Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/7166#discussion_r34177389
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixture.scala ---
@@ -140,6 +143,9 @@ class GaussianMixture private (
// Get length of the input vectors
val d = breezeData.first().length
+ // Logic for when to distribute the computation of the
[[MultivariateGaussian]]s
+ val distributeGaussians = d >= 30 && k >= 10
--- End diff --
The computation cost is `C1 * k * d^3` and the communication cost for
distributing Gaussian is `C2 * k * d^2`, where `C1` and `C2` are constants. So
if we run on local (assuming single thread), the total time is C1 * k * d^3, if
we distribute the work, the total time is `C1 * d^3 + C2 * k * d^2`. So we
should distribute the work when `(k - 1) / k * d > C2 / C1`, which is roughly
controlled by `d` for a non-trivial `k`. Based on your performance test, `C2 /
C1` is roughly 25. So we can use `(k - 1.0) / k * d > 25` here. The logic you
suggested didn't cover the case when k is small but d is very large.
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