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) ?

Answer 1

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)

Answer 2

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

Answer 3

You can do something like that:

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

Answer 4

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)

Answer 5

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

% posclass might be 1

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

Answer 6

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.