// Ceres Solver - A fast non-linear least squares minimizer // Copyright 2010, 2011, 2012 Google Inc. All rights reserved. // http://code.google.com/p/ceres-solver/ // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are met: // // * Redistributions of source code must retain the above copyright notice, // this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above copyright notice, // this list of conditions and the following disclaimer in the documentation // and/or other materials provided with the distribution. // * Neither the name of Google Inc. nor the names of its contributors may be // used to endorse or promote products derived from this software without // specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE // POSSIBILITY OF SUCH DAMAGE. // // Author: David Gallup (dgallup@google.com) // Sameer Agarwal (sameeragarwal@google.com) // This include must come before any #ifndef check on Ceres compile options. #include "ceres/internal/port.h" #ifndef CERES_NO_SUITESPARSE #include "ceres/canonical_views_clustering.h" #include "ceres/collections_port.h" #include "ceres/graph.h" #include "ceres/internal/macros.h" #include "ceres/map_util.h" #include "glog/logging.h" namespace ceres { namespace internal { typedef HashMap<int, int> IntMap; typedef HashSet<int> IntSet; class CanonicalViewsClustering { public: CanonicalViewsClustering() {} // Compute the canonical views clustering of the vertices of the // graph. centers will contain the vertices that are the identified // as the canonical views/cluster centers, and membership is a map // from vertices to cluster_ids. The i^th cluster center corresponds // to the i^th cluster. It is possible depending on the // configuration of the clustering algorithm that some of the // vertices may not be assigned to any cluster. In this case they // are assigned to a cluster with id = kInvalidClusterId. void ComputeClustering(const CanonicalViewsClusteringOptions& options, const Graph<int>& graph, vector<int>* centers, IntMap* membership); private: void FindValidViews(IntSet* valid_views) const; double ComputeClusteringQualityDifference(const int candidate, const vector<int>& centers) const; void UpdateCanonicalViewAssignments(const int canonical_view); void ComputeClusterMembership(const vector<int>& centers, IntMap* membership) const; CanonicalViewsClusteringOptions options_; const Graph<int>* graph_; // Maps a view to its representative canonical view (its cluster // center). IntMap view_to_canonical_view_; // Maps a view to its similarity to its current cluster center. HashMap<int, double> view_to_canonical_view_similarity_; CERES_DISALLOW_COPY_AND_ASSIGN(CanonicalViewsClustering); }; void ComputeCanonicalViewsClustering( const CanonicalViewsClusteringOptions& options, const Graph<int>& graph, vector<int>* centers, IntMap* membership) { time_t start_time = time(NULL); CanonicalViewsClustering cv; cv.ComputeClustering(options, graph, centers, membership); VLOG(2) << "Canonical views clustering time (secs): " << time(NULL) - start_time; } // Implementation of CanonicalViewsClustering void CanonicalViewsClustering::ComputeClustering( const CanonicalViewsClusteringOptions& options, const Graph<int>& graph, vector<int>* centers, IntMap* membership) { options_ = options; CHECK_NOTNULL(centers)->clear(); CHECK_NOTNULL(membership)->clear(); graph_ = &graph; IntSet valid_views; FindValidViews(&valid_views); while (valid_views.size() > 0) { // Find the next best canonical view. double best_difference = -std::numeric_limits<double>::max(); int best_view = 0; // TODO(sameeragarwal): Make this loop multi-threaded. for (IntSet::const_iterator view = valid_views.begin(); view != valid_views.end(); ++view) { const double difference = ComputeClusteringQualityDifference(*view, *centers); if (difference > best_difference) { best_difference = difference; best_view = *view; } } CHECK_GT(best_difference, -std::numeric_limits<double>::max()); // Add canonical view if quality improves, or if minimum is not // yet met, otherwise break. if ((best_difference <= 0) && (centers->size() >= options_.min_views)) { break; } centers->push_back(best_view); valid_views.erase(best_view); UpdateCanonicalViewAssignments(best_view); } ComputeClusterMembership(*centers, membership); } // Return the set of vertices of the graph which have valid vertex // weights. void CanonicalViewsClustering::FindValidViews( IntSet* valid_views) const { const IntSet& views = graph_->vertices(); for (IntSet::const_iterator view = views.begin(); view != views.end(); ++view) { if (graph_->VertexWeight(*view) != Graph<int>::InvalidWeight()) { valid_views->insert(*view); } } } // Computes the difference in the quality score if 'candidate' were // added to the set of canonical views. double CanonicalViewsClustering::ComputeClusteringQualityDifference( const int candidate, const vector<int>& centers) const { // View score. double difference = options_.view_score_weight * graph_->VertexWeight(candidate); // Compute how much the quality score changes if the candidate view // was added to the list of canonical views and its nearest // neighbors became members of its cluster. const IntSet& neighbors = graph_->Neighbors(candidate); for (IntSet::const_iterator neighbor = neighbors.begin(); neighbor != neighbors.end(); ++neighbor) { const double old_similarity = FindWithDefault(view_to_canonical_view_similarity_, *neighbor, 0.0); const double new_similarity = graph_->EdgeWeight(*neighbor, candidate); if (new_similarity > old_similarity) { difference += new_similarity - old_similarity; } } // Number of views penalty. difference -= options_.size_penalty_weight; // Orthogonality. for (int i = 0; i < centers.size(); ++i) { difference -= options_.similarity_penalty_weight * graph_->EdgeWeight(centers[i], candidate); } return difference; } // Reassign views if they're more similar to the new canonical view. void CanonicalViewsClustering::UpdateCanonicalViewAssignments( const int canonical_view) { const IntSet& neighbors = graph_->Neighbors(canonical_view); for (IntSet::const_iterator neighbor = neighbors.begin(); neighbor != neighbors.end(); ++neighbor) { const double old_similarity = FindWithDefault(view_to_canonical_view_similarity_, *neighbor, 0.0); const double new_similarity = graph_->EdgeWeight(*neighbor, canonical_view); if (new_similarity > old_similarity) { view_to_canonical_view_[*neighbor] = canonical_view; view_to_canonical_view_similarity_[*neighbor] = new_similarity; } } } // Assign a cluster id to each view. void CanonicalViewsClustering::ComputeClusterMembership( const vector<int>& centers, IntMap* membership) const { CHECK_NOTNULL(membership)->clear(); // The i^th cluster has cluster id i. IntMap center_to_cluster_id; for (int i = 0; i < centers.size(); ++i) { center_to_cluster_id[centers[i]] = i; } static const int kInvalidClusterId = -1; const IntSet& views = graph_->vertices(); for (IntSet::const_iterator view = views.begin(); view != views.end(); ++view) { IntMap::const_iterator it = view_to_canonical_view_.find(*view); int cluster_id = kInvalidClusterId; if (it != view_to_canonical_view_.end()) { cluster_id = FindOrDie(center_to_cluster_id, it->second); } InsertOrDie(membership, *view, cluster_id); } } } // namespace internal } // namespace ceres #endif // CERES_NO_SUITESPARSE