TikZ: Drawing the same data with scatter plots and parallel coordinates

Question

I am new to TikZ and trying to recreate the following image (which was created in R): (Translation: correlation = +1, correlation = -1, two clusters, circle, normal distribution)

Each "column" displays the same data, using a scatter plot and parallel coordinates. The graphics are of course fairly simple, so it would be possible to construct them by hand with the basic \draw -- and \fill circle commands. I am however looking for the best way to create, loop through, and draw the data, kind of like it is done in the R source.

(Note: The image doesn't have to look exactly like the above, that is the number of dots does not really matter, the dots in the clusters and normal distribution can have different coordinates and it would be nice if the circle was actually round and the font was the normal font used in my LaTeX document)

Answer 1

You can do this using PGFPlots. You can generate the x and y components for the different plots in a table, and then use them either in a normal scatterplot, or using the quiver style -- which is ordinarily used for drawing vector fields -- for the parallel plots.

\documentclass[landscape]{article}

\usepackage{pgfplots, pgfplotstable}
\begin{document}


% Create a function for generating inverse normally distributed numbers using the Box–Muller transform
\pgfmathdeclarefunction{invgauss}{2}{%
  \pgfmathparse{sqrt(-2*ln(#1))*cos(deg(2*pi*#2))}%
}


% Create the data columns. \pgfplotstablerow is the row index
\pgfplotstablenew[
    create on use/index/.style={
        create col/expr={\pgfplotstablerow}
    },
    create on use/negcorr/.style={
        create col/expr={24-\pgfplotstablerow}
    },
    create on use/clusterx/.style={ % Offset half the data by 4
        create col/expr={rand+(\pgfplotstablerow<12)*4}
    },
    create on use/clustery/.style={
        create col/expr={rand+(\pgfplotstablerow<12)*4}
    },
    create on use/circlex/.style={
        create col/expr={cos(\pgfplotstablerow*360/24)}
    },
    create on use/circley/.style={
        create col/expr={sin(\pgfplotstablerow*360/24)}
    },
    create on use/normalx/.style={
        create col/expr={invgauss(rnd,rnd)}
    },
    create on use/normaly/.style={
        create col/expr={invgauss(rnd,rnd)}
    },
    columns={index,negcorr,clusterx,clustery,circlex,circley,normalx,normaly}
]{24}\datatable

% Save the datatable to a file so it can be used with the quiver style
\pgfplotstablesave{\datatable}{data.csv}

% Create plot styles for the scatter and parallel plots
\pgfplotsset{
    scatterplot/.style args={#1,#2}{
        width=4cm, height=4cm,
        only marks, mark size=1,
        xtick=\empty, ytick=\empty,
        enlargelimits=false,
        table/x=#1,
        table/y=#2
    },
    parallel/.style args={#1,#2}{
        width=4cm, height=4cm,
        no markers,
        xtick=\empty, ytick=\empty,
        enlargelimits=false,
        table/x expr=24,
        table/y=#1,
        quiver={u=24,v=\thisrow{#2}-y} % The quiver plots use relative coordinates, so we'll have to subtract the y coordinate
    }
}

% Create commands for making the plots easier
\newcommand{\scatterplot}[2]{
    \begin{tikzpicture}[trim axis left, trim axis right]
        \begin{axis}[scatterplot={#1,#2}]
            \addplot [black] table {data.csv};
        \end{axis}
    \end{tikzpicture}
}

\newcommand{\parallelplot}[2]{
    \begin{tikzpicture}[trim axis left, trim axis right]
        \begin{axis}[parallel={#1,#2}]
            \addplot [black] table {data.csv};
        \end{axis}
    \end{tikzpicture}
}



\scatterplot{index}{index}%
\scatterplot{index}{negcorr}%
\scatterplot{clusterx}{clustery}%
\scatterplot{circlex}{circley}%
\scatterplot{normalx}{normaly}%

\parallelplot{index}{index}%
\parallelplot{index}{negcorr}%
\parallelplot{clusterx}{clustery}%
\parallelplot{circlex}{circley}%
\parallelplot{normalx}{normaly}%

\end{document}

Answer 2

Jake just went one step further and generated the data tables beautifully. So this is now obsolete as I wanted to give an example and finish off with saying This would be much better with actual data but nevermind :)

\documentclass[border=3mm]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{groupplots}
\pgfplotsset{compat=1.6}
\begin{document}
\begin{tikzpicture}
\begin{groupplot}[group style={group size=5 by 2},view={0}{0},xtick=\empty,ytick=\empty,ztick=\empty,enlargelimits=false]
    \nextgroupplot[view={90}{0}]
        \pgfplotsinvokeforeach{-10,...,10}{
        \addplot3[only marks] coordinates {(0,{#1},{-#1} ) (3,{#1},{-#1} )};
        }
    \nextgroupplot[view={90}{0}]
        \pgfplotsinvokeforeach{-10,...,10}{
        \addplot3[only marks] coordinates {(0,{#1},{-#1} ) (3,{-#1},{#1} )};
        }
    \nextgroupplot[view={90}{0},enlargelimits]
        \pgfplotsinvokeforeach{1,...,15}{
        \addplot3[only marks] coordinates {(0,{3+rand},{3+rand})};
        \addplot3[only marks] coordinates {(0,{-3+rand},{-3+rand}) (3,{-3+rand},{-3+rand})};
        }
    \nextgroupplot[view={90}{0},enlargelimits]
        \pgfplotsinvokeforeach{0,15,...,345}{
        \addplot3[only marks] coordinates {(0,{sin(#1+5)},{cos(#1+5)} ) (3,{sin(#1+95)},{cos(#1+95)} ) };
        }
    \nextgroupplot[view={90}{0}]
        \pgfplotsinvokeforeach{1,...,25}{
        \addplot3[only marks] coordinates {(0,{5*rand},{5*rand} ) (3,{5*rand},{5*rand})};
        }
    \nextgroupplot
        \pgfplotsinvokeforeach{-10,...,10}{
        \addplot3[no marks] coordinates {(0,{#1},{-#1} ) (3,{#1},{-#1} )};
        }
    \nextgroupplot
        \pgfplotsinvokeforeach{-10,...,10}{
        \addplot3[no marks] coordinates {(0,{#1},{-#1} ) (3,{#1},{#1} )};
        }
    \nextgroupplot[enlarge x limits=false]
        \pgfplotsinvokeforeach{1,...,15}{
        \addplot3[no marks] coordinates {(0,{3+rand},{3+rand}) (3,{3+rand},{3+rand})};
        \addplot3[no marks] coordinates {(0,{-3+rand},{-3+rand}) (3,{-3+rand},{-3+rand})};
        }
    \nextgroupplot
        \pgfplotsinvokeforeach{0,15,...,345}{
        \addplot3[no marks] coordinates {(0,{sin(#1+5)},{cos(#1+5)} ) (3,{sin(#1+95)},{cos(#1+95)} ) };
        }
        \nextgroupplot
        \pgfplotsinvokeforeach{1,...,25}{
        \addplot3[no marks] coordinates {(0,{5*rand},{5*rand} ) (3,{5*rand},{5*rand})};
        }
    \end{groupplot}
\end{tikzpicture}

\end{document}