My question is as follow. Imagine a random shape cluster of high dimension in an euclidian space, how can i get points which are at the edge of the cluster where edge are defined as segments connecting outermost points.
I can imagine to compute the similarity matrix and get points which are the most distant from others in average, unfortunately with this approach i can't be sure to get all points which are distributed homogeneously across the edge.
I can also try to use a defined parameter to fix a distance where the average distance points are considered to be part of the edge, but it needs a fine tuning which i want to prevent.
Thank's in advance for your precious help !
Peace
Your question is tricky because you are already assuming you have a clustering. Since a clustering can be made from distances (or dissimilarity measures) without a topology then finding the borders is not always trivial. K-means for instance relays on euclidean distances and here you can establish a proper topology, and then you can probably define "borders". However in general, clustering methods can be based on metrics lacking a proper topology for such objective. In this case, in order to answer your specific question, I would iterate each element on each cluster and check if there is a distance from this element to any other element on any other cluster that is lower than the lowest distance to the elements on the same cluster. If this is the case, then you have found an "edge" element on your cluster. If you are unable to find such elements then you are in a perfect clustering situation, and you probably will be unable to state that you have borders on your clustering. But in my experience, you will never be on this state, and if you follow the algorithm just described, you will find at least border elements for a number of your clusters.
Best regards.
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