MATLAB中复杂向量的速度有效分类

Question

I am trying to optimize this piece of code and get rid of the nested loop implemented. I am finding difficulties in applying a matrix to pdist function

For example, 1+j // -1+j // -1+j // -1-j are the initial points and i am trying to detect 0.5+0.7j to with point it belong by min distance approach .
any help is appreciated

function result = minDisDetector( newPoints, InitialPoints)
result = [];
for i=1:length(newPoints)
    minDistance = Inf;
    for j=1:length(InitialPoints)

        X = [real(newPoints(i)) imag(newPoints(i));real(InitialPoints(j)) imag(InitialPoints(j))];
        d = pdist(X,'euclidean');

        if d < minDistance
            minDistance = d;
            index = j;
        end
    end
    result = [result; InitialPoints(index)]; 
end     
end

Answer 1

You can use efficient euclidean distance calculation as listed in Speed-efficient classification in Matlab for a vectorized solution -

%// Setup the input vectors of real and imaginary into Mx2 & Nx2 arrays
A = [real(InitialPoints) imag(InitialPoints)];
Bt = [real(newPoints).' ; imag(newPoints).'];

%// Calculate squared euclidean distances. This is one of the vectorized
%// variations of performing efficient euclidean distance calculation using 
%// matrix multiplication linked earlier in this post.
dists = [A.^2 ones(size(A)) -2*A ]*[ones(size(Bt)) ; Bt.^2 ; Bt];

%// Find min index for each Bt & extract corresponding elements from InitialPoints
[~,min_idx] = min(dists,[],1);
result_vectorized = InitialPoints(min_idx);

---

Quick runtime tests with newPoints as 400 x 1 & InitialPoints as 1000 x 1 :

-------------------- With Original Approach
Elapsed time is 1.299187 seconds.
-------------------- With Proposed Approach
Elapsed time is 0.000263 seconds.

Answer 2

The solution is very simple. However you do need my cartprod.m function to generate a cartesian product.

First generate random complex data for each variable.

newPoints = exp(i * pi * rand(4,1));
InitialPoints = exp(i * pi * rand(100,1));

Generate the cartesian product of newPoints and InitialPoints using cartprod .

C = cartprod(newPoints,InitialPoints);

The difference of column 1 and column 2 is the distance in complex numbers. Then abs will find the magnitude of the distance.

A = abs( C(:,1) - C(:,2) );

Since the cartesian product is generated so that it permutates newPoints variables first like this:

 1     1
 2     1
 3     1
 4     1
 1     2
 2     2
 ...

We need to reshape it and get the minimum using min to find the minimum distance. We need the transpose to find the min for each newPoints . Otherwise without the transpose, we will get the min for each InitialPoints .

[m,i] = min( reshape( D, length(newPoints) , [] )' );

m gives you the min, while i gives you the indices. If you need to get the minimum initialPoints , just use:

result = initialPoints( mod(b-1,length(initialPoints) + 1 );

Answer 3

It is possible to eliminate the nested loop by introducing element-wise operations using the euclidean norm for calculating the distance as shown below.

    result = zeros(1,length(newPoints)); % initialize result vector
    for i=1:length(newPoints)
        dist = abs(newPoints(i)-InitialPoints); %calculate distances
        [value, index] =  min(dist);
        result(i) = InitialPoints(index);
    end