1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2010, 2011, 2012 Google Inc. All rights reserved. 3 // http://code.google.com/p/ceres-solver/ 4 // 5 // Redistribution and use in source and binary forms, with or without 6 // modification, are permitted provided that the following conditions are met: 7 // 8 // * Redistributions of source code must retain the above copyright notice, 9 // this list of conditions and the following disclaimer. 10 // * Redistributions in binary form must reproduce the above copyright notice, 11 // this list of conditions and the following disclaimer in the documentation 12 // and/or other materials provided with the distribution. 13 // * Neither the name of Google Inc. nor the names of its contributors may be 14 // used to endorse or promote products derived from this software without 15 // specific prior written permission. 16 // 17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27 // POSSIBILITY OF SUCH DAMAGE. 28 // 29 // Author: David Gallup (dgallup (at) google.com) 30 // Sameer Agarwal (sameeragarwal (at) google.com) 31 32 #ifndef CERES_NO_SUITESPARSE 33 34 #include "ceres/canonical_views_clustering.h" 35 36 #include "ceres/collections_port.h" 37 #include "ceres/graph.h" 38 #include "ceres/internal/macros.h" 39 #include "ceres/map_util.h" 40 #include "glog/logging.h" 41 42 namespace ceres { 43 namespace internal { 44 45 typedef HashMap<int, int> IntMap; 46 typedef HashSet<int> IntSet; 47 48 class CanonicalViewsClustering { 49 public: 50 CanonicalViewsClustering() {} 51 52 // Compute the canonical views clustering of the vertices of the 53 // graph. centers will contain the vertices that are the identified 54 // as the canonical views/cluster centers, and membership is a map 55 // from vertices to cluster_ids. The i^th cluster center corresponds 56 // to the i^th cluster. It is possible depending on the 57 // configuration of the clustering algorithm that some of the 58 // vertices may not be assigned to any cluster. In this case they 59 // are assigned to a cluster with id = kInvalidClusterId. 60 void ComputeClustering(const Graph<int>& graph, 61 const CanonicalViewsClusteringOptions& options, 62 vector<int>* centers, 63 IntMap* membership); 64 65 private: 66 void FindValidViews(IntSet* valid_views) const; 67 double ComputeClusteringQualityDifference(const int candidate, 68 const vector<int>& centers) const; 69 void UpdateCanonicalViewAssignments(const int canonical_view); 70 void ComputeClusterMembership(const vector<int>& centers, 71 IntMap* membership) const; 72 73 CanonicalViewsClusteringOptions options_; 74 const Graph<int>* graph_; 75 // Maps a view to its representative canonical view (its cluster 76 // center). 77 IntMap view_to_canonical_view_; 78 // Maps a view to its similarity to its current cluster center. 79 HashMap<int, double> view_to_canonical_view_similarity_; 80 CERES_DISALLOW_COPY_AND_ASSIGN(CanonicalViewsClustering); 81 }; 82 83 void ComputeCanonicalViewsClustering( 84 const Graph<int>& graph, 85 const CanonicalViewsClusteringOptions& options, 86 vector<int>* centers, 87 IntMap* membership) { 88 time_t start_time = time(NULL); 89 CanonicalViewsClustering cv; 90 cv.ComputeClustering(graph, options, centers, membership); 91 VLOG(2) << "Canonical views clustering time (secs): " 92 << time(NULL) - start_time; 93 } 94 95 // Implementation of CanonicalViewsClustering 96 void CanonicalViewsClustering::ComputeClustering( 97 const Graph<int>& graph, 98 const CanonicalViewsClusteringOptions& options, 99 vector<int>* centers, 100 IntMap* membership) { 101 options_ = options; 102 CHECK_NOTNULL(centers)->clear(); 103 CHECK_NOTNULL(membership)->clear(); 104 graph_ = &graph; 105 106 IntSet valid_views; 107 FindValidViews(&valid_views); 108 while (valid_views.size() > 0) { 109 // Find the next best canonical view. 110 double best_difference = -std::numeric_limits<double>::max(); 111 int best_view = 0; 112 113 // TODO(sameeragarwal): Make this loop multi-threaded. 114 for (IntSet::const_iterator view = valid_views.begin(); 115 view != valid_views.end(); 116 ++view) { 117 const double difference = 118 ComputeClusteringQualityDifference(*view, *centers); 119 if (difference > best_difference) { 120 best_difference = difference; 121 best_view = *view; 122 } 123 } 124 125 CHECK_GT(best_difference, -std::numeric_limits<double>::max()); 126 127 // Add canonical view if quality improves, or if minimum is not 128 // yet met, otherwise break. 129 if ((best_difference <= 0) && 130 (centers->size() >= options_.min_views)) { 131 break; 132 } 133 134 centers->push_back(best_view); 135 valid_views.erase(best_view); 136 UpdateCanonicalViewAssignments(best_view); 137 } 138 139 ComputeClusterMembership(*centers, membership); 140 } 141 142 // Return the set of vertices of the graph which have valid vertex 143 // weights. 144 void CanonicalViewsClustering::FindValidViews( 145 IntSet* valid_views) const { 146 const IntSet& views = graph_->vertices(); 147 for (IntSet::const_iterator view = views.begin(); 148 view != views.end(); 149 ++view) { 150 if (graph_->VertexWeight(*view) != Graph<int>::InvalidWeight()) { 151 valid_views->insert(*view); 152 } 153 } 154 } 155 156 // Computes the difference in the quality score if 'candidate' were 157 // added to the set of canonical views. 158 double CanonicalViewsClustering::ComputeClusteringQualityDifference( 159 const int candidate, 160 const vector<int>& centers) const { 161 // View score. 162 double difference = 163 options_.view_score_weight * graph_->VertexWeight(candidate); 164 165 // Compute how much the quality score changes if the candidate view 166 // was added to the list of canonical views and its nearest 167 // neighbors became members of its cluster. 168 const IntSet& neighbors = graph_->Neighbors(candidate); 169 for (IntSet::const_iterator neighbor = neighbors.begin(); 170 neighbor != neighbors.end(); 171 ++neighbor) { 172 const double old_similarity = 173 FindWithDefault(view_to_canonical_view_similarity_, *neighbor, 0.0); 174 const double new_similarity = graph_->EdgeWeight(*neighbor, candidate); 175 if (new_similarity > old_similarity) { 176 difference += new_similarity - old_similarity; 177 } 178 } 179 180 // Number of views penalty. 181 difference -= options_.size_penalty_weight; 182 183 // Orthogonality. 184 for (int i = 0; i < centers.size(); ++i) { 185 difference -= options_.similarity_penalty_weight * 186 graph_->EdgeWeight(centers[i], candidate); 187 } 188 189 return difference; 190 } 191 192 // Reassign views if they're more similar to the new canonical view. 193 void CanonicalViewsClustering::UpdateCanonicalViewAssignments( 194 const int canonical_view) { 195 const IntSet& neighbors = graph_->Neighbors(canonical_view); 196 for (IntSet::const_iterator neighbor = neighbors.begin(); 197 neighbor != neighbors.end(); 198 ++neighbor) { 199 const double old_similarity = 200 FindWithDefault(view_to_canonical_view_similarity_, *neighbor, 0.0); 201 const double new_similarity = 202 graph_->EdgeWeight(*neighbor, canonical_view); 203 if (new_similarity > old_similarity) { 204 view_to_canonical_view_[*neighbor] = canonical_view; 205 view_to_canonical_view_similarity_[*neighbor] = new_similarity; 206 } 207 } 208 } 209 210 // Assign a cluster id to each view. 211 void CanonicalViewsClustering::ComputeClusterMembership( 212 const vector<int>& centers, 213 IntMap* membership) const { 214 CHECK_NOTNULL(membership)->clear(); 215 216 // The i^th cluster has cluster id i. 217 IntMap center_to_cluster_id; 218 for (int i = 0; i < centers.size(); ++i) { 219 center_to_cluster_id[centers[i]] = i; 220 } 221 222 static const int kInvalidClusterId = -1; 223 224 const IntSet& views = graph_->vertices(); 225 for (IntSet::const_iterator view = views.begin(); 226 view != views.end(); 227 ++view) { 228 IntMap::const_iterator it = 229 view_to_canonical_view_.find(*view); 230 int cluster_id = kInvalidClusterId; 231 if (it != view_to_canonical_view_.end()) { 232 cluster_id = FindOrDie(center_to_cluster_id, it->second); 233 } 234 235 InsertOrDie(membership, *view, cluster_id); 236 } 237 } 238 239 } // namespace internal 240 } // namespace ceres 241 242 #endif // CERES_NO_SUITESPARSE 243