+++ /dev/null
-// See KmTree.cpp
-//
-// Author: David Arthur (darthur@gmail.com), 2009
-
-// Includes
-#include "KmTree.h"
-#include <iostream>
-#include <stdlib.h>
-#include <stdio.h>
-using namespace std;
-
-KmTree::KmTree(int n, int d, Scalar *points): n_(n), d_(d), points_(points) {
- // Initialize memory
- // DD: need to cast to long otherwise malloc will fail
- // if we need more than 2 gigabytes or so
- int node_size = sizeof(Node) + d_ * 3 * sizeof(Scalar);
- node_data_ = (char*)malloc((2*(long unsigned int)n-1) * node_size);
- point_indices_ = (int*)malloc(n * sizeof(int));
- for (int i = 0; i < n; i++)
- point_indices_[i] = i;
- KM_ASSERT(node_data_ != 0 && point_indices_ != 0);
-
- // Calculate the bounding box for the points
- Scalar *bound_v1 = PointAllocate(d_);
- Scalar *bound_v2 = PointAllocate(d_);
- KM_ASSERT(bound_v1 != 0 && bound_v2 != 0);
- PointCopy(bound_v1, points, d_);
- PointCopy(bound_v2, points, d_);
- for (int i = 1; i < n; i++)
- for (int j = 0; j < d; j++) {
- if (bound_v1[j] > points[i*d_ + j]) bound_v1[j] = points[i*d_ + j];
- if (bound_v2[j] < points[i*d_ + j]) bound_v1[j] = points[i*d_ + j];
- }
-
- // Build the tree
- char *temp_node_data = node_data_;
- top_node_ = BuildNodes(points, 0, n-1, &temp_node_data);
-
- // Cleanup
- PointFree(bound_v1);
- PointFree(bound_v2);
-}
-
-KmTree::~KmTree() {
- free(point_indices_);
- free(node_data_);
-}
-
-Scalar KmTree::DoKMeansStep(int k, Scalar *centers, int *assignment) const {
- // Create an invalid center for comparison purposes
- Scalar *bad_center = PointAllocate(d_);
- KM_ASSERT(bad_center != 0);
- memset(bad_center, 0xff, d_ * sizeof(Scalar));
-
- // Allocate data
- Scalar *sums = (Scalar*)calloc(k * d_, sizeof(Scalar));
- int *counts = (int*)calloc(k, sizeof(int));
- int num_candidates = 0;
- int *candidates = (int*)malloc(k * sizeof(int));
- KM_ASSERT(sums != 0 && counts != 0 && candidates != 0);
- for (int i = 0; i < k; i++)
- if (memcmp(centers + i*d_, bad_center, d_ * sizeof(Scalar)) != 0)
- candidates[num_candidates++] = i;
-
- // Find nodes
- Scalar result = DoKMeansStepAtNode(top_node_, num_candidates, candidates, centers, sums,
- counts, assignment);
-
- // Set the new centers
- for (int i = 0; i < k; i++) {
- if (counts[i] > 0) {
- PointScale(sums + i*d_, Scalar(1) / counts[i], d_);
- PointCopy(centers + i*d_, sums + i*d_, d_);
- } else {
- memcpy(centers + i*d_, bad_center, d_ * sizeof(Scalar));
- }
- }
-
- // Cleanup memory
- PointFree(bad_center);
- free(candidates);
- free(counts);
- free(sums);
- return result;
-}
-
-// Helper functions for constructor
-// ================================
-
-// Build a kd tree from the given set of points
-KmTree::Node *KmTree::BuildNodes(Scalar *points, int first_index, int last_index,
- char **next_node_data) {
- // Allocate the node
- Node *node = (Node*)(*next_node_data);
- (*next_node_data) += sizeof(Node);
- node->sum = (Scalar*)(*next_node_data);
- (*next_node_data) += sizeof(Scalar) * d_;
- node->median = (Scalar*)(*next_node_data);
- (*next_node_data) += sizeof(Scalar) * d_;
- node->radius = (Scalar*)(*next_node_data);
- (*next_node_data) += sizeof(Scalar) * d_;
-
- // Fill in basic info
- node->num_points = (last_index - first_index + 1);
- node->first_point_index = first_index;
-
- // Calculate the bounding box
- Scalar *first_point = points + point_indices_[first_index] * d_;
- Scalar *bound_p1 = PointAllocate(d_);
- Scalar *bound_p2 = PointAllocate(d_);
- KM_ASSERT(bound_p1 != 0 && bound_p2 != 0);
- PointCopy(bound_p1, first_point, d_);
- PointCopy(bound_p2, first_point, d_);
- for (int i = first_index+1; i <= last_index; i++)
- for (int j = 0; j < d_; j++) {
- Scalar c = points[point_indices_[i]*d_ + j];
- if (bound_p1[j] > c) bound_p1[j] = c;
- if (bound_p2[j] < c) bound_p2[j] = c;
- }
-
- // Calculate bounding box stats and delete the bounding box memory
- Scalar max_radius = -1;
- int split_d = -1;
- for (int j = 0; j < d_; j++) {
- node->median[j] = (bound_p1[j] + bound_p2[j]) / 2;
- node->radius[j] = (bound_p2[j] - bound_p1[j]) / 2;
- if (node->radius[j] > max_radius) {
- max_radius = node->radius[j];
- split_d = j;
- }
- }
- PointFree(bound_p2);
- PointFree(bound_p1);
-
- // If the max spread is 0, make this a leaf node
- if (max_radius == 0) {
- node->lower_node = node->upper_node = 0;
- PointCopy(node->sum, first_point, d_);
- if (last_index != first_index)
- PointScale(node->sum, Scalar(last_index - first_index + 1), d_);
- node->opt_cost = 0;
- return node;
- }
-
- // Partition the points around the midpoint in this dimension. The partitioning is done in-place
- // by iterating from left-to-right and right-to-left in the same way that partioning is done for
- // quicksort.
- Scalar split_pos = node->median[split_d];
- int i1 = first_index, i2 = last_index, size1 = 0;
- while (i1 <= i2) {
- bool is_i1_good = (points[point_indices_[i1]*d_ + split_d] < split_pos);
- bool is_i2_good = (points[point_indices_[i2]*d_ + split_d] >= split_pos);
- if (!is_i1_good && !is_i2_good) {
- int temp = point_indices_[i1];
- point_indices_[i1] = point_indices_[i2];
- point_indices_[i2] = temp;
- is_i1_good = is_i2_good = true;
- }
- if (is_i1_good) {
- i1++;
- size1++;
- }
- if (is_i2_good) {
- i2--;
- }
- }
-
- // Create the child nodes
- KM_ASSERT(size1 >= 1 && size1 <= last_index - first_index);
- node->lower_node = BuildNodes(points, first_index, first_index + size1 - 1, next_node_data);
- node->upper_node = BuildNodes(points, first_index + size1, last_index, next_node_data);
-
- // Calculate the new sum and opt cost
- PointCopy(node->sum, node->lower_node->sum, d_);
- PointAdd(node->sum, node->upper_node->sum, d_);
- Scalar *center = PointAllocate(d_);
- KM_ASSERT(center != 0);
- PointCopy(center, node->sum, d_);
- PointScale(center, Scalar(1) / node->num_points, d_);
- node->opt_cost = GetNodeCost(node->lower_node, center) + GetNodeCost(node->upper_node, center);
- PointFree(center);
- return node;
-}
-
-// Returns the total contribution of all points in the given kd-tree node, assuming they are all
-// assigned to a center at the given location. We need to return:
-//
-// sum_{x \in node} ||x - center||^2.
-//
-// If c denotes the center of mass of the points in this node and n denotes the number of points in
-// it, then this quantity is given by
-//
-// n * ||c - center||^2 + sum_{x \in node} ||x - c||^2
-//
-// The sum is precomputed for each node as opt_cost. This formula follows from expanding both sides
-// as dot products. See Kanungo/Mount for more info.
-Scalar KmTree::GetNodeCost(const Node *node, Scalar *center) const {
- Scalar dist_sq = 0;
- for (int i = 0; i < d_; i++) {
- Scalar x = (node->sum[i] / node->num_points) - center[i];
- dist_sq += x*x;
- }
- return node->opt_cost + node->num_points * dist_sq;
-}
-
-// Helper functions for DoKMeans step
-// ==================================
-
-// A recursive version of DoKMeansStep. This determines which clusters all points that are rooted
-// node will be assigned to, and updates sums, counts and assignment (if not null) accordingly.
-// candidates maintains the set of cluster indices which could possibly be the closest clusters
-// for points in this subtree.
-Scalar KmTree::DoKMeansStepAtNode(const Node *node, int k, int *candidates, Scalar *centers,
- Scalar *sums, int *counts, int *assignment) const {
- // Determine which center the node center is closest to
- Scalar min_dist_sq = PointDistSq(node->median, centers + candidates[0]*d_, d_);
- int closest_i = candidates[0];
- for (int i = 1; i < k; i++) {
- Scalar dist_sq = PointDistSq(node->median, centers + candidates[i]*d_, d_);
- if (dist_sq < min_dist_sq) {
- min_dist_sq = dist_sq;
- closest_i = candidates[i];
- }
- }
-
- // If this is a non-leaf node, recurse if necessary
- if (node->lower_node != 0) {
- // Build the new list of candidates
- int new_k = 0;
- int *new_candidates = (int*)malloc(k * sizeof(int));
- KM_ASSERT(new_candidates != 0);
- for (int i = 0; i < k; i++)
- if (!ShouldBePruned(node->median, node->radius, centers, closest_i, candidates[i]))
- new_candidates[new_k++] = candidates[i];
-
- // Recurse if there's at least two
- if (new_k > 1) {
- Scalar result = DoKMeansStepAtNode(node->lower_node, new_k, new_candidates, centers,
- sums, counts, assignment) +
- DoKMeansStepAtNode(node->upper_node, new_k, new_candidates, centers,
- sums, counts, assignment);
- free(new_candidates);
- return result;
- } else {
- free(new_candidates);
- }
- }
-
- // Assigns all points within this node to a single center
- PointAdd(sums + closest_i*d_, node->sum, d_);
- counts[closest_i] += node->num_points;
- if (assignment != 0) {
- for (int i = node->first_point_index; i < node->first_point_index + node->num_points; i++)
- assignment[point_indices_[i]] = closest_i;
- }
- return GetNodeCost(node, centers + closest_i*d_);
-}
-
-// Determines whether every point in the box is closer to centers[best_index] than to
-// centers[test_index].
-//
-// If x is a point, c_0 = centers[best_index], c = centers[test_index], then:
-// (x-c).(x-c) < (x-c_0).(x-c_0)
-// <=> (c-c_0).(c-c_0) < 2(x-c_0).(c-c_0)
-//
-// The right-hand side is maximized for a vertex of the box where for each dimension, we choose
-// the low or high value based on the sign of x-c_0 in that dimension.
-bool KmTree::ShouldBePruned(Scalar *box_median, Scalar *box_radius, Scalar *centers,
- int best_index, int test_index) const {
- if (best_index == test_index)
- return false;
-
- Scalar *best = centers + best_index*d_;
- Scalar *test = centers + test_index*d_;
- Scalar lhs = 0, rhs = 0;
- for (int i = 0; i < d_; i++) {
- Scalar component = test[i] - best[i];
- lhs += component * component;
- if (component > 0)
- rhs += (box_median[i] + box_radius[i] - best[i]) * component;
- else
- rhs += (box_median[i] - box_radius[i] - best[i]) * component;
- }
- return (lhs >= 2*rhs);
-}
-
-Scalar KmTree::SeedKMeansPlusPlus(int k, Scalar *centers) const {
- Scalar *dist_sq = (Scalar*)malloc(n_ * sizeof(Scalar));
- KM_ASSERT(dist_sq != 0);
-
- // Choose an initial center uniformly at random
- SeedKmppSetClusterIndex(top_node_, 0);
- int i = GetRandom(n_);
- memcpy(centers, points_ + point_indices_[i]*d_, d_*sizeof(Scalar));
- Scalar total_cost = 0;
- for (int j = 0; j < n_; j++) {
- dist_sq[j] = PointDistSq(points_ + point_indices_[j]*d_, centers, d_);
- total_cost += dist_sq[j];
- }
-
- // Repeatedly choose more centers
- for (int new_cluster = 1; new_cluster < k; new_cluster++) {
- while (1) {
- Scalar cutoff = (rand() / Scalar(RAND_MAX)) * total_cost;
- Scalar cur_cost = 0;
- for (i = 0; i < n_; i++) {
- cur_cost += dist_sq[i];
- if (cur_cost >= cutoff)
- break;
- }
- if (i < n_)
- break;
- }
- memcpy(centers + new_cluster*d_, points_ + point_indices_[i]*d_, d_*sizeof(Scalar));
- total_cost = SeedKmppUpdateAssignment(top_node_, new_cluster, centers, dist_sq);
- }
-
- // Clean up and return
- free(dist_sq);
- return total_cost;
-}
-
-// Helper functions for SeedKMeansPlusPlus
-// =======================================
-
-// Sets kmpp_cluster_index to 0 for all nodes
-void KmTree::SeedKmppSetClusterIndex(const Node *node, int value) const {
- node->kmpp_cluster_index = value;
- if (node->lower_node != 0) {
- SeedKmppSetClusterIndex(node->lower_node, value);
- SeedKmppSetClusterIndex(node->upper_node, value);
- }
-}
-
-Scalar KmTree::SeedKmppUpdateAssignment(const Node *node, int new_cluster, Scalar *centers,
- Scalar *dist_sq) const {
- // See if we can assign all points in this node to one cluster
- if (node->kmpp_cluster_index >= 0) {
- if (ShouldBePruned(node->median, node->radius, centers, node->kmpp_cluster_index, new_cluster))
- return GetNodeCost(node, centers + node->kmpp_cluster_index*d_);
- if (ShouldBePruned(node->median, node->radius, centers, new_cluster,
- node->kmpp_cluster_index)) {
- SeedKmppSetClusterIndex(node, new_cluster);
- for (int i = node->first_point_index; i < node->first_point_index + node->num_points; i++)
- dist_sq[i] = PointDistSq(points_ + point_indices_[i]*d_, centers + new_cluster*d_, d_);
- return GetNodeCost(node, centers + new_cluster*d_);
- }
-
- // It may be that the a leaf-node point is equidistant from the new center or old
- if (node->lower_node == 0)
- return GetNodeCost(node, centers + node->kmpp_cluster_index*d_);
- }
-
- // Recurse
- Scalar cost = SeedKmppUpdateAssignment(node->lower_node, new_cluster, centers, dist_sq) +
- SeedKmppUpdateAssignment(node->upper_node, new_cluster, centers, dist_sq);
- int i1 = node->lower_node->kmpp_cluster_index, i2 = node->upper_node->kmpp_cluster_index;
- if (i1 == i2 && i1 != -1)
- node->kmpp_cluster_index = i1;
- else
- node->kmpp_cluster_index = -1;
- return cost;
-}