[mlpack-git] [mlpack/mlpack] Spill trees (#747)

MarcosPividori notifications at github.com
Thu Aug 4 12:40:33 EDT 2016

Hi @sumedhghaisas! I have implemented generalized Spill Trees, to consider general splitting hyperplanes, not necessarily axis-orthogonal.

I added a new template parameter for Spill Trees: `HyperplaneType`, and I implemented two candidate classes: `AxisOrthogonalHyperplane` and `Hyperplane`.
+ `AxisOrthogonalHyperplane` consider an axis-parallel projection vector. So, we can project any vector in O(1) time, considering the appropiate dimension.
+ `Hyperplane` consider a general projection vector. So we can project any vector in O(d) time, through a dot product.

Inside the SpillTrees, I consider BallBound for non-axis-orthogonal hyperplanes, and HrectBound for axis-orthogonal hyperplanes.
Also, I replaced the methods: SplitValue() and SplitDimension() by HalfSpaceContains() and HalfSpaceIntersects(), which are more general.

Considering this abstraction, I managed to significantly simplify the Split methods: MeanSplit and Midpoint Split. Now, they share most of the code.

I think we could use this abstraction for BinarySpaceTrees too.

By default, SpillSearch considers `AxisOrthogonalHyperplanes` because they seem to be faster in many cases, but this is not always true. I think we should benchmark both methods and see which is faster and which is more accurate, I mean, which has the best relation between running time and relative approximation error.

I will add a new command line flag "--get_real_error" to compare the approximate neighbor search against the naive method and print the real relative error, so we can benchmark with different values of tau and different spill tree flavours.



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