I have 2 matrices, containing x,y data, how do i find the closest point and extract data about that point?

Hey matlabians!

A is a matrix with two columns, A= [X,Y], that give the position x and y.

B is a matrix with 3 columns,B=[X,Y,P], the position x and y, and P is simply a value assigned to that position in space.

I could use a nearest neighbour search to find the value of B closest to A, what i actually want is for every point A find the closest B and give A the value of P.

I have seen nearest neighbor analysis attempted elsewhere but that has always been for one dataset, is there a command for this? does anyone have any help, it would help me out no end. Many thanks Rich

[Image Analyst]

Is B a 3D matrix, or an N rows by 3 column matrix? What does P represent? A Z value? If the Pythagorean theorem of any use to you?

[Richard Sims]

A is a matrix with two columns, that give the position x and y.

B is a matrix with 3 columns, the position x and y, and P is simply a value assigned to that position in space.

I could use a nearest neighbour search to find the value of B closest to A, what i actually want is for every point A find the closest B and give A the value of P.

I apologize if my question wasn't clear before

Answer 1

[Shashank Prasanna]

Why don't you use knnsearch in MATLAB and the indices of the point that is closest in B that in A, and use the index to extract the P value.

IDX = knnsearch(B(:,1:2),A)
B(:,IDX)

[Richard Sims]

I have tried to run this code but i am not familiar with knnsearch and the matlab documentation is difficult to understand. What is the IDX value, is it equivalent to P?

The IDX value is the same length as A so i can't run the second line as they are not the same dimensions? Am i missing something? Sorry for my ignorance

[Shashank Prasanna]

IDX just means indexes. It is just the index inside B which corresponds to each point in A. Which means if A(4,:) has a nearest neighbour in B(2,:) then IDX(4) will be 2. IDX will be same length of A because there is one closes neighbour in B for every element in A. Try it out with a simple example and you will see.

[Richard Sims]

Oh i see now, that makes plenty more sense.

As A an B are different lengths is there a way to adjust your second line of code to make it work?

[Shashank Prasanna]

It doesn't have to be the same length. Those are just indices, which means if your B is smaller in length, an entry in A still has some value in B which is its neighbour. However I did make a type in my code above, here is an example

A=rand(4,2); % 4 rows
B=rand(2,3); % 2 rows and p, NOT same length

IDX = knnsearch(B(:,1:2),A)
B(IDX,3) 
% What this line does is that for all the indices in IDX, it picks out the p value in the 3rd argument. note IDX is longer then B. Try it out.

[Richard Sims]

This definitely works in your example and i am sure i can work it for my data just as easily, THANKYOU!

[Richard Sims]

do you perhaps know anyway of altering this code to find the nearest neighbor if A and B were latitude and longitudes?

The stdist command works using latitude and longitude distances but then i wouldn't be able to index the data any longer like in your example above. The knnsearch help box says it accepts custom distance functions but i don't seem to be able to find one. Sorry to keep bothering you!

[sensation]

Hi, what about finding the neareast number and its id betweeen two different size arrays?

for instance, I have an array: A: 540x1 values; and another array B, 540 X 4860 consisted of 540 blocks (each one represented by 3x3 matrix-so 9X540=4860).

What I want to do is to search through each of these 9 area block numbers, compare it with single number from B and retrieve that area.

A: 45 etc X 540

B: 5 6 9

4 15 16

21 55 2

        etc X 540 blocks like this;

result: would be 55 and id=8 since the counting in my code goes like:

234

516

789 Thanks a lot for any tip!

Answer 2

[Sean de Wolski]

How about using dsearchn() to find the nearest neighbors?

doc dsearchn

Answer 3

[Matt J]

This seems to come up a lot lately in conversation,

http://www.mathworks.com/matlabcentral/fileexchange/18937-ipdm-inter-point-distance-matrix

[Richard Sims]

If the two matrices were A= [X,Y], B=[X,Y] then i think this solution would be perfect for determining the distances.

However i want to find the value P from matrix B and assign it to A and i don't believe this works for such a problem A= [X,Y], B=[X,Y,P]

[Matt J]

You can also use the tool to obtain the indices i, of the distance minimizing B(i). Just get the associated P(i) from that. Here's a way you can do it using my more crude distance matrix tool below

   D=interdists([Ax(:),Ay(:)].', [Bx(:), By(:)].');

   [~,imin]=min(D,[],2);

   P_of_A=P(imin);  

function Graph=interdists(A,B)
%Finds the graph of distances between point coordinates
%
% (1) Graph=interdists(A,B)
%
% in:
% 
% A:  matrix whose columns are coordinates of points, for example 
%          [[x1;y1;z1], [x2;y2;z2] ,..., [xM;yM;zM]]
%     but the columns may be points in a space of any dimension, not just 3D.
% 
% B:  A second matrix whose columns are coordinates of points in the same
%     Euclidean space. Default B=A.
% 
% 
% out:
% 
% Graph: The MxN  matrix of separation distances in l2 norm between the coordinates. 
%        Namely, Graph(i,j) will be the distance between A(:,i) and B(:,j).
%
%
% (2) interdists(A,'noself') is the same as interdists(A), except the output 
%     diagonals will be NaN instead of zero. Hence, for example, operations
%     like min(interdists(A,'noself')) will ignore self-distances.
%
% See also getgraph

noself=false;
if nargin<2  
    B=A; 
elseif ischar(B)&&strcmpi(B,'noself')
    noself=true;
    B=A;
end

N=size(A,1);
B=reshape(B,N,1,[]);

Graph=l2norm(bsxfun(@minus, A, B),1);

Graph=squeeze(Graph);

if noself
    n=length(Graph);
   Graph(linspace(1,n^2,n))=nan; 
end

Answer 4

[sensation]

Hi, what about finding the neareast number and its id betweeen two different size arrays?

for instance, I have an array: A: 540x1 values; and another array B, 540 X 4860 consisted of 540 blocks (each one represented by 3x3 matrix-so 9X540=4860).

What I want to do is to search through each of these 9 area block numbers, compare it with single number from B and retrieve that area.

A: 45 etc X 540

B: 5 6 9

4 15 16

21 55 2

        etc X 540 blocks like this;

result: would be 55 and id=8 since the counting in my code goes like:

234

516

789

[Stephen23]

@sensation: ask a new question and put a link to this one.