2 ), Set Formula( Random Uniform() ) ), New column("Y", Numeric, Nominal, Set Property( "Value Colors", {-1 = 3, 1 = 4} ) ) ); // create graph of X1 versus X2 with Y assigned as colour gb = dt << Graph Builder( Size( 500, 500 ), Show Control Panel( 0 ), Variables( X( :X1 ), Y( :X2 ), Color( :Y ) ), Elements( Points( X, Y, Legend( 17 ) ) ), SendToReport( Dispatch( {}, "X1", ScaleBox, {Min(0),Max(1),Inc(1)} ), Dispatch( {}, "X2", ScaleBox, {Min(0),Max(1),Inc(1)} ), Dispatch( {}, "graph title", TextEditBox, {Set Text( "" )} ), Dispatch( {}, "Graph Builder", FrameBox, {Marker Size( 6 )} ) ) ); // draw line: y=mx+c m = -0.4; c = 0.7; p1 = {0,c}; p2 = {1,m+c}; rep = gb << Report; fb = rep[FrameBox(1)]; fb << Add Graphics Script( Line(p1,p2) ); // binary response // 1 if above line, -1 if below dt << Set Table Variable("m",m); dt << Set Table Variable("c",c); Column(dt,"Y") << Set Formula( If ( :X2 > m*:X1+c, 1 , -1 ) ); |

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