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Violin Plots for plotting multiple distributions (distributionPlot.m​)

version 1.15 (30.2 KB) by

Function for plotting multiple histograms side-by-side in 2D - better than boxplot.

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Editor's Note: This file was selected as MATLAB Central Pick of the Week

The zip-file contains the following files for visualizing distributions:
- distributionPlot.m: main function that allows creating violin plots
- myHistogram.m: generate histograms with 'ideal' bin width given the number of data points and the spread (Freedman-Diaconis rule). Note that for integer-valued data, each integer gets its own bin.

In addition, the zip file contains four helper functions: countEntries, colorCode2rgb, isEven, myErrorbar

If you want to overlay individual data points, you need to download the separate submission plotSpread (http://www.mathworks.com/matlabcentral/fileexchange/37105).

DistributionPlot allows visualizing multiple distributions side by side. It is useful for skewed unimodal data and indispensable for multimodal data. DistributionPlot is especially useful for showing the time evolution of a distribution.

Some of the examples from the help:

r = rand(1000,1);
rn = randn(1000,1)*0.38+0.5;
rn2 = [randn(500,1)*0.1+0.27;randn(500,1)*0.1+0.73];
rn2=min(rn2,1);rn2=max(rn2,0);
figure
ah(1)=subplot(2,4,1:2);
boxplot([r,rn,rn2])
ah(2)=subplot(2,4,3:4);
distributionPlot([r,rn,rn2],'histOpt',2); % histOpt=2 works better for uniform distributions than the default
set(ah,'ylim',[-1 2])
%--additional options
data = [randn(100,1);randn(50,1)+4;randn(25,1)+8];
subplot(2,4,5)
distributionPlot(data); % defaults
subplot(2,4,6)
distributionPlot(data,'colormap',copper,'showMM',5,'variableWidth',false) % show density via custom colormap only, show mean/std,
subplot(2,4,7:8)
distributionPlot({data(1:5:end),repmat(data,2,1)},'addSpread',true,'showMM',false,'histOpt',2) %auto-binwidth depends on # of datapoints; for small n, plotting the data is useful

Comments and Ratings (50)

Prasad

Prasad (view profile)

This is a great tool thank you. Is there an option to make the distribution plot higher in resolution? It looks pixelated.

I get around this by editing the ksdensity function call at 603. ksdensity takes a 'pts' argument where you can specify an arbitrary number of points to get finer resolution violin plots.

Great peace of code, just I was looking for. However, I have a question: Is there any way to normalize histograms across comparison (i.e. when using the option "widthDiv") such that both the left and right distributions will have the same area?

Nihanth Adina

Brian Katz

Brian Katz (view profile)

Sorry, this was my mistake in a way. If the data vector is a row, not a column, the result of the grouping are identical datasets. Could be good to put a check in here, to verify that the dimensions of the data and the grouping variable are the same.

Brian Katz

Brian Katz (view profile)

Can anyone confirm that this works with grouping the variable (and under which MatLab version)? I am having problems. Maybe an example would be good to confirm this. I get identical group data after grouping (R2017a).

Bazo Kara

Jonas

Jonas (view profile)

@Wynn, Markus: I have updated distributionPlot and renamed histogram.m

Dan

Dan (view profile)

Wynn

Wynn (view profile)

I'd like to echo Markus Millinger's comment that the code over-writes the MATLAB builtin 'histogram' function. Any chance of a patch with a renamed 'histogram.m'?

Anne Urai

Shilo

Shilo (view profile)

Great, Thanks, very useful!
Is there an option to use the addSpread function and color the dots using different values- so adding another dimension to the data?

Isobel

Isobel (view profile)

This is great, thanks. However, would you consider adding an option to cut plots off in the y-direction at the min and max of the dataset?

This is very nice! However, the function histogram clashes with the "new" Matlab function with the same name.

Amir

Amir (view profile)

Neat and nice. Much better than the box-plot for scientific work

Tiago

Tiago (view profile)

Johann

Johann (view profile)

Edgar Guevara

Edgar Guevara (view profile)

Displaying distributional differences provide more information of the samples and are very useful when distance from zero is meaningless.
Furthermore, the option to overlay the mean, SEM, sd and percentiles helps us better interpret the statistical analyses.
Overall, an invaluable option to the classic barplots and boxplots.

Holger Hoffmann

Holger Hoffmann (view profile)

Excellent, just what I needed. It served me very well.

I added a modified version to the MatLabFEx using the smooth kernel density (Violin Plot based on kernel density estimation).

Jonas

Jonas (view profile)

@Warwick: this looks like a bug - globalNorm=2 should do the trick, but at the moment, it seems like it would require equally spaced bins. I'll look into it.

Warwick

This is a great function. However I want to discriminate between two quite different distributions. I have a problem getting the Total area under the respective curves to be equal (to a nominal 1) for separate datasets (even with the same number of observations). Eg, Say I want to plot U and V left and right respectively where
U = normrnd(3.3,1.0,100,1);
V = normrnd(2.0,0.3,100,1);

then no matter what I do, they don't look anywhere near equal. Any ideas? or have I missed something obvious?

Dan K

Dan K (view profile)

This is a great tool... It would be nice if some of the functionality could be achieved without requiring toolboxes (e.g. I've cobbled together the code to do the smoothed histograms without the spline toolbox, using files from FEX).

Jonas

Jonas (view profile)

@all: thanks again for the suggestions, most of which are implemented now. Please note that plotSpread is now a submission on its own that needs to be downloaded separately.

Andres

Andres (view profile)

Very, very useful!

Jonas

Jonas (view profile)

@Yuri Kotliarov: I suggest you call addSpread.m directly, rather than via distributionPlot.m

@all: thanks for the good suggestions. I hope I can implement them soon!

Yuri K

Yuri K (view profile)

@Jonas, I didn't find if there is a way to change the width of dots spread (addSpread is 1). It doesn't seem to depend on distWidth. If I don't show the density (color is white), the distance between groups is quite large. Thanks.

Kelly Kearney

Kelly Kearney (view profile)

Overall, this is a great function, and I use it quite often to analyze model ensemble output. A few enhancements that could be nice:

- Add the option to display in a horizontal orientation.

- Add the option to filter outliers when calculating bin widths and kernal densities. Could also be nice to display these as points, as in boxplot, rather than connecting them via long lines to the main histogram.

- This is an edge case, but the function will error under the addSpread option if a column/group contains only NaNs and/or Infs.

Warwick

This is very good. I've just included some plots in a report. Thank you. Possibly you could add an extra feature within the options of 'showMM' = 6, say, which would be to draw a horizontal line of linewidth 2 for the median, and 25 & 75 pctiles at linewidth 1.

Jonas

Jonas (view profile)

@Yuri: I have implemented your suggestion (though I start the histograms from the very left or right side, respectively), and fixed the previous bug.

Yuri K

Yuri K (view profile)

@Jonas: Thanks for the answer. May I suggest a new feature? It would be nice to draw histogram at certain direction. Currently it's only centered, but also can be left- or right- directed. All you need to change is xBase variable at line 401: 0.5 to 0 for left direction, -0.5 to 0 for right direction. For someone it's easier to understand when the distributions looks like turned histograms.

Jonas

Jonas (view profile)

@Yuri Kotliarov: Currently, the only workaround is to call ksdensity outside of distributionPlot to ensure that the smoothing uses the same kernel:

x = zeros(10,1);
y = x+randn(10,1)*0.1;
[yy(:,2),yy(:,1)] = ksdensity(y,'width',0.01);
[xx(:,2),xx(:,1)] = ksdensity(x,'width',0.01);
distributionPlot({xx,yy},'showMM',false)

Unfortunately, the showMM option is bugged when you supply your own histograms at the moment, so you have to set that option to false.

Yuri K

Yuri K (view profile)

@Jonas: I have problem with smoothing (histOpt=1) when all values for a group are the same. In this case the distribution plot is very wide comparing to the same data with a little variance.
For example:
x = zeros(10,1);
y = x+randn(10,1)*0.1;
distributionPlot({x,y},'histOpt',1,'addSpread',1)

The same happens with a few outliers in x. I understand it's probably how ksdensity function works. But can you do anything to make the above cases comparable?

Alexander

Jonas

Jonas (view profile)

@Yuri: The new version of distributionPlot supports grouped data.

Yuri K

Yuri K (view profile)

Great! Thanks.

Jonas

Jonas (view profile)

@Yuri: No, it doesn't work with grouped data (yet). In the meantime, you can use a function like group2cell (http://www.mathworks.com/matlabcentral/fileexchange/11192-group2cell) to distribute your grouped data among cells to use with distributionPlot.

Jonas

Jonas (view profile)

@Brian: Thanks for the suggestions, and for sending me your sample code. I have not had time yet to update my code, though, but I will look into it!

Yuri K

Yuri K (view profile)

Does it work with grouped data, like boxplot does?

Brian Katz

Brian Katz (view profile)

This works quite well, giving a very interesting data presentation method. Some improvements could be the use of a colormap, rather than a fored gray scale. An example in teh help would also be a good addition.
I have started to try and make a combined plot which allows for both boxplot (using boxplotCsub) and distributionPlot. As both are symetrical, they can both be collapsed to one-sided and then combing, giving two very interesting looks at the same data sets.

Brian Katz

Brian Katz (view profile)

Very very cool.

Andrei Bejan

Denzel Li

Rob Campbell

Rob Campbell (view profile)

William Irwin

Chris Lydick

Oleg Komarov

Oleg Komarov (view profile)

Chiara

Chiara (view profile)

Christopher

Updates

1.15

renamed histogram to myHistogram to avoid clash with new Matlab function of the same name, added support for boxplot overlays

1.14

Improved documentation (more examples, link to plotSpread), added quantiles (thanks to Warwick for suggestion & testing). Also, belated thanks to Kelly for suggesting horizontal orientation.

1.13

Added the following new features:
- Horizontal plotting
- Plotting of half distributions
- Bugfixes

Additionally, plotSpread is now a separate submission.

1.12

Added option to align the bars at the left or the right (option "histOri"), as suggested by Yuri. Also, bugfix.

1.9

Improved normalization options. Thanks to Jake for the suggestion.

1.7

Fixed a bug in the code, and two mistakes in the example.

1.6

Made colorbar more meaningful if there is only one colormap and the bins are normalized globally (i.e. globalNorm is set to 1). Thanks to Brian Katz for the suggestion.

1.4

Changed input from optional arguments to parameterName/parameterValue pairs (note that the old syntax still works!).
Added several new features, such as support for grouped variables, overlay of data points, and user-defined colormaps.

1.3

Updated title to Violin Plot, because that's how (part) of these plots are called elsewhere.

1.2

Documented previously undocumented functionality, chose better screenshot to demonstrate how distributionPlot is better for comparing distributions than boxplot

1.1

Fixed cryptic error if the data was all NaNs (thanks Christopher for pointing it out!).
distributionPlot now also automatically converts arrays in cells to vectors and throws a warning.

MATLAB Release
MATLAB 7.6 (R2008a)
Acknowledgements

Inspired by: plot spread points (beeswarm plot)

Inspired: Violin Plot

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