version 1.0.0.0 (2.53 KB) by
Jeremy Heil

Draws a venn diagram for two or three sets with proportional areas.

15 Downloads

Updated 28 Oct 2004

No License

%

% function error = vennX( data, resolution )

%

% vennX - draws an area proportional venn diagram

%

% Draws a venn diagram (either two or three set) using

% circles, where the area of each region is proportional

% to the input values.

%

% INPUT:

% data - a vector of counts for each set partition

%

% For a two circle diagram:

% data is a three element vector of:

% |A|

% |A and B|

% |B|

%

% For a three circle diagram:

% data is a seven element vector of:

% |A|

% |A and B|

% |B|

% |B and C|

% |C|

% |C and A|

% |A and B and C|

%

% resolution - A measure of accuracy on the image,

% typical values are within 1/100 to 1/1000 of

% the maximum partition count. Note that smaller

% resolutions take longer compute time.

%

% OUTPUT:

% error - the difference in area of each partition

% between the actual area and the input vector

%

% EXAMPLES:

%

% vennX( [ 106 26 257 ], .05 )

%

% vennX( [ 75 143 210 ], .1 )

%

% vennX( [ 16 3 10 6 19 8 3 ], .05 )

%

%

% COMMENTS:

%

% The implementation is trivial, for the two circle case, two circles

% are drawn to scale and moved closer and closer together until the

% overlap is 'near' to the desired intersection. For the three

% circle case, it is repeated three times, once for each pair of

% circles. Hence the two circle case is almost exact, whereas the

% three circle case has much more error since the area |A and B and C|

% is derived. This means that large variations from random, especially

% close to zero, will have larger errors, for example

%

% vennX( [ 20 10 20 10 20 10 0], .1 )

%

% as opposed to

%

% vennX( [ 20 10 20 10 20 10 10], .1 )

%

% ENHANCEMENTS

%

% The implementation could be sped up tremendously using a MRA

% (multi-resolutional analysis) type algorithm. e.g. start with a

% resolution of .5 and find the distance between the circles, then use

% that as a seed for a resolution of .1, then .05, .01, etc.

%

% The error vector could be used as a measure to 'perturb' the position

% of the third circle as to minimize the error. This could be done

% with a simple gradient descent method. This would help the

% exceptions described above where the distribution deviates from

% random.

%

% When small mishapen areas are drawn, the text does not match up, e.g.

% vennX( [ 15 143 210 ], .1 )

%

%

% Original implementation and method by Jeremy Heil, for the Order of

% the Red Monkey, and the Tengu

%

% Oct. 2004

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Jeremy Heil (2020). Proportional Venn Diagrams (https://www.mathworks.com/matlabcentral/fileexchange/6116-proportional-venn-diagrams), MATLAB Central File Exchange. Retrieved .

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Compatible with any release

**Inspired:**
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Yonatan katzThanks for sharing. Nice function.

Nitin Sadrasgordon mcclureDanielle JorgensonIs there any way to center the venndiagram? I have a large circle that has 2575 and the other two have only 277 and 12.

Angela Piscowhen using for 3 circle diagram, if you replace line 137

[X,Y] = meshgrid( 0:resolution:size_x, 0:resolution:size_y );

with the following 2 lines the circles are not cut anymore:

sizeXY = max(size_x,size_y);

[X,Y] = meshgrid( (-.05*sizeXY):resolution:(1.05*sizeXY), (-.05*sizeXY):resolution:(1.05*sizeXY));

Yuri KDoes not show anything if there is no overlap. I'd like to see separated circles of size proportional to number of elements in them. Please don't make a new figure by default. Also how to make several diagrams have the same (or similar) resolution? I'm creating multiple diagrams on the same figure in subplots. Another suggestion - it would be nice to be able to customize colors and labels (position, font, etc).

manojNice work ! Thank you !

lizdoes this not work with the student version? I am attempting to make a simple venn diagram and it will not work.

JuliaI think the sub-set situation still works, except the number labels are not at the optimal place for display.

Matt J, I think you might be interpreting the inputting data slightly differently. I think the commenting of this function should be that if you are doing 2 sets, the 3 numbers should be:

data(1) = number of elements in A but not in B (as opposed to be interpreted as number of elements in A);

data(2) = number of elements in the intersect of A and B;

data(3) = number of elements in B but not in A;

Same is true for the 7-element (3-sets Venn diagram) data. Each data point represents the single color shade on the graph.

For example,

data(1) in the 7-element vector represents the number of elements in A but and Not in B or C.

data(2) represents the number of elements in the intersect of A and B but not in C.

I wrote this little utility that calculate these values if you just input your original sets. Your original sets can be 3 vectors or 3 cell arrays (with strings). If you leave the 3rd vector empty you'll get the 2-set diagram. Feedback welcome!

function vennX_calc(x,y,z)

%% Venn diagram for 2 sets;

if isempty(z)

if ~isnumeric(x) %cell array of strings;

if or(size(y,1)>1,size(x,1)>1) %colum vectors;

all=[x;y];

else

all=[x y];

end

allString = unique(all);

numericVec = 1:length(allString);

x = numericVec(ismember(allString,x));

y = numericVec(ismember(allString,y));

end

vec = NaN(1,3);

xNy = length(unique([x y]));

vec(1) = xNy - length(y);

vec(2) = length(x)+length(y)-xNy;

vec(3) = xNy - length(x);

%% Venn Diagram for 3 Sets;

else

if ~isnumeric(x) %cell array of strings;

if or(size(z,1)>1,or(size(y,1)>1,size(x,1)>1)) %colum vectors;

all=[x;y;z];

else

all=[x y z];

end

allString = unique(all);

numericVec = 1:length(allString);

x = numericVec(ismember(allString,x));

y = numericVec(ismember(allString,y));

z = numericVec(ismember(allString,z));

end

vec = NaN(1,7);

xIy = intersect(x,y);

yIz = intersect(y,z);

zIx = intersect(z,x);

xIyIz = intersect(xIy,z);

vec(7) = length(xIyIz);

vec(2) = length(xIy) - vec(7);

vec(4) = length(yIz) - vec(7);

vec(6) = length(zIx) - vec(7);

vec(1) = length(x) - vec(2) - vec(6) - vec(7);

vec(3) = length(y) - vec(2) - vec(4) - vec(7);

vec(5) = length(z) - vec(4) - vec(6) - vec(7);

end

vec %display the input vector;

%% draw the diagram;

vennX(vec,0.01);

end

matt jdoes this fail for the case where B is a subset of A? I entered A, B, and A&B where A&B=B and did not get what i expected

Pedro MartinsRichard MoffittTo get the pretty primary colors, you should change the code @142 to look like this:

img = img + 1 ...

img = img + 2 ...

img = img + 4 ...

and then use a colormap like this:

colormap([...

0,0,0;... %0

0,0,1;... %1

0,1,0;... %2

0,1,1;... %3

1,0,0;... %4

1,0,1;... %5

1,1,0;... %6

1,1,1]); %7

Oscar PuigA nice and simple script with great results.

Thanks!

Steve HaddockGreat! Thanks for this -- I was pretty surprised that I couldn't find it in the stats toolbox. Nice implementation.

John VeyseyVery nice! My incredibly picky comment: The default color scheme has some repetition. It could be made to have each of the 3 circles be (eg) primary colors, and then have the overlap regions reflect the colors of a color wheel ... but that may just be nerdy.