# Finding the 10 nearest points to every point (with corresponding distances) within a single variable

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Hi,

I need to find the 10 nearest points (with distances) to every other point within a group of points (i.e., 10 nearest neighrbors). Attached is the file containing all the points in question. I have previously tried to use "knnsearch" but to no avail. Can anyone produce the code that will do what I need?

Any help you could offer would be greatly appreciated.

Thanks,

Steve D.

##### 2 Comments

the cyclist
on 30 Sep 2019

Edited: the cyclist
on 30 Sep 2019

### Accepted Answer

Adam Danz
on 30 Sep 2019

Edited: Adam Danz
on 1 Oct 2019

After loading F_points, select one of the points by indicating its row index in the variable "pt". This solution computes the euclidean distance between that target point and all other points and then selects the 10 closest points. It then plots the results.

The index of all coordinates in order of proximity to the target point is stored in ascendIdx. The coordinates for the closest 10 points is stored in xyNearest.

xy = cell2mat(F_points)'; %[n x 2] matrix of (x,y) coordinates

pt = 20; % choose a target point in xy and we'll find the 10 nearest neighbors.

% Euclidean distance between xy(p,:) and all other points

dist = sqrt((xy(:,1)-xy(pt,1)).^2 + (xy(:,2)-xy(pt,2)).^2);

% Find the n closest values (excluding the point selected)

n = 10;

[~, ascendIdx] = sort(dist);

ascendIdx(ascendIdx==pt) = []; %remove the pt point

xyNearest = xy(ascendIdx(1:n),:);

% Plot

figure()

plot(xy(:,1),xy(:,2),'bo')

hold on

% Show the selected point

plot(xy(pt,1),xy(pt,2),'bo','MarkerFaceColor', 'y')

% Show nearest 'n' dots

plot(xyNearest(:,1),xyNearest(:,2),'r+')

% draw lines betwween target point and neightbors

% (not shown in figure below)

plot([xy(pt,1)*ones(n,1), xyNearest(:,1)]',...

[xy(pt,2)*ones(n,1), xyNearest(:,2)]', 'k-')

Results when pt = 20. The yellow dot is the one selected, the red + indicate the 10 closest neighbors.

[update]

To apply that for every point rather than just for one selected point, dist(n,m) below is a square matrix of the distance between point xy(n,:) and xy(m,:). ascendIdx is a square matrix of index values for each coordinate, sorted by closest distances. So, ascendIdx(p,q) is row index of q_th furthest point from xy(p,:).

xy = cell2mat(F_points)'; %[n x 2] matrix of (x,y) coordinates

dist = cell2mat(arrayfun(@(i)sqrt((xy(:,1)-xy(i,1)).^2 + (xy(:,2)-xy(i,2)).^2), 1:size(xy,1), 'UniformOutput', false));

n = 10;

[~, ascendIdx] = sort(dist);

See comments below for a comparison between this method and knnsearch() which is much slower.

##### 7 Comments

Konstantina Bantra
on 28 Feb 2020

Hello,

I have a very similar problem and I was wondering how would you loop through each point to extract each time the 10 closest points and specifically how you would set the value for pt in each loop iteration .

Adam Danz
on 28 Feb 2020

I think what you're looking for is the "update" section of my answer where you can apply the algorithm to every point to find the 10 closest points.

If you really want a loop, you can easily embed the first part of the answer within a for-loop.

### More Answers (1)

meghannmarie
on 30 Sep 2019

Edited: meghannmarie
on 30 Sep 2019

Try this:

load('F_points.mat')

f = cell2mat(F_points)';

Mdl = KDTreeSearcher(f);

[idx,distance] = knnsearch(Mdl,f,'k',11);

idx = idx(:,2:end);

distance = distance(:,2:end);

Each row in idx ocorresponds to the 10 closest points in each row in f. The first column is removed because that is the point itself so I search to 11 closest points.

##### 2 Comments

meghannmarie
on 1 Oct 2019

Edited: meghannmarie
on 1 Oct 2019

I put the data in a structure so you could see points with corresponding index to nearest neightbors and the distances.

The plot function here plots each point and its 10 neighbors in a separate figure and saves it. (is that what you want?) .This will save 953 figures in your working folder.

load('F_points.mat')

T = table();

T.xy = cell2mat(F_points)';

Mdl = KDTreeSearcher(f);

[idx,distance] = knnsearch(Mdl,xy,'k',11);

T.nearestIdx = idx(:,2:end);

T.nearestDistance = distance(:,2:end);

S = table2struct(T);

for n = 1:size(xy,1)

% Plot

h = figure();

plot(S(n).xy(1),S(n).xy(2),'bo','MarkerFaceColor', 'y')

hold on

% Show nearest 'n' dots

plot(xy(S(n).nearestIdx,1),xy(S(n).nearestIdx,2),'r*')

savefig(h,['pt_' num2str(n,'%03.0f') '.fig'])

close(h)

end

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