Extract the indices based on the minimum absolute value

Hi all,

I have two matrices: A and B. Each row of matrix A has an identifier (index). I want to get the identifiers of each row of matrix B based on how much the values in each row are close to each row of matrix A. For example, if the values in the first row of matrix B is the closest to those in the last row of matrix A, assign the identifier of the last row of matrix A to the first row of matrix B, and so on so forth.

My code below tries to do this by calculating the absolute value between each row of B and all the rows of A and chooses the one that returns the minimum absolute value to assign its identifier. However, I think there is something wrong with this as the resulting identifers of matrix B are computed the same as of A.

close
clear all

%define the number of random numbers
n = 10; 

%define the min and max ranges of random values
stvar = [0 4]; %on the 1st dim
ndvar = [-1 1]; %on the 2nd dim

%construct the first random matrix
A(:,1) = stvar(1)+(stvar(end)-stvar(1)).*rand(n,1); %first column
A(:,2) = ndvar(1)+(ndvar(end)-ndvar(1)).*rand(n,1); %second column
A = [A(:,1) A(:,2)]; %collect both columns into one matrix

%propose the identifiers of matrix A
iden_A = randi([1,n/2],n,1);

%construct the second random matrix
B(:,1) = stvar(1)+(stvar(end)-stvar(1)).*rand(n,1); %first column
B(:,2) = ndvar(1)+(ndvar(end)-ndvar(1)).*rand(n,1); %second column
B = [B(:,1) B(:,2)]; %collect both columns into one matrix

%finding the identifiers of matrix B
iden_B = [];
%go through all receiving pairs of space and direction
for i = 1:size(B,1)
    %define the B pair
    B_pair = [B(i,1) B(i,2)];
    for j = 1:size(A,1)
        abs_value(j,:) = [abs(A(j,1)-B_pair(1)) abs(A(j,2)-B_pair(2))];
    end
    [~,minloc] = find(min(abs_value(:,1)) & min(abs_value(:,2)));
    minloc = iden_A(i);
    iden_B = [iden_B ; minloc];
end

Any help would be appreicted.

Thanks

Answer 1

[Abhishek Kumar Singh]

Hi @LH

Instead of using the absolute difference for each dimension separately, compute the Euclidean distance between the rows of A and B. This is done using sqrt(sum((A - B_pair).^2, 2)). And then use min(distances) to find the index of the row in A that is closest to the current row in B.

This should ensure that each row in matrix B gets the identifier of the closest row in matrix A.

Refer to the snippet below:

close all
clear all

% Define the number of random numbers
n = 10; 

% Define the min and max ranges of random values
stvar = [0 4]; % on the 1st dim
ndvar = [-1 1]; % on the 2nd dim

% Construct the first random matrix
A(:,1) = stvar(1) + (stvar(end) - stvar(1)) * rand(n,1); % first column
A(:,2) = ndvar(1) + (ndvar(end) - ndvar(1)) * rand(n,1); % second column
A = [A(:,1) A(:,2)]; % collect both columns into one matrix

% Propose the identifiers of matrix A
iden_A = randi([1, n/2], n, 1);

% Construct the second random matrix
B(:,1) = stvar(1) + (stvar(end) - stvar(1)) * rand(n,1); % first column
B(:,2) = ndvar(1) + (ndvar(end) - ndvar(1)) * rand(n,1); % second column
B = [B(:,1) B(:,2)]; % collect both columns into one matrix

% Finding the identifiers of matrix B
iden_B = [];

% Go through all receiving pairs of space and direction
for i = 1:size(B,1)
    % Define the B pair
    B_pair = B(i,:);
    
    % Calculate the Euclidean distance between B_pair and all rows of A
    distances = sqrt(sum((A - B_pair).^2, 2));
    
    % Find the index of the minimum distance
    [~, minloc] = min(distances);
    
    % Assign the identifier of the closest row in A to the current row in B
    iden_B = [iden_B; iden_A(minloc)];
end

% Display the results
disp('Matrix A:');

Matrix A:

disp(A);

    3.7020    0.4212
    0.6053   -0.3360
    1.0224    0.9213
    3.7692    0.6286
    2.7539    0.9528
    3.5434   -0.5355
    2.4248    0.8720
    0.8152   -0.8384
    1.6536    0.9495
    3.6147   -0.7808

disp('Identifiers of Matrix A:');

Identifiers of Matrix A:

disp(iden_A);

     1
     2
     5
     5
     5
     3
     1
     2
     5
     4

disp('Matrix B:');

Matrix B:

disp(B);

    0.9341    0.0032
    0.7069   -0.3004
    2.5137   -0.5250
    1.8370    0.5525
    3.6043   -0.0645
    2.3333    0.9780
    1.9238   -0.2512
    3.7867   -0.5267
    2.2506    0.4221
    3.3141   -0.4006

disp('Identifiers of Matrix B:');

Identifiers of Matrix B:

disp(iden_B);

     2
     2
     3
     5
     3
     1
     1
     3
     1
     3

Let's go through the first few rows of B and verify the calculations:

Row 1 of B: ( [0.9341, 0.0032] )

• Calculate Euclidean distances to each row in A:

distances = sqrt(sum((A - [0.9341, 0.0032]).^2, 2))

= [2.8259, 0.3990, 0.9344, 2.8985, 1.9816, 2.7432, 1.6181, 0.8511, 1.0655, 2.8735]

• The minimum distance is 0.3990, which corresponds to row 2 in A.
• Identifier for row 2 in A is 2.
• So, iden_B(1) = 2.

Row 2 of B: ( [0.7069, -0.3004] )

• Calculate Euclidean distances to each row in A:

distances = sqrt(sum((A - [0.7069, -0.3004]).^2, 2))

= [3.0764, 0.1033, 1.2538, 3.1488, 2.2337, 2.8363, 1.9807, 0.5451, 1.3885, 2.9975]

• The minimum distance is 0.1033, which corresponds to row 2 in A.
• Identifier for row 2 in A is 2.
• So, iden_B(2) = 2.

Answer 2

[Torsten]

Maybe you mean

%define the number of random numbers
n = 10; 

%define the min and max ranges of random values
stvar = [0 4]; %on the 1st dim
ndvar = [-1 1]; %on the 2nd dim

%construct the first random matrix
A(:,1) = stvar(1)+(stvar(end)-stvar(1)).*rand(n,1); %first column
A(:,2) = ndvar(1)+(ndvar(end)-ndvar(1)).*rand(n,1); %second column
A = [A(:,1) A(:,2)]; %collect both columns into one matrix

%propose the identifiers of matrix A
iden_A = randi([1,n/2],n,1);

%construct the second random matrix
B(:,1) = stvar(1)+(stvar(end)-stvar(1)).*rand(n,1); %first column
B(:,2) = ndvar(1)+(ndvar(end)-ndvar(1)).*rand(n,1); %second column
B = [B(:,1) B(:,2)]; %collect both columns into one matrix

%finding the identifiers of matrix B
iden_B = [];
%go through all receiving pairs of space and direction
for i = 1:size(B,1)
    %define the B pair
    B_pair = [B(i,1) B(i,2)];
    for j = 1:size(A,1)
        abs_value(j,:) = [abs(A(j,1)-B_pair(1)) abs(A(j,2)-B_pair(2))];
    end
    [~,minloc] = min(sqrt(abs_value(:,1).^2+abs_value(:,2).^2));
    iden_B = [iden_B ; iden_A(minloc)];
end
iden_A

iden_A = 10x1

1 3 4 1 2 4 1 3 3 3

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iden_B

iden_B = 10x1

3 3 1 1 1 3 4 1 4 3

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