KmTree.h

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// BEWARE: BETA VERSION
// --------------------
//
// A k-d tree that vastly speeds up an iteration of k-means (in any number of
// dimensions). The main
// idea for this data structure is from Kanungo/Mount. This is used internally
// by Kmeans.cpp, and
// will most likely not need to be used directly.
//
// The stucture works as follows:
//   - All data points are placed into a tree where we choose child nodes by
//   partitioning all data
//     points along a plane parallel to the axis.
//   - We maintain for each node, the bounding box of all data points stored at
//   that node.
//   - To do a k-means iteration, we need to assign points to clusters and
//   calculate the sum and
//     the number of points assigned to each cluster. For each node in the tree,
//     we can rule out
//     some cluster centers as being too far away from every single point in
//     that bounding box.
//     Once only one cluster is left, all points in the node can be assigned to
//     that cluster in
//     batch.
//
// Author: David Arthur (darthur@gmail.com), 2009

#ifndef KM_TREE_H__
#define KM_TREE_H__

// Includes
#include "KmUtils.h"

// KmTree class definition
class KmTree
{
   public:
    // Constructs a tree out of the given n data points living in R^d.
    KmTree(int n, int d, Scalar* points);
    ~KmTree();

    // Given k cluster centers, this runs a full k-means iterations, choosing
    // the next set of
    // centers and returning the cost function for this set of centers. If
    // assignment is not null,
    // it should be an array of size n that will be filled with the index of the
    // cluster (0 - k-1)
    // that each data point is assigned to. The new center values will overwrite
    // the old ones.
    Scalar DoKMeansStep(int k, Scalar* centers, int* assignment) const;

    // Choose k initial centers for k-means using the kmeans++ seeding
    // procedure. The resulting
    // centers are returned via the centers variable, which should be
    // pre-allocated to size k*d.
    // The cost of the initial clustering is returned.
    Scalar SeedKMeansPlusPlus(int k, Scalar* centers) const;

   private:
    struct Node
    {
        int num_points;  // Number of points stored in this node
        int first_point_index;  // The smallest point index stored in this node
        Scalar *median, *radius;  // Bounding box center and half side-lengths
        Scalar* sum;  // Sum of the points stored in this node
        Scalar opt_cost;  // Min cost for putting all points in this node in 1
        // cluster
        Node *lower_node, *upper_node;  // Child nodes
        mutable int kmpp_cluster_index;  // The cluster these points are
        // assigned to or -1 if variable
    };

    // Helper functions for constructor
    Node* BuildNodes(
        Scalar* points, int first_index, int last_index, char** next_node_data);
    Scalar GetNodeCost(const Node* node, Scalar* center) const;

    // Helper functions for DoKMeans step
    Scalar DoKMeansStepAtNode(
        const Node* node, int k, int* candidates, Scalar* centers, Scalar* sums,
        int* counts, int* assignment) const;
    bool ShouldBePruned(
        Scalar* box_median, Scalar* box_radius, Scalar* centers, int best_index,
        int test_index) const;

    // Helper functions for SeedKMeansPlusPlus
    void SeedKmppSetClusterIndex(const Node* node, int index) const;
    Scalar SeedKmppUpdateAssignment(
        const Node* node, int new_cluster, Scalar* centers,
        Scalar* dist_sq) const;

    int n_, d_;
    Scalar* points_;
    Node* top_node_;
    char* node_data_;
    int* point_indices_;
};

#endif