manipulating matrix for outlier detection

%ids are the point numbers, L is the measurement which need to be checked for outlier.
ids=[1;2;3;4;5;6;7;8;9;10];
L=[0.16;0.2;0.18;0.4;0.14;0.15;0.11;0.17;0.15;0.18]; %measurement
% To perform outlier detection for 0.16;
L_1=[0.2;0.18;0.4;0.14;0.15;0.11;0.17;0.15;0.18]; %without first row of L (0.16)
L_ort_1=mean(L_1);
for i=1:9 % n=9
  V(i)=L_1(i)-L_ort_1;
end
V=V(:);
S=sqrt((V'*V)/7);
d=abs(L_ort_1-0.16)  %0.16 is subjected to outlier detection
Sd=((S^2)/8)+S^2;
t_1=d/Sd;
t_statistics_1=tinv(0.995,7);
if t_statistics_1 > t_1
  % there is no outlier for 0.16 (id=1) go on to check second number (0.20).
  %L_2=[0.16;0.18;0.4;0.14;0.15;0.11;0.17;0.15;0.18]  %without 0.20 (second number)
  % do the same things to L2 for detection of 0.20....................
  if t_statistics_1 < t_1
    % there is outlier for 0.16, save its id (1) and go on to check second number (0.20)
  end
end

I need to write this kind of loop for this outlier detection for each row of L.

Thanks in advance.

Answer 1

[Image Analyst]

So, what's stopping you?

If you want an outlier detection method developed by the Mathworks, see this by the amazing Brett Shoelson: http://www.mathworks.com/matlabcentral/fileexchange/3961-deleteoutliers

You might also look at Median Absolute Deviation which is a more robust method than looking at the z score, which can be influenced by the outlier itself which you want to get rid of ( not a good thing obviously).

[Greg Heath]

Correct. However, the sensitivity of the zscore method can be mitigated via iterated removal or modification, plots and human intervention.

Greg

Answer 2

[Greg Heath]

The best way to detect outliers

 1. Standardize the data to zero-mean/unit variance
 2. Plot
 3. Find outliers where abs(x) > mean + alpha*sigma
     where alpha is a user determined parameter

Hope this helps.

Thank you for formally accepting my answer

Greg