--- /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;
+}
git://source.jalview.org / jabaws.git / blobdiff