Matlab - 如何从一组二维点中删除异常值？

Question

My question has two parts:

1. I have two 1D arrays containing X and Y values. How can I create another 1D array where each element is a 2D point?
2. How to remove outliers from the resulting array?

For example, something like this:

x = [1 3 2 4 2 3 400];
y = [2 3 1 4 2 1 500];
xy = [[1 2] [3 3] [2 1] [4 4] [2 2] [3 1] [400 500]];
result = rmoutliers(xy, 'mean');

The result should look like:

result = [[1 2] [3 3] [2 1] [4 4] [2 2] [3 1]]

My goal is to remove outlier points in a set of points like this (the points forming a line at the top):

Answer 1

First create an nx2 matrix.

x = [1 3 2 4 2 3 400]';
y = [2 3 1 4 2 1 500]';
xy = [x, y]

Now xy takes the following form:

xy = 
     1     2
     3     3
     2     1
     4     4
     2     2
     3     1
   400   500

Now pass this matrix through rmoutliers:

result = rmoutliers(xy);

The value of result should now be:

result =
     1     2
     3     3
     2     1
     4     4
     2     2
     3     1

As a note, there is no way to make a 1D array where each point has 2 dimensions because... well then you have a 2-dimensional array by definition. Keep things simple and just build a 2-dimensional matrix from the start!

Answer 2

The function rmoutliers.m should resemble something like the following:

function [result] = rmoutliers(x, y, tol)
% rmoutliers: main function,
% removes outliers with absolute value > tol(a scalar)
% out of [x,y] series
dist = calcDist(x, y);
mean = calcMean(dist);
result = zeros(2,length(x));

for i = 1:length(dist)
    result(:,i) = [x(i), y(i)];
    if abs(dist(i) - mean) > tol
        result(:,i) = [-1, -1];
    end  
end

result(result == -1) = [];
result = reshape(result, 2, []);

end



function [dist] = calcDist(x, y)
%calcDist: calculates absolute value of
% each pair of elements in [x, y]
% (the distance from the origin)
dist = sqrt(x.^2 + y.^2);

end



function [mean] = calcMean(dist)
%calcMean: average of input array
mean = sum(dist) / length(dist);

end

All that goes in its own file rmoutliers.m in your Documents/MATLAB directory. It should be evoked from the main Matlab prompt by typing:

x = [1 3 2 4 2 3 400];
y = [2 3 1 4 2 1 500];
result = rmoutliers(x, y, 100);

where 100 is just an example of the tolerance factor that will be used to determine the threshold of difference from the mean of an outlier.

EDIT: forgot to output members of result as pairs. You can use the cell structure for that. After having run the program, type at the prompt:

C = cell(1,length(x));
for i = 1:length(x)
    C(i) = {result(1,i), result(2,i)};
end

% to read from cell structure:
D = cell2mat(C);
D = reshape(D,2, []);