Matlab, how to calculate AUC (Area Under Curve)?

Question

I have the file data.txt with two columns and N rows, something like this:

0.009943796 0.4667975
0.009795735 0.46777886
0.009623984 0.46897832
0.009564759 0.46941447
0.009546991 0.4703958
0.009428543 0.47224948
0.009375241 0.47475737
0.009298249 0.4767201
[...]

Every couple of values in the file correspond to one point coordinates (x,y). If plotted, this points generate a curve. I would like to calculate the area under curve (AUC) of this curve.

So I load the data:

data = load("data.txt");
X = data(:,1);
Y = data(:,2);

So, X contains all the x coordinates of the points, and Y all the y coordinates.

How could I calculate the area under curve (AUC) ?

It depends. Is the [trapezoidal rule](http://en.wikipedia.org/wiki/Trapezium_rule) good enough for you? — Oliver Charlesworth, Dec 28 '11 at 19:46
http://www.mathworks.com/matlabcentral/fileexchange/24597-area-under-a-curve — Robert Harvey, Dec 28 '11 at 19:47
@Robert: that looks like it's the area under the curve of a *function* (Matlab has a whole bunch of `quad`xxxx() functions). OP is looking for numerical integration of data. — Jason S, Dec 28 '11 at 19:53

score 4 · Accepted Answer · answered Dec 28 '11 at 19:49

4

Easiest way is the trapezoidal rule function trapz.

If your data is known to be smooth, you could try using Simpson's rule, but there's nothing built-in to MATLAB for integrating numerical data via Simpson's rule. (& I'm not sure how to use it for x/y data where x doesn't increase steadily)

answered Dec 28 '11 at 19:49

Jason S

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Thanx guys, I have tried with trapz(), but it strangely gives me always negative values. Why this? If it is an area, it should be always positive... Any idea? Thanx! – DavideChicco.it Dec 28 '11 at 20:02
3

If the curve go below 0 the area actually will be decreased. This is just integral, remember. To get the positive AUC you might need to change the baseline. For example, subtract the `min(Y)` from `Y`. Or you can use `abs(Y)` to sum up positive and negative areas. – yuk Dec 28 '11 at 20:20
2

Technically, if you use `trapz(x,y)`, the sign of the result depends on the sign of y and the sign of the change in x. (remember: this is integral of y dx) So if your y values are positive but x is decreasing, you'd get a negative number. It's actually a little more complicated than that: for closed curves, the sign should be positive for clockwise encircling and negative for counterclockwise encircling (see http://en.wikipedia.org/wiki/Green%27s_theorem#Area_Calculation ). – Jason S Dec 28 '11 at 22:34

score 4 · Answer 2 · answered Mar 01 '12 at 18:46

4

just add AUC = trapz(X,Y) to your program and you will get the area under the curve

answered Mar 01 '12 at 18:46

Simon

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score 2 · Answer 3 · answered Jul 16 '13 at 19:06

2

[~,~,~,AUC] = perfcurve(labels,scores,posclass);

% posclass might be 1

http://www.mathworks.com/matlabcentral/newsreader/view_thread/252131

answered Jul 16 '13 at 19:06

Nucular

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score 1 · Answer 4 · answered May 02 '13 at 11:33

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Source: Link

An example in MATLAB to help you get your answer ...

x=[3 10 15 20 25 30];
y=[27 14.5 9.4 6.7 5.3 4.5];
trapz(x,y)

In case you have negative values in y, you can do like,

y=max(y,0)

answered May 02 '13 at 11:33

Faheem

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score 1 · Answer 5 · answered Jan 02 '12 at 13:27

1

You can do something like that:

AUC = sum((Y(1:end-1)+Y(2:end))/2.*...
  (X(2:end)-X(1:end-1)));

answered Jan 02 '12 at 13:27

Oli

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Oli, could you pls add an explanation or link for the equation you used? – Tin Feb 21 '17 at 10:32

score 0 · Answer 6 · answered Jun 19 '14 at 05:56

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There are some options to trapz for the person ready to do some coding by themselves. This link shows the implementation of Simpson's rule, with python code included. There is also a File Exchange on simpsons rule.

answered Jun 19 '14 at 05:56

patrik

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Matlab, how to calculate AUC (Area Under Curve)?

6 Answers6

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