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Document MeanSplitBallTree.

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Ryan Curtin
2024-09-30 14:48:28 -04:00
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doc/developer/trees.md
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@@ -1268,7 +1268,7 @@ TreeType policy API:
- [`KDTree`](../user/core/trees/kdtree.md)
- `MeanSplitKDTree`
- `BallTree`
- `MeanSplitBallTree`
- [`MeanSplitBallTree`](../user/core/trees/mean_split_ball_tree.md)
- `RTree`
- `RStarTree`
- `StandardCoverTree`
doc/sidebar.html
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<code>KDTree</code>
</a>
</li>
<li>
<a href="LINKROOTuser/core/trees/mean_split_ball_tree.html">
<code>MeanSplitBallTree</code>
</a>
</li>
<li>
<a href="LINKROOTuser/core/trees/binary_space_tree.html">
<code>BinarySpaceTree</code>
doc/user/core/trees.md
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@@ -6,6 +6,7 @@ the [same API](../../developer/trees.md), allowing easy plug-and-play usage of
different trees. The following tree types are available in mlpack:
* [`KDTree`](trees/kdtree.md)
* [`MeanSplitBallTree`](trees/mean_split_ball_tree.md)
* [`BinarySpaceTree`](trees/binary_space_tree.md)
*Note:* this documentation is a work in progress. Not all trees are documented
doc/user/core/trees/mean_split_ball_tree.md
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# `MeanSplitBallTree`
<!-- TODO: link to knn.md once it's done -->
The `MeanSplitBallTree` class represents a `k`-dimensional binary space
partitioning tree where each node contains points within a ball. This is a
well-known data structure for efficient distance operations (such as nearest
neighbor search) in low to moderate dimensions.
mlpack's `MeanSplitBallTree` implementation supports three template parameters
for configurable behavior, and implements all the functionality required by the
[TreeType API](../../../developer/trees.md#the-treetype-api), plus some
additional functionality specific to ball trees.
<!-- TODO: clean up -->
The `BallTree` is very similar to mlpack's [`KDTree`](kdtree.md), but the
`BallTree` may perform better in higher dimensions, as distances calculations
are slightly simplified; but, nodes may overlap, causing bounding operations to
be less effective. `BallTree` also supports distance metrics that are not
[`LMetric`](../distances.md#lmetric), making it more flexible than `KDTree`.
***Note:*** many online sources claim that ball trees are better/faster than
kd-trees as the dimensionality increases, or that ball trees are better/faster
in general than kd-trees. This is not what has been observed with mlpack's
implementations, so before deciding on `BallTree`, be sure that you have tested
with [`KDTree`](kdtree.md) first.
* [Template parameters](#template-parameters)
* [Constructors](#constructors)
* [Basic tree properties](#basic-tree-properties)
* [Bounding distances with the tree](#bounding-distances-with-the-tree)
* [Tree traversals](#tree-traversals)
* [Example usage](#example-usage)
## See also
<!-- TODO: add links to all distance-based algorithms and other trees? -->
* [`BallTree`](ball_tree.md)
* [Ball tree on Wikipedia](https://en.wikipedia.org/wiki/Ball_tree)
* [`BinarySpaceTree`](binary_space_tree.md)
* [`MeanSplit`](binary_space_tree.md#meansplit)
* [Binary space partitioning on Wikipedia](https://dl.acm.org/doi/pdf/10.1145/361002.361007)
* [Tree-Independent Dual-Tree Algorithms (pdf)](https://www.ratml.org/pub/pdf/2013tree.pdf)
## Template parameters
In accordance with the [TreeType
API](../../../developer/trees.md#template-parameters-required-by-the-treetype-policy)
(see also [this more detailed section](../../../developer/trees.md#template-parameters)),
the `MeanSplitBallTree` class takes three template parameters:
```
MeanSplitBallTree<DistanceType, StatisticType, MatType>
```
* `DistanceType`: the [distance metric](../distances.md) to use for distance
computations. By default, this is
[`EuclideanDistance`](../distances.md#lmetric).
* [`StatisticType`](binary_space_tree.md#statistictype): this holds auxiliary
information in each tree node. By default,
[`EmptyStatistic`](binary_space_tree.md#emptystatistic) is used, which holds
no information.
* `MatType`: the type of matrix used to represent points. Must be a type
matching the [Armadillo API](../../matrices.md). By default, `arma::mat` is
used, but other types such as `arma::fmat` or similar will work just fine.
The `MeanSplitBallTree` class itself is a convenience typedef of the generic
[`BinarySpaceTree`](binary_space_tree.md) class, using the
[`BallBound`](binary_space_tree.md#ballbound) class as the bounding structure,
and using the [`MeanSplit`](binary_space_tree.md#meansplit) splitting strategy
for construction, which splits a node in the dimension of maximum variance on
the midpoint of the bound's range in that dimension.
## Constructors
`MeanSplitBallTree`s are efficiently constructed by permuting points in a
dataset in a quicksort-like algorithm. However, this means that the ordering of
points in the tree's dataset (accessed with `node.Dataset()`) after construction
may be different.
---
* `node = MeanSplitBallTree(data, maxLeafSize=20)`
* `node = MeanSplitBallTree(data, oldFromNew, maxLeafSize=20)`
* `node = MeanSplitBallTree(data, oldFromNew, newFromOld, maxLeafSize=20)`
- Construct a `MeanSplitBallTree` on the given `data`, using `maxLeafSize` as
the maximum number of points held in a leaf.
- By default, `data` is copied. Avoid a copy by using `std::move()` (e.g.
`std::move(data)`); when doing this, `data` will be set to an empty matrix.
- Optionally, construct mappings from old points to new points. `oldFromNew`
and `newFromOld` will have length `data.n_cols`, and:
* `oldFromNew[i]` indicates that point `i` in the tree's dataset was
originally point `oldFromNew[i]` in `data`; that is,
`node.Dataset().col(i)` is the point `data.col(oldFromNew[i])`.
* `newFromOld[i]` indicates that point `i` in `data` is now point
`newFromOld[i]` in the tree's dataset; that is,
`node.Dataset().col(newFromOld[i])` is the point `data.col(i)`.
---
* `node = MeanSplitBallTree<DistanceType, StatisticType, MatType>(data, maxLeafSize=20)`
* `node = MeanSplitBallTree<DistanceType, StatisticType, MatType>(data, oldFromNew, maxLeafSize=20)`
* `node = MeanSplitBallTree<DistanceType, StatisticType, MatType>(data, oldFromNew, newFromOld, maxLeafSize=20)`
- Construct a `MeanSplitBallTree` on the given `data`, using custom template
parameters to control the behavior of the tree, using `maxLeafSize` as the
maximum number of points held in a leaf.
- By default, `data` is copied. Avoid a copy by using `std::move()` (e.g.
`std::move(data)`); when doing this, `data` will be set to an empty matrix.
- Optionally, construct mappings from old points to new points. `oldFromNew`
and `newFromOld` will have length `data.n_cols`, and:
* `oldFromNew[i]` indicates that point `i` in the tree's dataset was
originally point `oldFromNew[i]` in `data`; that is,
`node.Dataset().col(i)` is the point `data.col(oldFromNew[i])`.
* `newFromOld[i]` indicates that point `i` in `data` is now point
`newFromOld[i]` in the tree's dataset; that is,
`node.Dataset().col(newFromOld[i])` is the point `data.col(i)`.
---
* `node = MeanSplitBallTree()`
- Construct an empty ball tree with no children and no points.
---
***Notes:***
- The name `node` is used here for `MeanSplitBallTree` objects instead of
`tree`, because each `MeanSplitBallTree` object is a single node in the tree.
The constructor returns the node that is the root of the tree.
- In a `MeanSplitBallTree`, it is not guaranteed that the ball bounds for nodes
are disjoint; they may be overlapping. This is because for many datasets, it
is geometrically impossible to construct two disjoint balls that cover the
entire set of points.
- Inserting individual points or removing individual points from a
`MeanSplitBallTree` is not supported, because this generally results in a
ball tree with very loose bounding balls. It is better to simply build a new
`MeanSplitBallTree` on the modified dataset. For trees that support
individual insertion and deletions, see the `RectangleTree` class and all its
variants (e.g. `RTree`, `RStarTree`, etc.).
- See also the
[developer documentation on tree constructors](../../../developer/trees.md#constructors-and-destructors).
<!-- TODO: add links to RectangleTree above when it is documented -->
---
### Constructor parameters:
| **name** | **type** | **description** | **default** |
|----------|----------|-----------------|-------------|
| `data` | [`arma::mat`](../../matrices.md) | [Column-major](../../matrices.md#representing-data-in-mlpack) matrix to build the tree on. Pass with `std::move(data)` to avoid copying the matrix. | _(N/A)_ |
| `maxLeafSize` | `size_t` | Maximum number of points to store in each leaf. | `20` |
| `oldFromNew` | `std::vector<size_t>` | Mappings from points in `node.Dataset()` to points in `data`. | _(N/A)_ |
| `newFromOld` | `std::vector<size_t>` | Mappings from points in `data` to points in `node.Dataset()`. | _(N/A)_ |
## Basic tree properties
Once a `MeanSplitBallTree` object is constructed, various properties of the tree
can be accessed or inspected. Many of these functions are required by the
[TreeType API](../../../developer/trees.md#the-treetype-api).
### Navigating the tree
* `node.NumChildren()` returns the number of children in `node`. This is
either `2` if `node` has children, or `0` if `node` is a leaf.
* `node.IsLeaf()` returns a `bool` indicating whether or not `node` is a leaf.
* `node.Child(i)` returns a `MeanSplitBallTree&` that is the `i`th child.
- `i` must be `0` or `1`.
- This function should only be called if `node.NumChildren()` is not `0`
(e.g. if `node` is not a leaf). Note that this returns a valid
`MeanSplitBallTree&` that can itself be used just like the root node of the
tree!
- `node.Left()` and `node.Right()` are convenience functions specific to
`MeanSplitBallTree` that will return `MeanSplitBallTree*` (pointers) to the
left and right children, respectively, or `NULL` if `node` has no children.
* `node.Parent()` will return a `MeanSplitBallTree*` that points to the parent
of `node`, or `NULL` if `node` is the root of the `MeanSplitBallTree`.
---
### Accessing members of a tree
* `node.Bound()` will return an
[`BallBound&`](binary_space_tree.md#ballbound) object that represents the
bounding ball of `node`. This may not be the smallest possible bounding ball
that encloses all the descendant points of `node`, but it is a reasonably
close approximation.
* `node.Stat()` will return an `EmptyStatistic&` (or a `StatisticType&` if a
[custom `StatisticType`](#template-parameters) was specified as a template
parameter) holding the statistics of the node that were computed during tree
construction.
* `node.Distance()` will return a
[`EuclideanDistance&`](../distances.md#lmetric) (or a `DistanceType&` if a
[custom `DistanceType`](#template-parameters) was specified as a template
parameter).
See also the
[developer documentation](../../../developer/trees.md#basic-tree-functionality)
for basic tree functionality in mlpack.
---
### Accessing data held in a tree
* `node.Dataset()` will return a `const arma::mat&` that is the dataset the
tree was built on. Note that this is a permuted version of the `data` matrix
passed to the constructor.
- If a [custom `MatType`](#template-parameters) is being used, the return
type will be `const MatType&` instead of `const arma::mat&`.
* `node.NumPoints()` returns a `size_t` indicating the number of points held
directly in `node`.
- If `node` is not a leaf, this will return `0`, as `MeanSplitBallTree` only
holds points directly in its leaves.
- If `node` is a leaf, then the number of points will be less than or equal
to the `maxLeafSize` that was specified when the tree was constructed.
* `node.Point(i)` returns a `size_t` indicating the index of the `i`'th point
in `node.Dataset()`.
- `i` must be in the range `[0, node.NumPoints() - 1]` (inclusive).
- `node` must be a leaf (as non-leaves do not hold any points).
- The `i`'th point in `node` can then be accessed as
`node.Dataset().col(node.Point(i))`.
- In a `MeanSplitBallTree`, because of the permutation of points done [during
construction](#constructors), point indices are contiguous:
`node.Point(i + j)` is the same as `node.Point(i) + j` for valid `i` and
`j`.
- Accessing the actual `i`'th point itself can be done with, e.g.,
`node.Dataset().col(node.Point(i))`.
* `node.NumDescendants()` returns a `size_t` indicating the number of points
held in all descendant leaves of `node`.
- If `node` is the root of the tree, then `node.NumDescendants()` will be
equal to `node.Dataset().n_cols`.
* `node.Descendant(i)` returns a `size_t` indicating the index of the `i`'th
descendant point in `node.Dataset()`.
- `i` must be in the range `[0, node.NumDescendants() - 1]` (inclusive).
- `node` does not need to be a leaf.
- The `i`'th descendant point in `node` can then be accessed as
`node.Dataset().col(node.Descendant(i))`.
- In a `MeanSplitBallTree`, because of the permutation of points done [during
construction](#constructors), point indices are contiguous:
`node.Descendant(i + j)` is the same as `node.Descendant(i) + j` for valid
`i` and `j`.
- Accessing the actual `i`'th descendant itself can be done with, e.g.,
`node.Dataset().col(node.Descendant(i))`.
* `node.Begin()` returns a `size_t` indicating the index of the first
descendant point of `node`.
- This is equivalent to `node.Descendant(0)`.
* `node.Count()` returns a `size_t` indicating the number of descendant points of `node`.
- This is equivalent to `node.NumDescendants()`.
---
### Accessing computed bound quantities of a tree
The following quantities are cached for each node in a `MeanSplitBallTree`, and
so accessing them does not require any computation.
* `node.FurthestPointDistance()` returns a `double` representing the distance
between the center of the bounding ball of `node` and the furthest point held
by `node`.
- If `node` is not a leaf, this returns 0 (because `node` does not hold any
points).
- If `node` is a leaf, this is equivalent to `node.Bound().Radius()`.
* `node.FurthestDescendantDistance()` returns a `double` representing the
distance between the center of the bounding ball of `node` and the furthest
descendant point held by `node`.
- This will be less than or equal to `node.Radius()`.
* `node.MinimumBoundDistance()` returns a `double` representing minimum
possible distance from the center of the node to any edge of the
hyperrectangle bound.
- This is equivalent to `node.Bound().Radius()`.
* `node.ParentDistance()` returns a `double` representing the distance between
the center of the bounding hyperrectangle of `node` and the center of the
bounding hyperrectangle of its parent.
- If `node` is the root of the tree, `0` is returned.
***Notes:***
- If a [custom `MatType`](#template-parameters) was specified when constructing
the `MeanSplitBallTree`, then the return type of each method is the element
type of the given `MatType` instead of `double`. (e.g., if `MatType` is
`arma::fmat`, then the return type is `float`.)
- For more details on each bound quantity, see the
[developer documentation](../../../developer/trees.md#complex-tree-functionality-and-bounds)
on bound quantities for trees.
---
### Other functionality
* `node.Center(center)` stores the center of the bounding ball of `node` in
`center`.
- `center` should be of type `arma::vec&`. (If a [custom
`MatType`](#template-parameters) was specified when constructing the
`MeanSplitBallTree`, the type is instead the column vector type for the
given `MatType`; e.g., `arma::fvec&` when `MatType` is `arma::fmat`.)
- `center` will be set to have size equivalent to the dimensionality of the
dataset held by `node`.
- This is equivalent to calling `node.Bound().Center(center)`.
* A `MeanSplitBallTree` can be serialized with
[`data::Save()` and `data::Load()`](../../load_save.md#mlpack-objects).
## Bounding distances with the tree
The primary use of trees in mlpack is bounding distances to points or other tree
nodes. The following functions can be used for these tasks.
* `node.GetNearestChild(point)`
* `node.GetFurthestChild(point)`
- Return a `size_t` indicating the index of the child (`0` for left, `1` for
right) that is closest to (or furthest from) `point`, with respect
to the `MinDistance()` (or `MaxDistance()`) function.
- If there is a tie, `0` (the left child) is returned.
- If `node` is a leaf, `0` is returned.
- `point` should be of type `arma::vec`. (If a [custom
`MatType`](#template-parameters) was specified when constructing the
`MeanSplitBallTree`, the type is instead the column vector type for the
given `MatType`; e.g., `arma::fvec` when `MatType` is `arma::fmat`.)
* `node.GetNearestChild(other)`
* `node.GetFurthestChild(other)`
- Return a `size_t` indicating the index of the child (`0` for left, `1` for
right) that is closest to (or furthest from) the `MeanSplitBallTree` node
`other`, with respect to the `MinDistance()` (or `MaxDistance()`) function.
- If there is a tie, `2` (an invalid index) is returned. ***Note that this
behavior differs from the version above that takes a point.***
- If `node` is a leaf, `0` is returned.
---
* `node.MinDistance(point)`
* `node.MinDistance(other)`
- Return a `double` indicating the minimum possible distance between `node`
and `point`, or the `MeanSplitBallTree` node `other`.
- This is equivalent to the minimum possible distance between any point
contained in the bounding hyperrectangle of `node` and `point`, or between
any point contained in the bounding hyperrectangle of `node` and any point
contained in the bounding hyperrectangle of `other`.
- `point` should be of type `arma::vec`. (If a [custom
`MatType`](#template-parameters) was specified when constructing the
`MeanSplitBallTree`, the type is instead the column vector type for the
given `MatType`, and the return type is the element type of `MatType`;
e.g., `point` should be `arma::fvec` when `MatType` is `arma::fmat`, and
the returned distance is `float`).
* `node.MaxDistance(point)`
* `node.MaxDistance(other)`
- Return a `double` indicating the maximum possible distance between `node`
and `point`, or the `MeanSplitBallTree` node `other`.
- This is equivalent to the maximum possible distance between any point
contained in the bounding hyperrectangle of `node` and `point`, or between
any point contained in the bounding hyperrectangle of `node` and any point
contained in the bounding hyperrectangle of `other`.
- `point` should be of type `arma::vec`. (If a [custom
`MatType`](#template-parameters) was specified when constructing the
`MeanSplitBallTree`, the type is instead the column vector type for the
given `MatType`, and the return type is the element type of `MatType`;
e.g., `point` should be `arma::fvec` when `MatType` is `arma::fmat`, and
the returned distance is `float`).
* `node.RangeDistance(point)`
* `node.RangeDistance(other)`
- Return a [`Range`](../math.md#range) whose lower bound is
`node.MinDistance(point)` or `node.MinDistance(other)`, and whose upper
bound is `node.MaxDistance(point)` or `node.MaxDistance(other)`.
- `point` should be of type `arma::vec`. (If a
[custom `MatType`](#template-parameters) was specified when constructing
the `MeanSplitBallTree`, the type is instead the column vector type for the
given `MatType`, and the return type is a `RangeType` with element type the
same as `MatType`; e.g., `point` should be `arma::fvec` when `MatType` is
`arma::fmat`, and the returned type is
[`RangeType<float>`](../math.md#range)).
### Tree traversals
Like every mlpack tree, the `MeanSplitBallTree` class provides a [single-tree
and dual-tree traversal](../../../developer/trees.md#traversals) that can be
paired with a [`RuleType` class](../../../developer/trees.md#rules) to implement
a single-tree or dual-tree algorithm.
* `MeanSplitBallTree::SingleTreeTraverser`
- Implements a depth-first single-tree traverser.
* `MeanSplitBallTree::DualTreeTraverser`
- Implements a dual-depth-first dual-tree traverser.
In addition to those two classes, which are required by the
[`TreeType` policy](../../../developer/trees.md), an additional traverser is
available:
* `MeanSplitBallTree::BreadthFirstDualTreeTraverser`
- Implements a dual-breadth-first dual-tree traverser.
- ***Note:*** this traverser is not useful for all tasks; because the
`BallTree` only holds points in the leaves, this means that no base cases
(e.g. comparisons between points) will be called until *all* pairs of
intermediate nodes have been scored!
## Example usage
Build a `MeanSplitBallTree` on the `cloud` dataset and print basic statistics
about the tree.
```c++
// See https://datasets.mlpack.org/cloud.csv.
arma::mat dataset;
mlpack::data::Load("cloud.csv", dataset, true);
// Build the ball tree with a leaf size of 10. (This means that nodes are split
// until they contain 10 or fewer points.)
//
// The std::move() means that `dataset` will be empty after this call, and no
// data will be copied during tree building.
//
// Note that the '<>' isn't necessary if C++20 is being used (e.g.
// `mlpack::MeanSplitBallTree tree(...)` will work fine in C++20 or newer).
mlpack::MeanSplitBallTree<> tree(std::move(dataset));
// Print the bounding box of the root node.
std::cout << "Bounding ball of root node:" << std::endl;
std::cout << " - Center: " << tree.Bound().Center();
std::cout << " - Radius: " << tree.Bound().Radius();
std::cout << std::endl;
// Print the number of descendant points of the root, and of each of its
// children.
std::cout << "Descendant points of root: "
<< tree.NumDescendants() << "." << std::endl;
std::cout << "Descendant points of left child: "
<< tree.Left()->NumDescendants() << "." << std::endl;
std::cout << "Descendant points of right child: "
<< tree.Right()->NumDescendants() << "." << std::endl;
std::cout << std::endl;
```
---
Build two `MeanSplitBallTree`s on subsets of the corel dataset and compute
minimum and maximum distances between nodes in the trees.
```c++
// See https://datasets.mlpack.org/corel-histogram.csv.
arma::mat dataset;
mlpack::data::Load("corel-histogram.csv", dataset, true);
// Build ball trees on the first half and the second half of points.
mlpack::MeanSplitBallTree<> tree1(dataset.cols(0, dataset.n_cols / 2));
mlpack::MeanSplitBallTree<> tree2(dataset.cols(dataset.n_cols / 2 + 1,
dataset.n_cols - 1));
// Compute the maximum distance between the trees.
std::cout << "Maximum distance between tree root nodes: "
<< tree1.MaxDistance(tree2) << "." << std::endl;
// Get the leftmost grandchild of the first tree's root---if it exists.
if (!tree1.IsLeaf() && !tree1.Child(0).IsLeaf())
{
mlpack::MeanSplitBallTree<>& node1 = tree1.Child(0).Child(0);
// Get the rightmost grandchild of the second tree's root---if it exists.
if (!tree2.IsLeaf() && !tree2.Child(1).IsLeaf())
{
mlpack::MeanSplitBallTree<>& node2 = tree2.Child(1).Child(1);
// Print the minimum and maximum distance between the nodes.
mlpack::Range dists = node1.RangeDistance(node2);
std::cout << "Possible distances between two grandchild nodes: ["
<< dists.Lo() << ", " << dists.Hi() << "]." << std::endl;
// Print the minimum distance between the first node and the first
// descendant point of the second node.
const size_t descendantIndex = node2.Descendant(0);
const double descendantMinDist =
node1.MinDistance(node2.Dataset().col(descendantIndex));
std::cout << "Minimum distance between grandchild node and descendant "
<< "point: " << descendantMinDist << "." << std::endl;
// Which child of node2 is closer to node1?
const size_t closerIndex = node2.GetNearestChild(node1);
if (closerIndex == 0)
std::cout << "The left child of node2 is closer to node1." << std::endl;
else if (closerIndex == 1)
std::cout << "The right child of node2 is closer to node1." << std::endl;
else // closerIndex == 2 in this case.
std::cout << "Both children of node2 are equally close to node1."
<< std::endl;
// And which child of node1 is further from node2?
const size_t furtherIndex = node1.GetFurthestChild(node2);
if (furtherIndex == 0)
std::cout << "The left child of node1 is further from node2."
<< std::endl;
else if (furtherIndex == 1)
std::cout << "The right child of node1 is further from node2."
<< std::endl;
else // furtherIndex == 2 in this case.
std::cout << "Both children of node1 are equally far from node2."
<< std::endl;
}
}
```
---
Build a `MeanSplitBallTree` on 32-bit floating point data and save it to disk.
```c++
// See https://datasets.mlpack.org/corel-histogram.csv.
arma::fmat dataset;
mlpack::data::Load("corel-histogram.csv", dataset);
// Build the MeanSplitBallTree using 32-bit floating point data as the matrix
// type. We will still use the default EmptyStatistic and EuclideanDistance
// parameters. A leaf size of 100 is used here.
mlpack::MeanSplitBallTree<mlpack::EuclideanDistance,
mlpack::EmptyStatistic,
arma::fmat> tree(std::move(dataset), 100);
// Save the MeanSplitBallTree to disk with the name 'tree'.
mlpack::data::Save("tree.bin", "tree", tree);
std::cout << "Saved tree with " << tree.Dataset().n_cols << " points to "
<< "'tree.bin'." << std::endl;
```
---
Load a 32-bit floating point `BallTree` from disk, then traverse it manually and
find the number of leaf nodes with fewer than 10 children.
```c++
// This assumes the tree has already been saved to 'tree.bin' (as in the example
// above).
// This convenient typedef saves us a long type name!
typedef mlpack::MeanSplitBallTree<mlpack::EuclideanDistance,
mlpack::EmptyStatistic,
arma::fmat> TreeType;
TreeType tree;
mlpack::data::Load("tree.bin", "tree", tree);
std::cout << "Tree loaded with " << tree.NumDescendants() << " points."
<< std::endl;
// Recurse in a depth-first manner. Count both the total number of leaves, and
// the number of leaves with fewer than 10 points.
size_t leafCount = 0;
size_t totalLeafCount = 0;
std::stack<TreeType*> stack;
stack.push(&tree);
while (!stack.empty())
{
TreeType* node = stack.top();
stack.pop();
if (node->NumPoints() < 10)
++leafCount;
++totalLeafCount;
if (!node->IsLeaf())
{
stack.push(node->Left());
stack.push(node->Right());
}
}
// Note that it would be possible to use TreeType::SingleTreeTraverser to
// perform the recursion above, but that is more well-suited for more complex
// tasks that require pruning and other non-trivial behavior; so using a simple
// stack is the better option here.
// Print the results.
std::cout << leafCount << " out of " << totalLeafCount << " leaves have fewer "
<< "than 10 points." << std::endl;
```
---
Build a `MeanSplitBallTree` and map between original points and new points.
```c++
// See https://datasets.mlpack.org/cloud.csv.
arma::mat dataset;
mlpack::data::Load("cloud.csv", dataset, true);
// Build the tree.
std::vector<size_t> oldFromNew, newFromOld;
mlpack::MeanSplitBallTree<> tree(dataset, oldFromNew, newFromOld);
// oldFromNew and newFromOld will be set to the same size as the dataset.
std::cout << "Number of points in dataset: " << dataset.n_cols << "."
<< std::endl;
std::cout << "Size of oldFromNew: " << oldFromNew.size() << "." << std::endl;
std::cout << "Size of newFromOld: " << newFromOld.size() << "." << std::endl;
std::cout << std::endl;
// See where point 42 in the tree's dataset came from.
std::cout << "Point 42 in the permuted tree's dataset:" << std::endl;
std::cout << " " << tree.Dataset().col(42).t();
std::cout << "Was originally point " << oldFromNew[42] << ":" << std::endl;
std::cout << " " << dataset.col(oldFromNew[42]).t();
std::cout << std::endl;
// See where point 7 in the original dataset was mapped.
std::cout << "Point 7 in original dataset:" << std::endl;
std::cout << " " << dataset.col(7).t();
std::cout << "Mapped to point " << newFromOld[7] << ":" << std::endl;
std::cout << " " << tree.Dataset().col(newFromOld[7]).t();
```