Radius in FindClusters

Questions
1

How can I cluster the list so that elements that are within specified distance or less from each other gather together in the sublist? Thanks.

 t = RandomInteger[1000, 50];
    FindClusters[ t, DistanceFunction -> ManhattanDistance]

Matbe some other functionlike SplitBy or GatherBy should be used, but how to insert the condition on the radius (two cases - one with the specified region in which to gather elements, and another with specified maximum distance from one another) ?

2

Hi Al Guy,

I do not have an other idea than using brute force: Increasing the number of clusters, until the desired result is reached.

ClearAll["Global`*"]

maxElemDist[clusters_List] := Max[(Differences /@ (Sort /@ clusters)) /. {} -> Sequence[]]

t = RandomInteger[1000, 50];
(* the goal, e.g.: *)
elemDistLimit = 20; 

numberOfClusters = 1;
While[elemDistLimit <= maxElemDist[clusters = FindClusters[t, numberOfClusters]],
 numberOfClusters++]

(* result: *)
clusters

(* lets check: *)
maxElemDist[clusters]

Maybe this already helps.

Regards – Henrik

3

I see. Actually Gather is supposed to do the job but it doesn’t:

t = {17, 9, 29, 23, 1, 32, 14, 21, 11, 24, 2, 7, 31, 16, 22, 5, 3, 18,
    20, 25, 30, 26, 12, 8, 15, 13, 27, 19, 4, 10, 6, 28};
Gather[t, (Abs[#1 - #2] <= 1) &]

In this case the should all line up in one sublist. They don’t. Why?

4

I got the Gather part: it just tests all possible combinations of elements in the sublist, not to neighbors. Any way to change that?

5

I understand the documentation in a way that Gather collects elements which have some property in common.