<p>Can you explain, that you mean using phi as metric? How we can use this to compute the distance between points? (And we can't compute phi(one observation) for all mixture, becouse it gives us O(m) complexity. ) <br>
And you propose to build a tree only on means, or on all dataset? (In <a href="http://www.ri.cmu.edu/pub_files/pub1/moore_andrew_1998_2/moore_andrew_1998_2.pdf">http://www.ri.cmu.edu/pub_files/pub1/moore_andrew_1998_2/moore_andrew_1998_2.pdf</a> we built kd tree on the all dataset, because it helps us to faster compute each em_fit iteration).<br>
Thanks.</p>

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