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@@ -1261,6 +1261,11 @@ to write a fully custom split:
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with maximum width
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* [`MeanSplit`](#meansplit): splits on the mean value of the points in the
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dimension with maximum width
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* [`RPTreeMeanSplit`](#rptreemeansplit): projects points onto a random vector,
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splitting on the median value of the projections, or in some cases on the
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distance from the mean value
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* [`RPTreeMaxSplit`](#rptreemaxsplit): projects points onto a random vector,
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splitting on a random offset of the median of projected points
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* [Custom `SplitType`s](#custom-splittypes): implement a fully custom
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`SplitType` class
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@@ -1296,7 +1301,7 @@ The splitting strategy for the `MeanSplit` class is, given a set of points:
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* Compute the mean value `m` of the points in dimension `d`.
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* Split in dimension `d`.
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* Points less than `m` will go to the left child.
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* Points greater than `m` will go to the right child.
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* Points greater than or equal to `m` will go to the right child.
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In practice, the `MeanSplit` splitting strategy often results in a tree with
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fewer leaf nodes than `MidpointSplit`, because each split is more likely to be
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@@ -1309,6 +1314,67 @@ task*.
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For implementation details, see
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[the source code](/src/mlpack/core/tree/binary_space_tree/mean_split_impl.hpp).
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### `RPTreeMeanSplit`
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The `RPTreeMeanSplit` class is a splitting strategy that can be used by
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[`BinarySpaceTree`](#binaryspacetree). It is the splitting strategy used by the
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[`RPTree`](rp_tree.md) class, and uses a random projection to split points. The
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general idea is described in the paper by
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[Dasgupta and Freund](https://www.cs.cornell.edu/~abrahao/tdg/papers/p537.pdf),
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as the `RPTree-Mean` version of the `ChooseRule()` function.
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The splitting strategy for the `RPTreeMeanSplit` class is, given a set of
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points:
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* Draw a random vector `z`.
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* Sample up to 100 points and compute `d`, the average pairwise distance
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between the points.
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* If `10 * d` is less than or equal to the squared diameter of the bounding box
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of the points:
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- Project all points onto the vector `z`, and compute the median `v` of the
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projected values.
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- Points with projected value less than `v` will go to the left child.
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- Points with projected value greater than or equal to `v` will go to the
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right child.
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* Otherwise:
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- Compute the mean `s` of all points.
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- Points with distance from `s` less than the median distance from `s`
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will go to the left child.
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- Points with distance from `s` greater than or equal to the median distance
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from `s` will go to the right child.
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The implementation strategy differs slightly from the `RPTree-Mean` version in
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the paper: instead of computing the true average pairwise distance between all
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points, a sample of 100 points is used.
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For implementation details, see
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[the source code](/src/mlpack/core/tree/binary_space_tree/rp_tree_mean_split_impl.hpp).
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### `RPTreeMaxSplit`
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The `RPTreeMaxSplit` class is a splitting strategy that can be used by
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[`BinarySpaceTree`](#binaryspacetree). It is the splitting strategy used by the
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[`MaxRPTree`](max_rp_tree.md) class, and uses a random projection to split
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points. The general idea is described in the paper by
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[Dasgupta and Freund](https://www.cs.cornell.edu/~abrahao/tdg/papers/p537.pdf),
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as the `RPTree-Max` version of the `ChooseRule()` function.
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The splitting strategy for the `RPTreeMaxSplit` class is, given a set of points,
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* Draw a random vector `z`.
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* Sample up to 100 points (call this sample `S`).
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* Compute `v`, the median value of projections of points in `S` onto `z`.
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* Points with projection onto `z` less than `v` will go to the left child.
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* Points with projection onto `z` greater than or equal to `v` will go to the
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right child.
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The implementation strategy differs slightly from the `RPTree-Max` version in
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the paper: instead of computing the median on all points, a sample of 100 points
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is used.
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For implementation details, see
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[the source code](/src/mlpack/core/tree/binary_space_tree/rp_tree_max_split_impl.hpp).
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### Custom `SplitType`s
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Custom split strategies for a binary space tree can be implemented via the
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@@ -1529,7 +1595,7 @@ std::cout << "Saved tree with " << tree.Dataset().n_cols << " points to "
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---
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Load a 32-bit floating point `BinarySpaceTree` from disk, then traverse it
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manually and find the number of leaf nodes with less than 10 children.
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manually and find the number of leaf nodes with less than 10 points.
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```c++
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// This assumes the tree has already been saved to 'tree.bin' (as in the example
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Ryan Curtin