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Represent three dimensions of data on a 2D ListPlot?

Jacob Lapenna

Jacob Lapenna, USBR

Posted 7 years ago

Is it possible to make a List Plot in which each point is colored based on the count of that point's `{x,y}` occurrence in the data set? Specifically, I have data of the form `data={{x1,y1}->c1, ... ,{xn,yn}->cn}` where `cn` is the nth count for the occurrence of `{xn,yn}` in the data set. I can almost get what I want in two ways: Method 1: ListPlot[{#1} & @@@ data,PlotMarkers -> cf /@ #2 & @@@ data] where cf is my ColorDataFunction[], and I have neglected my plotting options for clarity. Method 2: ListPlot[{#1} & @@@ data,PlotStyle -> cf /@ #2 & @@@ data] again where cf is my ColorDataFunction[], and I have neglected my plotting options for clarity. For method 1, the rendered markers are large squares, and for method 2, the markers are automatically sized. In both cases, I loose control of marker size and shape customization.

POSTED BY: Jacob Lapenna

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Moderation Team

Moderation Team, WOLFRAM

Posted 7 years ago

POSTED BY: Moderation Team

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 7 years ago

I would try with graphics primitives: data = {{0, 0} -> 2, {1, 1} -> 1, {-2, -3} -> 1}; nmax = Max[data[[All, -1]]]; Graphics[{PointSize[Large], data /. ({x_, y_} -> n_Integer) :> {Hue[n/nmax], Point[{x, y}]}}]

POSTED BY: Gianluca Gorni

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 7 years ago

Apart from Gianlucas short and elegant solution I think it might be a good idea to reorder your data first. This way you can make sure that "interesting" points are not overlapped by "uninteresting" ones. Here a minimal example (using List of List instead of List of Rules): data = RandomInteger[100, {100^2, 2}]; tdata0 = Tally[data]; tdata1 = GatherBy[SortBy[tdata0, Last], Last]; tdata2 = Transpose /@ tdata1; tdata3 = First[Transpose@tdata2]; Here in this case we have 7 different occurences: Length[tdata3] (* Out: 7 *) Now in the most simple case we can do ListPlot[tdata3, AspectRatio -> Automatic, PlotStyle -> {Directive[GrayLevel[0], PointSize[1 s]], Directive[GrayLevel[.5], PointSize[2 s]], Directive[RGBColor[0, 0, 1], PointSize[3 s]], Directive[RGBColor[1, 0, 0], PointSize[4 s]], Directive[RGBColor[1, 1, 0], PointSize[5 s]], Directive[RGBColor[0, 0, 1], PointSize[6 s]], Directive[RGBColor[0, 1, 0], PointSize[7 s]]} /. s -> .005] which already results in: Well, of course if you do not have that many data, then Gianlucas solution is surely preferable!

Apart from Gianlucas short and elegant solution I think it might be a good idea to reorder your data first. This way you can make sure that "interesting" points are not overlapped by "uninteresting" ones. Here a minimal example (using List of List instead of List of Rules):

data = RandomInteger[100, {100^2, 2}];
tdata0 = Tally[data];
tdata1 = GatherBy[SortBy[tdata0, Last], Last];
tdata2 = Transpose /@ tdata1;
tdata3 = First[Transpose@tdata2];

Here in this case we have 7 different occurences:

Length[tdata3]
(* Out:    7 *)

Now in the most simple case we can do

ListPlot[tdata3, AspectRatio -> Automatic, 
 PlotStyle -> {Directive[GrayLevel[0], PointSize[1 s]], 
    Directive[GrayLevel[.5], PointSize[2 s]], 
    Directive[RGBColor[0, 0, 1], PointSize[3 s]], 
    Directive[RGBColor[1, 0, 0], PointSize[4 s]], 
    Directive[RGBColor[1, 1, 0], PointSize[5 s]], 
    Directive[RGBColor[0, 0, 1], PointSize[6 s]], 
    Directive[RGBColor[0, 1, 0], PointSize[7 s]]} /. s -> .005]

which already results in:

enter image description here