automatic circles that enclose clusters of similar data something like lineCoeff = polyfit(x, y, n) (regression line)

hello, I have generated a pca plot and there are obvious clusters of the data but to make it more evident I would like to draw centroids (or similar shape fitting the same purpose) around the similar data in the pca plot. Is there a way to do this in matlab? I did try John D'Errico's function: incircle(): but I don't think its quite what I am looking for. i kind of want regression centroids around the clusters of similar data.

Update: John says that won't work so to be more specific, I would like a regression line to go into 3D plot.

Thank you for your response. I have included an example of what i am looking for below.

[Jan]

What are the available inputs? Do you have a list of points belonging to each cluster and you search the minimal circle including them?

[Neo]

That sounds like it would work!!! I do have a list of points belonging to each cluster. How would i search for the minimal circle including them? Do you have an example that i could learn from?

It would be placed into a "for loop" that says if this value matches then it will be placed here. From there the minimal circle including them will be generated. How would i do that?

[Neo]

@Jan I hope you do respond because even if its not the answer I would like to know how to do this!!

Answer 1

[John D'Errico]

incircle has nothing to do with your problem. Sorry.

You would first want to use some sort of clustering algorithm on your data. k-means is the go-to tool for that.

Once you have the data clustered into groups, I would then just use the centroids from k-means itself as the center of the circles.

Alternatively, you could use my circumcircles tool to compute the circles, but the k-means centroids seem to make sense.

Finally, once you decide on the center of the circles, the radii are easy to generate as the distance to the farthest point in that cluster.

[Neo]

The k clustering algorithm I used was pca (it clustered the data for me) so I guess now I just need centroids from pca itself as the center of the circles.

The centroid I want is the golden circles in the pic I showed. I just want those circles to pop up automatically over the data point clusters. Is there an example code you can demonstrate with that does this?

[John D'Errico]

NO. PCA does NOT cluster data! PCA is used to reduce the dimensionality of higher dimensional data. The result in this case is a 2-dimensional set of points. Your eyes may see clusters of points, but the computer still does not know which points belong to which cluster.

load fisheriris
whos

  Name           Size            Bytes  Class     Attributes

  ans            1x41               82  char                
  cmdout         1x33               66  char                
  meas         150x4              4800  double              
  species      150x1             18100  cell                

So there are 4 variables in the data.

 [COEFF, SCORE, LATENT] = pca(meas);

Now, plot the scores for the first two components resultin from the PCA.

 plot(SCORE(:,1),SCORE(:,2),'o')

There are clearly two groups of data in this. But PCA has not told you which points belong in which group!!!!! That is not what PCA does. I'll see how well kmeans will do.

[IDX, C] = kmeans(SCORE(:,1:2),2,'distance','cityblock');
plot(SCORE(IDX==1,1),SCORE(IDX==1,2),'ro')
hold on
plot(SCORE(IDX==2,1),SCORE(IDX==2,2),'go')

It seems the kmeans code has mis-clustered one point, at least for this problem. regardless, how do we now find the circle that surrounds the clusters?

For this, I will use my minboundircle code, as found on the file exchange.

[C1,R1] = minboundcircle(SCORE(IDX == 1,1),SCORE(IDX == 1,2))

C1 = 1×2

1.4271 -0.0275

R1 = 2.3856

[C2,R2] = minboundcircle(SCORE(IDX == 2,1),SCORE(IDX == 2,2))

C2 = 1×2

-1.9934 0.0457

R2 = 1.3507

theta = linspace(0,2*pi)';
plot(R1*cos(theta) + C1(1),R1*sin(theta) + C1(2),'r-')
plot(R2*cos(theta) + C2(1),R2*sin(theta) + C2(2),'g-')
axis equal
hold off

As I said, the use of k-means here has missed the mark just a little, because it mis-clustered that one point.

A quick check shows the point that was misclassified was point number 99. (I identified that point using an old utility of mine, called selectdata.)

IDX(99)

ans = 2

IDX(99) = 1; % reclass that point into the other group.

And now replot the corrected circles.

plot(SCORE(IDX==1,1),SCORE(IDX==1,2),'ro')
hold on
plot(SCORE(IDX==2,1),SCORE(IDX==2,2),'go')

[C1,R1] = minboundcircle(SCORE(IDX == 1,1),SCORE(IDX == 1,2))

C1 = 1×2

1.3988 -0.0370

R1 = 2.4148

[C2,R2] = minboundcircle(SCORE(IDX == 2,1),SCORE(IDX == 2,2))

C2 = 1×2

-2.6177 0.1986

R2 = 1.1628

theta = linspace(0,2*pi)';
plot(R1*cos(theta) + C1(1),R1*sin(theta) + C1(2),'r-')
plot(R2*cos(theta) + C2(1),R2*sin(theta) + C2(2),'g-')
axis equal
hold off

[Neo]

I see that k means is different from PCA.

I had data from xls file imported than attempted to make a 3d plot

Here's my k means attempt to make a 3d Plot with my data (spoiler alert it did not work):

idx = kmeans(C,3,'NumDimensions',3,'Perplexity',per,'Algorithm','exact','Distance');

figure(1)

clf

hold off

title("k means 3D");

fs = 12;

for i = 1:nObs

value = 0;

if(ismember(seg(i),gg) == 1)

if(strcmp(datasheet(i,2),"happy")==1)

text(Y(i,1),Y(i,2),Y(i,3),ds(i),'Color',,[value,0,1],,'fontsize',fs,'bold','fontweight');

elseif(strcmp(datasheet(i,2),"joyful")==1)

text(Y(i,1),Y(i,2),Y(i,3),ds(i),'Color',,[1,0,value],'fontsize',fs,'bold','fontweight');

elseif(strcmp(datasheet(i,2),"exercise")==1)

text(Y(i,1),Y(i,2),Y(i,3),ds(i),'Color'[0,1,value]'fontsize',fs,'bold','fontweight');

end

end

end

minx = 1.1*min(Y(:,1));

maxx = 1.1*max(Y(:,1));

miny = 1.1*min(Y(:,2));

maxy = 1.1*max(Y(:,2));

minz = 1.1*min(Y(:,3));

maxz = 1.1*max(Y(:,3));

axis([minx,maxx,miny,maxy,minz,maxz])

[Neo]

Can you suggest how I could fix this?

[Neo]

Dr. D’ricco can you make a kmeans plot from this example code I have made? It isn’t homework I’m practicing my skills in Matlab

[Neo]

@John D'Errico I attempted kmeans and ask for your correction to make it working with min bound circle included for clusters if that makes sense thanks for your time or you can refer me to another working example I can learn from. Thanks @John D'Errico