mlpack

MeanSplitBallTree

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.

In general, a MeanSplitBallTree will be a better balanced tree and have fewer nodes than a BallTree. However, counterintuitively, a more balanced tree can be worse for search tasks like nearest neighbor search, because unbalanced nodes are more easily pruned away during search. In general, using a BallTree for nearest neighbor search is faster, but this is not true for every dataset or task.

mlpack’s MeanSplitBallTree implementation supports three template parameters for configurable behavior, and implements all the functionality required by the TreeType API, plus some additional functionality specific to ball trees.

🔗 See also

🔗 Template parameters

In accordance with the TreeType API (see also this more detailed section), the MeanSplitBallTree class takes three template parameters:

MeanSplitBallTree<DistanceType, StatisticType, MatType>

The MeanSplitBallTree class itself is a convenience typedef of the generic BinarySpaceTree class, using the BallBound class as the bounding structure, and using the 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.

If no template parameters are explicitly specified, then defaults are used:

MeanSplitBallTree<> = MeanSplitBallTree<EuclideanDistance, EmptyStatistic, arma::mat>

🔗 Constructors

MeanSplitBallTrees 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.

Notes:

🔗 Constructor parameters:

name type description default
data arma::mat Column-major 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.

🔗 Accessing members of a tree

See also the developer documentation for basic tree functionality in mlpack.

🔗 Accessing data held in a tree

🔗 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.

Notes:

🔗 Other functionality

🔗 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.

🔗 Tree traversals

Like every mlpack tree, the MeanSplitBallTree class provides a single-tree and dual-tree traversal that can be paired with a RuleType class to implement a single-tree or dual-tree algorithm.

In addition to those two classes, which are required by the TreeType policy, an additional traverser is available:

🔗 Example usage

Build a MeanSplitBallTree on the cloud dataset and print basic statistics about the tree.

// 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 MeanSplitBallTrees on subsets of the corel dataset and compute minimum and maximum distances between nodes in the trees.

// 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.

// 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 points.

// 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!
using TreeType = mlpack::MeanSplitBallTree<mlpack::EuclideanDistance,
                                           mlpack::EmptyStatistic,
                                           arma::fmat>;

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.

// 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();