<p>In <a href="https://github.com/mlpack/mlpack/pull/726#discussion_r75018312">src/mlpack/core/tree/binary_space_tree/rp_tree_max_split_impl.hpp</a>:</p>
<pre style='color:#555'>&gt; +  // Find the median of scalar products of the samples and the normal vector.
&gt; +  for (size_t k = 0; k &lt; samples.n_elem; k++)
&gt; +    values[k] = arma::dot(data.col(samples[k]), direction);
&gt; +
&gt; +  const ElemType maximum = arma::max(values);
&gt; +  const ElemType minimum = arma::min(values);
&gt; +  if (minimum == maximum)
&gt; +    return false;
&gt; +
&gt; +  splitVal = arma::median(values);
&gt; +
&gt; +  // Add a random deviation to the median.
&gt; +  // This algorithm differs from the method suggested in the
&gt; +  // random projection tree paper.
&gt; +  splitVal += math::Random((minimum - splitVal) * 0.75,
&gt; +      (maximum - splitVal) * 0.75);
</pre>
<p>Other than the clear speed improvement, why did you choose to go with this simpler approach?  I am not sure it will still satisfy the theoretical guarantees given by the paper (I have not spent a huge amount of time thinking about the necessary conditions for that).</p>

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