Hello, currently I'm working on outlier detection techniques. Can I detect outliers in multivariate datasets with three-sigma rule? If yes, then how?

m=mean(meas)

m =

    5.8433    3.0573    3.7580    1.1993

>> d=std(m)

d =

    1.9185

>> d=3*std(m)

d =

    5.7555

Answer 1

[Adam Danz]

Are you asking how to do this programmatically or conceptually? You want to detect all values that are greater than three standard deviations from the mean.

Here's a demo with fake data to work through conceptually. In the plot, data outside of 3sd along the y axis are circled.

%fake data
rng(180)
d = normrnd(166,42,1,5000); 
m = mean(d); 
sd = std(d); 
outliers = false(size(d)); 
outliers(d < m-sd*3) = true; 
outliers(d > m+sd*3) = true; 

figure
t = 1:length(d); 
plot(t, d, 'b.')
hold on
plot(t(outliers), d(outliers), 'ro')
rh = refline(0,m); 
set(rh, 'color', 'm')
rh2 = refline(0,m+sd*3); 
rh3 = refline(0,m-sd*3); 
set([rh2,rh3], 'color', 'm', 'linestyle', '--')

legend('data', 'outliers', 'mean', '3rd sd')

[Image Analyst]

This:

outliers = false(size(d)); 
outliers(d < m-sd*3) = true; 
outliers(d > m+sd*3) = true;

could be simplified to this:

outliers = abs(d - m) > sd * 3;