Clustering in matlab

Question

I have a 3d box with some points in it (1800). Like this:

Now I have to cluster these points and it can't be done with k-means because you don't now the number of clusters. An other problem is that the box is periodic. So the points at the side top and bottom can belong to eacht other. Like in this image:

The right en left belong to each other. How can I define these clusters with a specific distance as threshold, and implement that the box is periodic (so when you are one the end of one axis look at the beginning if these distances are below the threshold)?

Kind regards, Glenn

Answer 1

The Wikipedia article on cluster analysis will answer your question.

Look for density based clustering algorithms, as your data looks very much like the design scenario of density based clustering to me.

Answer 2

Well, first things first, you can indeed use K-Means. Of course you will need to use a cluster validity index (google Silhouette width index, Calinski-Harabasz index, Dunn's index, etc.).

If you really don't want to use K-Means for some other reason, you may wish to use a hierarchical clustering algorithm such as the Ward Method (description in Wikipedia). You won't need to know the number of clusters a priori (however, can you truly claim that you are creating a taxonomy without being able to answer the most basic of questions: how many taxons are there?).

The fact that your box is periodic raises an interesting challenge. My first thought here is that the best way to approach the problem is not by changing the distance measure (which you could do), but by transforming the data (feature extraction). Your box has 6 sides, but because its periodic its like if it had 3 sides. So, the left side and right side are "the same" (as are the top and bottom, and the front and back). How about redefining each object over three features? each feature is the distance between the object and one of the "three" sides.

Best of luck!