In a previous article, I introduced a clustering algorithm capable of quickly handling hundreds of thousands of vectors, that first compresses the vectors to a single dimension using the norm operator.
Though originally intended to cluster velocity scalars, I’ve also used this algorithm to find the perimeter of a statistical sphere, that isn’t smooth or completely solid, which is what you’ll likely end up with using real-world sensor data. In this case, the sphere consists of 327,627 Euclidean 3-vectors. Clustering the data took 4.6819 minutes, running on an iMac, which is all that’s necessary to identify the perimeter of the sphere, since you can then simply select the last cluster in the list of clusters, and color those points in the display. In the image below, the maximum cluster is colored blue, the rest colored gray.
A statistical sphere, with the perimeter colored blue.
Octave Code:
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