Changing the indices in kmeans clustering

I am using kmeans function to cluster a given dataset. I have predefined indices for each data point in the set. I need to check the accuracy level of the clustering by comparing the data point indices. The problem is that kmeans uses its own indexing, thus, creating errors when comparing the defined indices and the kmeans indices. (For example, I have data points with indices "2" and "6", but the kmeans results in indices "1" and "2". This makes the comparison void.)

It is possible to instruct MATLAB to use the predefined indices for the kmeans cluster assignment?

Answer 1

[Image Analyst]

I made a nice demo for this last month.

Click here for code from my earlier solution

For example, here is how I reassigned arbitrary class numbers according to distance from the origin:

And for another example, I reassigned arbitrary class numbers according to distance from the origin. See attached code.

Answer 2

[the cyclist]

I am not certain how robust this solution will be, but I think one possibility is to input initial centroid guesses that are near your predefined indices. For example,

rng default

N = 2000;
x = [randn(N/2,1); 5+randn(N/2,1)];
y = [randn(N/4,1); 5+randn(N/4,1); randn(N/4,1); 5+randn(N/4,1)];

figure
scatter(x,y)

% Don't make an initial guess
[idx_noguess,C_noguess] = kmeans([x,y],4)

% Make an initial guess that is close
initialCentroidGuess = [5 5; 0 5; 5 0; 0 0];
[idx_guess,C_guess] = kmeans([x,y],[],'Start',initialCentroidGuess)

resulting in

C_noguess =

    4.9852    4.9874
    5.0432    0.0325
   -0.0624    0.0335
   -0.0689    5.0692

C_guess =

    4.9852    4.9874
   -0.0689    5.0692
    5.0432    0.0325
   -0.0624    0.0335

Notice how when I make an initial guess, the final values are "aligned" with how I primed them.

Answer 3

[Walter Roberson]

It is possible to instruct MATLAB to use the predefined indices for the kmeans cluster assignment?

No.

Also, the solution from "the cyclist" only reduces the problem and does not fix it. It is possible (though not common) for the identity of clusters to swap.

About the best you can do is ask to return the cluster centers, and then find the distance from each to your initial centers, min(), build an index map, and process the returned indices through the index map.

However, it would not be uncommon for two different clusters to both be closest to the same point, so you have to be careful with the matching process.

Answer 4

[the cyclist]

There is a different solution, but it can only be applied after-the-fact, when you have seen how kmeans has assigned the clusters. You could create a map from the indices output by MATLAB to the predefined ones:

map = [1 3 4 2];

which is interpreted as

• kmeans index 1 should map to your predefined index 1
• kmeans index 2 should map to your predefined index 3
• kmeans index 3 should map to your predefined index 4
• kmeans index 4 should map to your predefined index 2

Then, if you simply do

redefined_index = map(original_index_from_kmeans);

you'll get the indices you need.