Hey there,
I'm sorry for the lag in the response. When I review what you've written and
take a look, I think that the problem that you are trying to solve is actually
different. mlpack's minimum spanning tree code calculates the minimum spanning
tree of the input points---it doesn't take in a dissimilarity (or distance)
matrix as input. Instead the reason that the mlpack implementation is fast is
that it can avoid calculating the entire dissimilarity matrix by pruning away
parts of work.
However, that strategy, which uses a dual-tree algorithm, only works if the
distance used is a valid metric. In your case, the metric appears to be
```
d(p_i, p_j) = max(d(p_i, p_j), d(p_i, N_5(p_i)), d(N_5(p_j), p_j))
```
where `N_5()` is the fifth nearest neighbor of the input point. I am not sure
if that's a valid metric.
However, if it is (i.e. if you can prove it), then what you can do is implement
a new distance metric that follows the API given in this tutorial:
http://www.mlpack.org/docs/mlpack-2.1.0/doxygen.php?doc=metrics.html
and then you can use a custom `TreeType` for the `DualTreeBoruvka` class (note:
because this is not a Euclidean metric, you can't use typical trees like KD
trees or anything. You'll have to use cover trees or vantage point trees).
Like if your metric was called `MyMetric` you could do
```
DualTreeBoruvka<MyMetric, arma::mat, tree::StandardCoverTree>();
```
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