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comparison clustalomega/clustal-omega-0.2.0/src/kmpp/KmTree.cpp @ 0:ff1768533a07
Migrated tool version 0.2 from old tool shed archive to new tool shed repository
author | clustalomega |
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date | Tue, 07 Jun 2011 17:04:25 -0400 |
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1 // See KmTree.cpp | |
2 // | |
3 // Author: David Arthur (darthur@gmail.com), 2009 | |
4 | |
5 // Includes | |
6 #include "KmTree.h" | |
7 #include <iostream> | |
8 #include <stdlib.h> | |
9 #include <stdio.h> | |
10 using namespace std; | |
11 | |
12 KmTree::KmTree(int n, int d, Scalar *points): n_(n), d_(d), points_(points) { | |
13 // Initialize memory | |
14 // DD: need to cast to long otherwise malloc will fail | |
15 // if we need more than 2 gigabytes or so | |
16 int node_size = sizeof(Node) + d_ * 3 * sizeof(Scalar); | |
17 node_data_ = (char*)malloc((2*(long unsigned int)n-1) * node_size); | |
18 point_indices_ = (int*)malloc(n * sizeof(int)); | |
19 for (int i = 0; i < n; i++) | |
20 point_indices_[i] = i; | |
21 KM_ASSERT(node_data_ != 0 && point_indices_ != 0); | |
22 | |
23 // Calculate the bounding box for the points | |
24 Scalar *bound_v1 = PointAllocate(d_); | |
25 Scalar *bound_v2 = PointAllocate(d_); | |
26 KM_ASSERT(bound_v1 != 0 && bound_v2 != 0); | |
27 PointCopy(bound_v1, points, d_); | |
28 PointCopy(bound_v2, points, d_); | |
29 for (int i = 1; i < n; i++) | |
30 for (int j = 0; j < d; j++) { | |
31 if (bound_v1[j] > points[i*d_ + j]) bound_v1[j] = points[i*d_ + j]; | |
32 if (bound_v2[j] < points[i*d_ + j]) bound_v1[j] = points[i*d_ + j]; | |
33 } | |
34 | |
35 // Build the tree | |
36 char *temp_node_data = node_data_; | |
37 top_node_ = BuildNodes(points, 0, n-1, &temp_node_data); | |
38 | |
39 // Cleanup | |
40 PointFree(bound_v1); | |
41 PointFree(bound_v2); | |
42 } | |
43 | |
44 KmTree::~KmTree() { | |
45 free(point_indices_); | |
46 free(node_data_); | |
47 } | |
48 | |
49 Scalar KmTree::DoKMeansStep(int k, Scalar *centers, int *assignment) const { | |
50 // Create an invalid center for comparison purposes | |
51 Scalar *bad_center = PointAllocate(d_); | |
52 KM_ASSERT(bad_center != 0); | |
53 memset(bad_center, 0xff, d_ * sizeof(Scalar)); | |
54 | |
55 // Allocate data | |
56 Scalar *sums = (Scalar*)calloc(k * d_, sizeof(Scalar)); | |
57 int *counts = (int*)calloc(k, sizeof(int)); | |
58 int num_candidates = 0; | |
59 int *candidates = (int*)malloc(k * sizeof(int)); | |
60 KM_ASSERT(sums != 0 && counts != 0 && candidates != 0); | |
61 for (int i = 0; i < k; i++) | |
62 if (memcmp(centers + i*d_, bad_center, d_ * sizeof(Scalar)) != 0) | |
63 candidates[num_candidates++] = i; | |
64 | |
65 // Find nodes | |
66 Scalar result = DoKMeansStepAtNode(top_node_, num_candidates, candidates, centers, sums, | |
67 counts, assignment); | |
68 | |
69 // Set the new centers | |
70 for (int i = 0; i < k; i++) { | |
71 if (counts[i] > 0) { | |
72 PointScale(sums + i*d_, Scalar(1) / counts[i], d_); | |
73 PointCopy(centers + i*d_, sums + i*d_, d_); | |
74 } else { | |
75 memcpy(centers + i*d_, bad_center, d_ * sizeof(Scalar)); | |
76 } | |
77 } | |
78 | |
79 // Cleanup memory | |
80 PointFree(bad_center); | |
81 free(candidates); | |
82 free(counts); | |
83 free(sums); | |
84 return result; | |
85 } | |
86 | |
87 // Helper functions for constructor | |
88 // ================================ | |
89 | |
90 // Build a kd tree from the given set of points | |
91 KmTree::Node *KmTree::BuildNodes(Scalar *points, int first_index, int last_index, | |
92 char **next_node_data) { | |
93 // Allocate the node | |
94 Node *node = (Node*)(*next_node_data); | |
95 (*next_node_data) += sizeof(Node); | |
96 node->sum = (Scalar*)(*next_node_data); | |
97 (*next_node_data) += sizeof(Scalar) * d_; | |
98 node->median = (Scalar*)(*next_node_data); | |
99 (*next_node_data) += sizeof(Scalar) * d_; | |
100 node->radius = (Scalar*)(*next_node_data); | |
101 (*next_node_data) += sizeof(Scalar) * d_; | |
102 | |
103 // Fill in basic info | |
104 node->num_points = (last_index - first_index + 1); | |
105 node->first_point_index = first_index; | |
106 | |
107 // Calculate the bounding box | |
108 Scalar *first_point = points + point_indices_[first_index] * d_; | |
109 Scalar *bound_p1 = PointAllocate(d_); | |
110 Scalar *bound_p2 = PointAllocate(d_); | |
111 KM_ASSERT(bound_p1 != 0 && bound_p2 != 0); | |
112 PointCopy(bound_p1, first_point, d_); | |
113 PointCopy(bound_p2, first_point, d_); | |
114 for (int i = first_index+1; i <= last_index; i++) | |
115 for (int j = 0; j < d_; j++) { | |
116 Scalar c = points[point_indices_[i]*d_ + j]; | |
117 if (bound_p1[j] > c) bound_p1[j] = c; | |
118 if (bound_p2[j] < c) bound_p2[j] = c; | |
119 } | |
120 | |
121 // Calculate bounding box stats and delete the bounding box memory | |
122 Scalar max_radius = -1; | |
123 int split_d = -1; | |
124 for (int j = 0; j < d_; j++) { | |
125 node->median[j] = (bound_p1[j] + bound_p2[j]) / 2; | |
126 node->radius[j] = (bound_p2[j] - bound_p1[j]) / 2; | |
127 if (node->radius[j] > max_radius) { | |
128 max_radius = node->radius[j]; | |
129 split_d = j; | |
130 } | |
131 } | |
132 PointFree(bound_p2); | |
133 PointFree(bound_p1); | |
134 | |
135 // If the max spread is 0, make this a leaf node | |
136 if (max_radius == 0) { | |
137 node->lower_node = node->upper_node = 0; | |
138 PointCopy(node->sum, first_point, d_); | |
139 if (last_index != first_index) | |
140 PointScale(node->sum, Scalar(last_index - first_index + 1), d_); | |
141 node->opt_cost = 0; | |
142 return node; | |
143 } | |
144 | |
145 // Partition the points around the midpoint in this dimension. The partitioning is done in-place | |
146 // by iterating from left-to-right and right-to-left in the same way that partioning is done for | |
147 // quicksort. | |
148 Scalar split_pos = node->median[split_d]; | |
149 int i1 = first_index, i2 = last_index, size1 = 0; | |
150 while (i1 <= i2) { | |
151 bool is_i1_good = (points[point_indices_[i1]*d_ + split_d] < split_pos); | |
152 bool is_i2_good = (points[point_indices_[i2]*d_ + split_d] >= split_pos); | |
153 if (!is_i1_good && !is_i2_good) { | |
154 int temp = point_indices_[i1]; | |
155 point_indices_[i1] = point_indices_[i2]; | |
156 point_indices_[i2] = temp; | |
157 is_i1_good = is_i2_good = true; | |
158 } | |
159 if (is_i1_good) { | |
160 i1++; | |
161 size1++; | |
162 } | |
163 if (is_i2_good) { | |
164 i2--; | |
165 } | |
166 } | |
167 | |
168 // Create the child nodes | |
169 KM_ASSERT(size1 >= 1 && size1 <= last_index - first_index); | |
170 node->lower_node = BuildNodes(points, first_index, first_index + size1 - 1, next_node_data); | |
171 node->upper_node = BuildNodes(points, first_index + size1, last_index, next_node_data); | |
172 | |
173 // Calculate the new sum and opt cost | |
174 PointCopy(node->sum, node->lower_node->sum, d_); | |
175 PointAdd(node->sum, node->upper_node->sum, d_); | |
176 Scalar *center = PointAllocate(d_); | |
177 KM_ASSERT(center != 0); | |
178 PointCopy(center, node->sum, d_); | |
179 PointScale(center, Scalar(1) / node->num_points, d_); | |
180 node->opt_cost = GetNodeCost(node->lower_node, center) + GetNodeCost(node->upper_node, center); | |
181 PointFree(center); | |
182 return node; | |
183 } | |
184 | |
185 // Returns the total contribution of all points in the given kd-tree node, assuming they are all | |
186 // assigned to a center at the given location. We need to return: | |
187 // | |
188 // sum_{x \in node} ||x - center||^2. | |
189 // | |
190 // If c denotes the center of mass of the points in this node and n denotes the number of points in | |
191 // it, then this quantity is given by | |
192 // | |
193 // n * ||c - center||^2 + sum_{x \in node} ||x - c||^2 | |
194 // | |
195 // The sum is precomputed for each node as opt_cost. This formula follows from expanding both sides | |
196 // as dot products. See Kanungo/Mount for more info. | |
197 Scalar KmTree::GetNodeCost(const Node *node, Scalar *center) const { | |
198 Scalar dist_sq = 0; | |
199 for (int i = 0; i < d_; i++) { | |
200 Scalar x = (node->sum[i] / node->num_points) - center[i]; | |
201 dist_sq += x*x; | |
202 } | |
203 return node->opt_cost + node->num_points * dist_sq; | |
204 } | |
205 | |
206 // Helper functions for DoKMeans step | |
207 // ================================== | |
208 | |
209 // A recursive version of DoKMeansStep. This determines which clusters all points that are rooted | |
210 // node will be assigned to, and updates sums, counts and assignment (if not null) accordingly. | |
211 // candidates maintains the set of cluster indices which could possibly be the closest clusters | |
212 // for points in this subtree. | |
213 Scalar KmTree::DoKMeansStepAtNode(const Node *node, int k, int *candidates, Scalar *centers, | |
214 Scalar *sums, int *counts, int *assignment) const { | |
215 // Determine which center the node center is closest to | |
216 Scalar min_dist_sq = PointDistSq(node->median, centers + candidates[0]*d_, d_); | |
217 int closest_i = candidates[0]; | |
218 for (int i = 1; i < k; i++) { | |
219 Scalar dist_sq = PointDistSq(node->median, centers + candidates[i]*d_, d_); | |
220 if (dist_sq < min_dist_sq) { | |
221 min_dist_sq = dist_sq; | |
222 closest_i = candidates[i]; | |
223 } | |
224 } | |
225 | |
226 // If this is a non-leaf node, recurse if necessary | |
227 if (node->lower_node != 0) { | |
228 // Build the new list of candidates | |
229 int new_k = 0; | |
230 int *new_candidates = (int*)malloc(k * sizeof(int)); | |
231 KM_ASSERT(new_candidates != 0); | |
232 for (int i = 0; i < k; i++) | |
233 if (!ShouldBePruned(node->median, node->radius, centers, closest_i, candidates[i])) | |
234 new_candidates[new_k++] = candidates[i]; | |
235 | |
236 // Recurse if there's at least two | |
237 if (new_k > 1) { | |
238 Scalar result = DoKMeansStepAtNode(node->lower_node, new_k, new_candidates, centers, | |
239 sums, counts, assignment) + | |
240 DoKMeansStepAtNode(node->upper_node, new_k, new_candidates, centers, | |
241 sums, counts, assignment); | |
242 free(new_candidates); | |
243 return result; | |
244 } else { | |
245 free(new_candidates); | |
246 } | |
247 } | |
248 | |
249 // Assigns all points within this node to a single center | |
250 PointAdd(sums + closest_i*d_, node->sum, d_); | |
251 counts[closest_i] += node->num_points; | |
252 if (assignment != 0) { | |
253 for (int i = node->first_point_index; i < node->first_point_index + node->num_points; i++) | |
254 assignment[point_indices_[i]] = closest_i; | |
255 } | |
256 return GetNodeCost(node, centers + closest_i*d_); | |
257 } | |
258 | |
259 // Determines whether every point in the box is closer to centers[best_index] than to | |
260 // centers[test_index]. | |
261 // | |
262 // If x is a point, c_0 = centers[best_index], c = centers[test_index], then: | |
263 // (x-c).(x-c) < (x-c_0).(x-c_0) | |
264 // <=> (c-c_0).(c-c_0) < 2(x-c_0).(c-c_0) | |
265 // | |
266 // The right-hand side is maximized for a vertex of the box where for each dimension, we choose | |
267 // the low or high value based on the sign of x-c_0 in that dimension. | |
268 bool KmTree::ShouldBePruned(Scalar *box_median, Scalar *box_radius, Scalar *centers, | |
269 int best_index, int test_index) const { | |
270 if (best_index == test_index) | |
271 return false; | |
272 | |
273 Scalar *best = centers + best_index*d_; | |
274 Scalar *test = centers + test_index*d_; | |
275 Scalar lhs = 0, rhs = 0; | |
276 for (int i = 0; i < d_; i++) { | |
277 Scalar component = test[i] - best[i]; | |
278 lhs += component * component; | |
279 if (component > 0) | |
280 rhs += (box_median[i] + box_radius[i] - best[i]) * component; | |
281 else | |
282 rhs += (box_median[i] - box_radius[i] - best[i]) * component; | |
283 } | |
284 return (lhs >= 2*rhs); | |
285 } | |
286 | |
287 Scalar KmTree::SeedKMeansPlusPlus(int k, Scalar *centers) const { | |
288 Scalar *dist_sq = (Scalar*)malloc(n_ * sizeof(Scalar)); | |
289 KM_ASSERT(dist_sq != 0); | |
290 | |
291 // Choose an initial center uniformly at random | |
292 SeedKmppSetClusterIndex(top_node_, 0); | |
293 int i = GetRandom(n_); | |
294 memcpy(centers, points_ + point_indices_[i]*d_, d_*sizeof(Scalar)); | |
295 Scalar total_cost = 0; | |
296 for (int j = 0; j < n_; j++) { | |
297 dist_sq[j] = PointDistSq(points_ + point_indices_[j]*d_, centers, d_); | |
298 total_cost += dist_sq[j]; | |
299 } | |
300 | |
301 // Repeatedly choose more centers | |
302 for (int new_cluster = 1; new_cluster < k; new_cluster++) { | |
303 while (1) { | |
304 Scalar cutoff = (rand() / Scalar(RAND_MAX)) * total_cost; | |
305 Scalar cur_cost = 0; | |
306 for (i = 0; i < n_; i++) { | |
307 cur_cost += dist_sq[i]; | |
308 if (cur_cost >= cutoff) | |
309 break; | |
310 } | |
311 if (i < n_) | |
312 break; | |
313 } | |
314 memcpy(centers + new_cluster*d_, points_ + point_indices_[i]*d_, d_*sizeof(Scalar)); | |
315 total_cost = SeedKmppUpdateAssignment(top_node_, new_cluster, centers, dist_sq); | |
316 } | |
317 | |
318 // Clean up and return | |
319 free(dist_sq); | |
320 return total_cost; | |
321 } | |
322 | |
323 // Helper functions for SeedKMeansPlusPlus | |
324 // ======================================= | |
325 | |
326 // Sets kmpp_cluster_index to 0 for all nodes | |
327 void KmTree::SeedKmppSetClusterIndex(const Node *node, int value) const { | |
328 node->kmpp_cluster_index = value; | |
329 if (node->lower_node != 0) { | |
330 SeedKmppSetClusterIndex(node->lower_node, value); | |
331 SeedKmppSetClusterIndex(node->upper_node, value); | |
332 } | |
333 } | |
334 | |
335 Scalar KmTree::SeedKmppUpdateAssignment(const Node *node, int new_cluster, Scalar *centers, | |
336 Scalar *dist_sq) const { | |
337 // See if we can assign all points in this node to one cluster | |
338 if (node->kmpp_cluster_index >= 0) { | |
339 if (ShouldBePruned(node->median, node->radius, centers, node->kmpp_cluster_index, new_cluster)) | |
340 return GetNodeCost(node, centers + node->kmpp_cluster_index*d_); | |
341 if (ShouldBePruned(node->median, node->radius, centers, new_cluster, | |
342 node->kmpp_cluster_index)) { | |
343 SeedKmppSetClusterIndex(node, new_cluster); | |
344 for (int i = node->first_point_index; i < node->first_point_index + node->num_points; i++) | |
345 dist_sq[i] = PointDistSq(points_ + point_indices_[i]*d_, centers + new_cluster*d_, d_); | |
346 return GetNodeCost(node, centers + new_cluster*d_); | |
347 } | |
348 | |
349 // It may be that the a leaf-node point is equidistant from the new center or old | |
350 if (node->lower_node == 0) | |
351 return GetNodeCost(node, centers + node->kmpp_cluster_index*d_); | |
352 } | |
353 | |
354 // Recurse | |
355 Scalar cost = SeedKmppUpdateAssignment(node->lower_node, new_cluster, centers, dist_sq) + | |
356 SeedKmppUpdateAssignment(node->upper_node, new_cluster, centers, dist_sq); | |
357 int i1 = node->lower_node->kmpp_cluster_index, i2 = node->upper_node->kmpp_cluster_index; | |
358 if (i1 == i2 && i1 != -1) | |
359 node->kmpp_cluster_index = i1; | |
360 else | |
361 node->kmpp_cluster_index = -1; | |
362 return cost; | |
363 } |