Kmeans failed to converge after 10 million iterations! (BIG DATA)

Hello everyone,

I'm working with a matrix X ( 11 000 000 x 27 (single) matrix )

I want to cluster my data into k clusters, where k can be any integer from 4 to 20. I have standardise my data as I have values with very different units, and I'm using the kmeans() function in R2018a MATLAB.

X = bsxfun(@minus, X, mean(X));

X = bsxfun(@rdivide,X,std(X));

rng(0) % for repeatability

[km_ind,~,sumd] = kmeans(X,k,'MaxIter',10000000,'Replicates',5);

I have tried with up to 10 million 'MaxIter', but I still don't get convergence. I have tried different values for k and it doesn't change the warning message. Sometimes it gives me the warning message in a matter of seconds, and I doubt 10 million iterations were done in a couple of seconds.

Warning: Failed to converge in 10000000 iterations during replicate 1.

In kmeans/loopBody (line 476)

In internal.stats.parallel.smartForReduce (line 136)

In kmeans (line 343)

What am I missing ? what am I doing wrong ? any suggestions?

Thanks very much

EDIT 1: I have uploaded the first 60 000 observations of my data (already standardised). I also have problems when clustering this subset, and does not converge after a 10 million iterations.

EDIT 2: New information: I've compared the clustering results using: - 10^9 iterations (thousahd million iterations!) - 10^8 iterations - 10^7 iterations - 10^5 iterations - 10^4 iterations - 10^3 iterations - 10^2 iterations - 10 iterations and some more in between 10 and 50 iterations, and although I always receive the non-convergence warning, the result actually stops changing somewhere in between iteration 15th and 20th. What could make matlab yield the non-convergence message even when there actually seems to be a convergence in the results?

[the cyclist]

Are you able to upload your data in a MAT file, so we can try it out? (I don't remember if the site will allow a file that large to be uploaded.)

If you get the same issue with a smaller random sample, maybe upload that data?

[Ame ZL]

Hi,

I've uploaded the first 60 000 observations just now (in my code below is X ),

I'm copying the exact code that I just tried with this subset, and that in less than a second gave me the results with the warning that failed to converge after 10 million iterations.

rng(7)%for repeatability

[km_ind,~,sumd] = kmeans(X,4,'MaxIter',10000000);

Thanks for your help

[Ame ZL]

New information:

I've compared the clustering results using:

- 10^9 iterations (thousahd million iterations!)

- 10^8 iterations

- 10^7 iterations

- 10^5 iterations

- 10^4 iterations

- 10^3 iterations

- 10^2 iterations

- 10 iterations

and some more in between 10 and 50 iterations, and although I always receive the non-convergence warning, the result actually stops changing somewhere in between iteration 15th and 20th.

What could make matlab yield the non-convergence message even when there actually seems to be a convergence in the results?

Answer 1

[Image Analyst]

What makes you think there are 4 to 20 clusters? Any basis to justify that belief?

If you have some that you think are in different clusters, then use them as training points and try k nearest neighbors. I believe, from the nature of KNN, it must converge. Or try random forest, which is kind of like an ad hoc big if-then-else statement.

[Ame ZL]

Hi,

I'm actually trying a hybrid supervised - unsupervised method, and the ground truth data analysis yield 4 clusters. But as they are not necessarily completely 'identifiable' between each other, I was also attempting to use the 'elbow' method to obtain the best cluster number, hence I've been trying between 4 and 20.

As per the other algorithms, well my study is comparing the repeatability of different supervised and unsupervised methods in a particular application. I'll (and have) also try other methods, but being kmeans such a simple method is the first (and probably only) unsupervised method that I wanted to try.

But beyond all my objectives I can't make the algorithm converge, so is not possible for me to advance forward.

Thanks

[xiaoyu Guo]

Hi, did you solved this problem yet? I have the same problem as yours and I don't know what to do. I am looking forward to your early reply. Thank you *~*

[Image Analyst]

xiaoyu, post your data and number of clusters in a new question.

[xiaoyu Guo]

Hi, friend. Thank you for your respones, this is my code and the warning messege ^..^

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   50.5495  -50.5495  -50.5495   50.5495   50.5495
   50.5495  -50.5495   50.5495  -50.5495  -50.5495
  -50.5495   50.5495   50.5495  -50.5495  -50.5495
   50.5495  -50.5495   50.5495  -50.5495  -50.5495
   50.5495  -50.5495  -50.5495  -50.5495   50.5495
  -50.6719   50.5495  -50.5495  -50.5495  -50.7624
  -30.3484  -50.5495  -50.5495   31.3433  -50.5495
   50.5495   50.5495   50.5495  -50.5495  -50.5495
   50.9496  -50.9455  -50.5495  -50.5495  -51.0070
  -50.5495  -50.5495  -50.5495  -50.5495  -50.5514
  -50.9228  -50.5961   50.6760  -50.5495   50.6378
   50.5495  -50.5495   50.5495  -50.5495  -50.5495
  -50.5495  -50.5495  -50.5495  -50.5495  -50.5495
   50.5495   50.5495   50.5495   50.5495  -50.5495
   50.5495   50.5495   50.5495  -50.5495   50.5495
   50.5495   50.5495   50.5495  -50.5495  -50.5495
   50.5495  -50.5495  -50.5495   50.5495  -50.5495
  -51.8893  -51.8876   51.8676  -51.8697   51.8467
   50.6673  -50.7316  -50.8992   51.2138   50.7708
   50.5495   50.5495   15.7765   11.8970   50.5495
  -50.5495  -50.5495  -50.5495   50.5495  -50.5495
  -50.5495  -50.5495  -50.5495  -50.5495  -50.5495
   50.5495   -8.2574    2.4745   50.5495   50.5495
   50.1603   50.0487  -50.0276  -50.0394  -50.0278
  -50.5495   50.5495  -50.5495  -50.5495  -50.5495
  -50.5495  -50.5495  -50.5495  -50.5495  -50.5495
  -50.5495   50.5495  -50.5495   50.5495   50.5495
   50.5495  -50.5495  -50.5495  -50.5495  -50.5495
  -50.5495  -50.4651   50.5495  -50.3473  -50.3293
   23.2047  -53.5870   50.5495  -56.2688   50.5495
  -50.5495   50.5495  -50.5495  -50.5495   50.5495
  -50.5495  -50.5495  -50.5495  -50.5495   50.5495
   50.5495  -52.4671  -50.5495   50.5495  -50.5495
   50.5495  -50.5495   50.5495   50.5495   50.5495
  -50.5495  -50.5495  -50.5495  -50.5495   50.5495
  -52.0829   52.0714   52.0757  -52.0764  -52.0851
  -51.1122  -51.0331  -51.2328  -50.9995  -50.5495
   50.5495   50.7897   50.6055  -50.5495  -50.7466
  -28.3830  -50.5495  -50.5495  -12.3907  -50.5495
  -50.5495  -50.5495   50.5495   50.5495  -50.5495
   50.5495  -50.5495   50.5495   50.5495   50.5495
  -50.7739   50.7787   50.5495  -50.6297  -50.7468
  -50.5495  -50.5495   50.5495  -50.5495  -50.5495
   52.0654   52.1130   52.0709   52.0657   52.0963
  -50.5495  -50.5495  -50.5495   50.5495  -50.5495
   -8.1983  -50.5495  -50.5495  -18.5050   50.5495
  -50.5495   50.5495   50.5495   50.5495   50.5495
  -50.5495   50.5495   50.5495  -50.5495   50.5495
  -50.5495  -50.5495  -50.5495   50.5495  -50.5495
   50.5495  -50.5495  -50.5495   50.5495   50.5495
  -50.5495  -50.5495  -50.5495  -50.5495  -50.5495
  -19.2620   50.5495  -50.5495   19.6786   50.5495
  -50.5495   50.5495  -50.5495   50.5495  -50.5495
   50.5495   50.5495   50.5495   50.5495  -50.5495
  -50.5495   50.5495  -50.5495   50.5495   50.5495
  -50.5495  -50.5495  -50.5495  -50.5495   50.5495
  -50.5495  -50.5495   50.5495   50.5495  -50.5495
   50.5495  -50.5495  -50.5495  -50.5495  -50.5495
   50.5495  -50.5495  -50.5495  -50.5495  -50.5495
   50.5495  -50.5495  -50.5495  -50.5495   50.5495
   50.5495  -50.5495  -50.5495  -50.5495  -50.5495
  -50.9010   50.8318  -50.7511  -50.5495  -50.7897
   51.1295  -51.2401  -51.1991  -51.1824   51.1085
  -50.5495   50.5495  -50.5495   50.5495  -50.5495
  -50.5495  -50.5495   50.5495   50.5495  -50.5495
  -50.5495  -50.5495  -50.5495  -50.5495  -50.5495
];

    
for i=2:16      % i want to know the best k in k-means
    cidx = kmeans(locations,i,'distance','cityblock','MaxIter',200000000);  
    disp('number1')
    value(1,i) = mean(silhouette(locations,cidx,'cityblock')); 
    disp('number2')
end
   

[Image Analyst]

xiaoyu, this is not a Answer to AME's question. Post the link to your totally separate, new discussion thread so that we don't keep sending emails to Ame about new activity on this thread, by editing your question above to remove the code and data and give the link to the new question that is all your own.