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

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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

Antworten (1)

Adam Danz
Adam Danz am 24 Jun. 2018
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')
  1 Kommentar
Image Analyst
Image Analyst am 24 Jun. 2018
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;

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