## Wolfram Function Repository function

Here is a WFR candidate [`ParallelCoordinatesPlot`](https://www.wolframcloud.com/obj/antononcube/DeployedResources/Function/ParallelCoordinatesPlot) :

[![enter image description here][1]](https://www.wolframcloud.com/obj/antononcube/DeployedResources/Function/ParallelCoordinatesPlot)

## Package

I implemented the package ["ParallelCoordinatesPlot.m"](https://github.com/antononcube/MathematicaForPrediction/blob/master/Misc/ParallelCoordinatesPlot.m) for doing this kind of plots and put it in GitHub. I plan to improve it some more. It is especially interesting to have automatic selection of the axes order that produces most discernible results.

    Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/Misc/ParallelCoordinatesPlot.m"]

    data = ExampleData[{"Statistics", "FisherIris"}];
    colNames = ExampleData[{"Statistics", "FisherIris"}, "ColumnDescriptions"];

    aData = GroupBy[data, #[[-1]] &, #[[All, 1 ;; -2]] &];

    grs = Table[ParallelCoordinatesPlot[aData, Most[colNames], "Colors" -> Random, "AxesOrder" -> Random, Direction -> dir, ImageSize -> Medium], {dir, {"Horizontal", "Vertical"}}, {m, 3}];
    Grid[grs, Alignment -> Left, Dividers -> All]

[![enter image description here][2]][2]

## First answer

Below is given a function definition to do this. It can be improved and "productized" some more, especially with legend's colors specification. (Currently random colors are picked from a hard coded color scheme.)

Get the "Fisher Iris" data and columns names:

    data = ExampleData[{"Statistics", "FisherIris"}];
    colNames = ExampleData[{"Statistics", "FisherIris"}, "ColumnDescriptions"]

Group the data according to the species of iris:

    aData = GroupBy[data, #[[-1]] &, #[[All, 1 ;; -2]] &];

Make the parallel plot:

    ParallelListLinePlot[aData, Most[colNames]]

[![enter image description here][3]][3]

(Several plot evaluations might be needed in order to produce more discernible coloring.)

## Definition

    Clear[ParallelListLinePlot];
    ParallelListLinePlot[data_?MatrixQ, opts : OptionsPattern[]] :=
      ParallelListLinePlot[data, Range[Length[data[[1]]]], MinMax /@ Transpose[data], opts];

    ParallelListLinePlot[data_?MatrixQ, colNames_List, opts : OptionsPattern[]] :=  
      ParallelListLinePlot[data, colNames, MinMax /@ Transpose[data], opts];

    ParallelListLinePlot[data_?MatrixQ, colNames_List, minMaxes_?MatrixQ, opts : OptionsPattern[]] :=
      Block[{divisions, data2, grBase, grid, xs, n = 5, c = 0.1},
        divisions = FindDivisions[#, n] & /@ minMaxes;
        data2 = 
         Transpose[
          MapThread[
           Rescale[#1, #2, {0, 1}] &, {Transpose[data], 
            MinMax /@ divisions}]];
        xs = Range[Length[data[[1]]]];
        grBase = 
         ListLinePlot[data2, opts, Axes -> False, 
          GridLines -> {Range[Length[data[[1]]]], None}];
        grid =
         Graphics[{
           Line[{{#, 0}, {#, 1}}] & /@ xs,
           MapThread[
            Function[{x, ds},
             MapThread[{Line[{{x - c, #2}, {x + c, #2}}], 
                Text[#1, {x - c, #2}, {2, 0}]} &, {N@ds, Rescale[ds]}]
             ],
            {xs, divisions}],
           MapThread[Text[#2, {#1, 0}, {0, 3}] &, {xs, colNames}]
           }];
        Show[grBase, grid]
        ] /; MatrixQ[data, NumberQ] && MatrixQ[minMaxes, NumberQ] && 
        Dimensions[minMaxes] == {Dimensions[data][[2]], 2};

    ParallelListLinePlot[aData_Association, colNames_List, opts : OptionsPattern[]] :=
      Block[{minMaxes, cols, grs},
        minMaxes = MinMax /@ Transpose[Join @@ Values[aData]];
        cols = RandomSample[ColorData[11, "ColorList"], Length[aData]];
        grs = 
         MapThread[
          ParallelListLinePlot[#1, colNames, minMaxes, PlotStyle -> #2, 
            opts] &, {Values@aData, cols}];
        Legended[Show[grs], SwatchLegend[cols, Keys[aData]]]
        ] /; MatrixQ[Join @@ Values[aData], NumberQ];


  [1]: https://i.sstatic.net/fOVesm.png
  [2]: https://i.sstatic.net/SzpTO.png
  [3]: https://i.sstatic.net/DZpG8.png