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) ?

Inexpensive

It depends. Is the trapezoidal rule good enough for you? – Attenborough

mathworks.com/matlabcentral/fileexchange/… – Quentinquercetin

@Robert: that looks like it's the area under the curve of a function (Matlab has a whole bunch of quadxxxx() functions). OP is looking for numerical integration of data. – Chappie

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)

Chappie

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! – Inexpensive

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. – Pigling

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 en.wikipedia.org/wiki/Green%27s_theorem#Area_Calculation ). – Chappie

Answer 2

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

Somewhere

Answer 3

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

% posclass might be 1

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

Annalee

Answer 4

You can do something like that:

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

Biogenesis

Oli, could you pls add an explanation or link for the equation you used? – Besought

Answer 5

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)

Granville

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.

Midtown