How to cluster lines ?

How to cluster lines ?

Here below an example:

x = [1  1 2  3 4 5  6  7   1   1   2  3  3   4  4  5 15 15 15 16 16 16 17 18 20 20 21
     2  5 9  5 4 9  6  7   3   7   3  5  7   6  7 14 14 19 23 22 15 16 17 20 22 21 23
     ];
y = [2 10 3 20 5 2  4  6 100 106 102 93 90 100 81 77 66 59 74 60 62 35 48 69 30 58 55
     6  8 3 11 8 2 10 21  66 108  75 92 90 100 82 72 67 55 75 60 68 55 53 70 32 37 32
     ];
plot(x,y,'LineWidth',2,'color','k') ;

Answer 1

[Image Analyst]

I'd pass in both endpoints of each line to kmeans and let it figure it out. Demo attached.

If you have a situation where one endpoint is in one cluster and the other is in a different cluster you might decide to assign both end points to whatever cluster is nearer one of the endpoints.

[Sim]

thanks @Image Analyst, I have tried to use k-means clustering as you have suggested

x = [1  1 2  3 4 5  6  7   1   1   2  3  3   4  4  5 15 15 15 16 16 16 17 18 20 20 21
     2  5 9  5 4 9  6  7   3   7   3  5  7   6  7 14 14 19 23 22 15 16 17 20 22 21 23
     ];
y = [2 10 3 20 5 2  4  6 100 106 102 93 90 100 81 77 66 59 74 60 62 35 48 69 30 58 55
     6  8 3 11 8 2 10 21  66 108  75 92 90 100 82 72 67 55 75 60 68 55 53 70 32 37 32
     ];

X = [x(1,:) x(2,:)];
Y = [y(1,:) y(2,:)];
numGroups = 3;
groupLabels = kmeans([X',Y'],numGroups);


hold on
plot(x,y,'LineWidth',2,'color','k') ;
gscatter(X, Y, groupLabels,[],[],30);

......but it looks like that k-means clustering does not work perfectly.....

Since here 4 edges would have endpoints with two colors, I should check manually & visually those edges and re-assign the correct color/cluster...... I do not know.... hmmmmm....

[Sim]

I have also tried another algorithm for clustering, called spectral cluster, but it looks like even worse...

x = [1  1 2  3 4 5  6  7   1   1   2  3  3   4  4  5 15 15 15 16 16 16 17 18 20 20 21
     2  5 9  5 4 9  6  7   3   7   3  5  7   6  7 14 14 19 23 22 15 16 17 20 22 21 23
     ];
y = [2 10 3 20 5 2  4  6 100 106 102 93 90 100 81 77 66 59 74 60 62 35 48 69 30 58 55
     6  8 3 11 8 2 10 21  66 108  75 92 90 100 82 72 67 55 75 60 68 55 53 70 32 37 32
     ];

X = [x(1,:) x(2,:)];
Y = [y(1,:) y(2,:)];
numGroups = 3;
groupLabels = spectralcluster([X',Y'],numGroups);

hold on
plot(x,y,'LineWidth',2,'color','k') ;
gscatter(X, Y, groupLabels,[],[],30);

[Image Analyst]

If I just plot x and y

x = [1  1 2  3 4 5  6  7   1   1   2  3  3   4  4  5 15 15 15 16 16 16 17 18 20 20 21
    2  5 9  5 4 9  6  7   3   7   3  5  7   6  7 14 14 19 23 22 15 16 17 20 22 21 23
    ];
y = [2 10 3 20 5 2  4  6 100 106 102 93 90 100 81 77 66 59 74 60 62 35 48 69 30 58 55
    6  8 3 11 8 2 10 21  66 108  75 92 90 100 82 72 67 55 75 60 68 55 53 70 32 37 32
    ];
% Plot endpoints
plot(x, y, '.', 'MarkerSize', 30)

How do I know which (x,y) pair corresponds to the two end points of a single line?

[Sim]

hope this drawing clarifies a bit...