High speed classification for complex vectors in MATLAB
I am trying to optimize this piece of code and get rid of the nested loop. I am at a loss to apply matrix to pdist function
For example, 1 + j // - 1 + j // - 1 + j // - 1-j are starting points and I am trying to detect 0.5 + 0.7j with the point it refers to using the minimum distance method.
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
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You can use the efficient calculation of Euclidean distances given in for - Speed-efficient classification in Matlab
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
how 400 x 1
and InitialPoints
how 1000 x 1
:
-------------------- With Original Approach
Elapsed time is 1.299187 seconds.
-------------------- With Proposed Approach
Elapsed time is 0.000263 seconds.
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The solution is very simple. However, you need my cartprod.m function to create 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));
Produce the Cartesian product newPoints
and InitialPoints
with cartprod
.
C = cartprod(newPoints,InitialPoints);
The difference between column 1 and column 2 is the distance in complex numbers. Then he abs
will find the distance.
A = abs( C(:,1) - C(:,2) );
Since the Cartesian product is generated so that it first rearranges the variables newPoints
as follows:
1 1
2 1
3 1
4 1
1 2
2 2
...
We need reshape
it and get the minimum, using min
to find the minimum distance. We need to transpose to find the min for each newPoints
. Otherwise, without transposition, we get min for each InitialPoints
.
[m,i] = min( reshape( D, length(newPoints) , [] )' );
m
gives you min and i
gives you the indices. If you need to get the minimum InitialPoints
, just use:
result = initialPoints( mod(b-1,length(initialPoints) + 1 );
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You can eliminate the nested loop by introducing rudimentary operations using the Euclidean norm to calculate 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
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