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// tree/cluster-utils.cc // Copyright 2012 Arnab Ghoshal // Copyright 2009-2011 Microsoft Corporation; Saarland University // See ../../COPYING for clarification regarding multiple authors // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED // WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE, // MERCHANTABLITY OR NON-INFRINGEMENT. // See the Apache 2 License for the specific language governing permissions and // limitations under the License. #include <functional> #include <queue> #include <vector> using std::vector; #include "base/kaldi-math.h" #include "util/stl-utils.h" #include "tree/cluster-utils.h" namespace kaldi { typedef uint16 uint_smaller; typedef int16 int_smaller; // ============================================================================ // Some convenience functions used in the clustering routines // ============================================================================ BaseFloat SumClusterableObjf(const std::vector<Clusterable*> &vec) { BaseFloat ans = 0.0; for (size_t i = 0; i < vec.size(); i++) { if (vec[i] != NULL) { BaseFloat objf = vec[i]->Objf(); if (KALDI_ISNAN(objf)) { KALDI_WARN << "SumClusterableObjf, NaN objf"; } else { ans += objf; } } } return ans; } BaseFloat SumClusterableNormalizer(const std::vector<Clusterable*> &vec) { BaseFloat ans = 0.0; for (size_t i = 0; i < vec.size(); i++) { if (vec[i] != NULL) { BaseFloat objf = vec[i]->Normalizer(); if (KALDI_ISNAN(objf)) { KALDI_WARN << "SumClusterableObjf, NaN objf"; } else { ans += objf; } } } return ans; } Clusterable* SumClusterable(const std::vector<Clusterable*> &vec) { Clusterable *ans = NULL; for (size_t i = 0; i < vec.size(); i++) { if (vec[i] != NULL) { if (ans == NULL) ans = vec[i]->Copy(); else ans->Add(*(vec[i])); } } return ans; } void EnsureClusterableVectorNotNull(std::vector<Clusterable*> *stats) { KALDI_ASSERT(stats != NULL); std::vector<Clusterable*>::iterator itr = stats->begin(), end = stats->end(); if (itr == end) return; // Nothing to do. Clusterable *nonNullExample = NULL; for (; itr != end; ++itr) { if (*itr != NULL) { nonNullExample = *itr; break; } } if (nonNullExample == NULL) { KALDI_ERR << "All stats are NULL."; // crash. logic error. } itr = stats->begin(); Clusterable *nonNullExampleCopy = nonNullExample->Copy(); // sets stats to zero. do this just once (on copy) for efficiency. nonNullExampleCopy->SetZero(); for (; itr != end; ++itr) { if (*itr == NULL) { *itr = nonNullExampleCopy->Copy(); } } delete nonNullExampleCopy; } void AddToClusters(const std::vector<Clusterable*> &stats, const std::vector<int32> &assignments, std::vector<Clusterable*> *clusters) { KALDI_ASSERT(assignments.size() == stats.size()); int32 size = stats.size(); if (size == 0) return; // Nothing to do. KALDI_ASSERT(clusters != NULL); int32 max_assignment = *std::max_element(assignments.begin(), assignments.end()); if (static_cast<int32> (clusters->size()) <= max_assignment) clusters->resize(max_assignment + 1, NULL); // extend with NULLs. for (int32 i = 0; i < size; i++) { if (stats[i] != NULL) { if ((*clusters)[assignments[i]] == NULL) (*clusters)[assignments[i]] = stats[i]->Copy(); else (*clusters)[assignments[i]]->Add(*(stats[i])); } } } void AddToClustersOptimized(const std::vector<Clusterable*> &stats, const std::vector<int32> &assignments, const Clusterable &total, std::vector<Clusterable*> *clusters) { #ifdef KALDI_PARANOID // Make sure "total" is actually the sum of stats in "stats". { BaseFloat stats_norm = SumClusterableNormalizer(stats), tot_norm = total.Normalizer(); AssertEqual(stats_norm, tot_norm, 0.01); } #endif KALDI_ASSERT(assignments.size() == stats.size()); int32 size = stats.size(); if (size == 0) return; // Nothing to do. KALDI_ASSERT(clusters != NULL); int32 num_clust = 1 + *std::max_element(assignments.begin(), assignments.end()); if (static_cast<int32> (clusters->size()) < num_clust) clusters->resize(num_clust, NULL); // extend with NULLs. std::vector<int32> num_stats_for_cluster(num_clust, 0); int32 num_total_stats = 0; for (int32 i = 0; i < size; i++) { if (stats[i] != NULL) { num_total_stats++; num_stats_for_cluster[assignments[i]]++; } } if (num_total_stats == 0) return; // Nothing to do. // it will only ever be efficient to subtract for at most one index. int32 subtract_index = -1; for (int32 c = 0; c < num_clust; c++) { if (num_stats_for_cluster[c] > num_total_stats - num_stats_for_cluster[c]) { subtract_index = c; if ((*clusters)[c] == NULL) (*clusters)[c] = total.Copy(); else (*clusters)[c]->Add(total); break; } } for (int32 i = 0; i < size; i++) { if (stats[i] != NULL) { int32 assignment = assignments[i]; if (assignment != (int32) subtract_index) { if ((*clusters)[assignment] == NULL) (*clusters)[assignment] = stats[i]->Copy(); else (*clusters)[assignment]->Add(*(stats[i])); } if (subtract_index != -1 && assignment != subtract_index) (*clusters)[subtract_index]->Sub(*(stats[i])); } } } // ============================================================================ // Bottom-up clustering routines // ============================================================================ class BottomUpClusterer { public: BottomUpClusterer(const std::vector<Clusterable*> &points, BaseFloat max_merge_thresh, int32 min_clust, std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out) : ans_(0.0), points_(points), max_merge_thresh_(max_merge_thresh), min_clust_(min_clust), clusters_(clusters_out != NULL? clusters_out : &tmp_clusters_), assignments_(assignments_out != NULL ? assignments_out : &tmp_assignments_) { nclusters_ = npoints_ = points.size(); dist_vec_.resize((npoints_ * (npoints_ - 1)) / 2); } BaseFloat Cluster(); ~BottomUpClusterer() { DeletePointers(&tmp_clusters_); } private: void Renumber(); void InitializeAssignments(); void SetInitialDistances(); ///< Sets up distances and queue. /// CanMerge returns true if i and j are existing clusters, and the distance /// (negated objf-change) "dist" is accurate (i.e. not outdated). bool CanMerge(int32 i, int32 j, BaseFloat dist); /// Merge j into i and delete j. void MergeClusters(int32 i, int32 j); /// Reconstructs the priority queue from the distances. void ReconstructQueue(); void SetDistance(int32 i, int32 j); BaseFloat& Distance(int32 i, int32 j) { KALDI_ASSERT(i < npoints_ && j < i); return dist_vec_[(i * (i - 1)) / 2 + j]; } BaseFloat ans_; const std::vector<Clusterable*> &points_; BaseFloat max_merge_thresh_; int32 min_clust_; std::vector<Clusterable*> *clusters_; std::vector<int32> *assignments_; std::vector<Clusterable*> tmp_clusters_; std::vector<int32> tmp_assignments_; std::vector<BaseFloat> dist_vec_; int32 nclusters_; int32 npoints_; typedef std::pair<BaseFloat, std::pair<uint_smaller, uint_smaller> > QueueElement; // Priority queue using greater (lowest distances are highest priority). typedef std::priority_queue<QueueElement, std::vector<QueueElement>, std::greater<QueueElement> > QueueType; QueueType queue_; }; BaseFloat BottomUpClusterer::Cluster() { KALDI_VLOG(2) << "Initializing cluster assignments."; InitializeAssignments(); KALDI_VLOG(2) << "Setting initial distances."; SetInitialDistances(); KALDI_VLOG(2) << "Clustering..."; while (nclusters_ > min_clust_ && !queue_.empty()) { std::pair<BaseFloat, std::pair<uint_smaller, uint_smaller> > pr = queue_.top(); BaseFloat dist = pr.first; int32 i = (int32) pr.second.first, j = (int32) pr.second.second; queue_.pop(); if (CanMerge(i, j, dist)) MergeClusters(i, j); } KALDI_VLOG(2) << "Renumbering clusters to contiguous numbers."; Renumber(); return ans_; } void BottomUpClusterer::Renumber() { KALDI_VLOG(2) << "Freeing up distance vector."; { vector<BaseFloat> tmp; tmp.swap(dist_vec_); } // Commented the following out since it was causing the process to take up too // much memory with larger models. While the swap() method of STL types swaps // the data pointers, std::swap() creates a temporary copy. -Arnab // KALDI_VLOG(2) << "Freeing up the queue"; // // first free up memory by getting rid of queue. this is a special trick // // to force STL to free memory. // { // QueueType tmp; // std::swap(tmp, queue_); // } // called after clustering, renumbers to make clusters contiguously // numbered. also processes assignments_ to remove chains of references. KALDI_VLOG(2) << "Creating new copy of non-NULL clusters."; std::vector<uint_smaller> mapping(npoints_, static_cast<uint_smaller> (-1)); // mapping from intermediate to final clusters. std::vector<Clusterable*> new_clusters(nclusters_); int32 clust = 0; for (int32 i = 0; i < npoints_; i++) { if ((*clusters_)[i] != NULL) { KALDI_ASSERT(clust < nclusters_); new_clusters[clust] = (*clusters_)[i]; mapping[i] = clust; clust++; } } KALDI_ASSERT(clust == nclusters_); KALDI_VLOG(2) << "Creating new copy of assignments."; std::vector<int32> new_assignments(npoints_); for (int32 i = 0; i < npoints_; i++) { // now reprocess assignments_. int32 ii = i; while ((*assignments_)[ii] != ii) ii = (*assignments_)[ii]; // follow the chain. KALDI_ASSERT((*clusters_)[ii] != NULL); // cannot have assignment to nonexistent cluster. KALDI_ASSERT(mapping[ii] != static_cast<uint_smaller>(-1)); new_assignments[i] = mapping[ii]; } clusters_->swap(new_clusters); assignments_->swap(new_assignments); } void BottomUpClusterer::InitializeAssignments() { clusters_->resize(npoints_); assignments_->resize(npoints_); for (int32 i = 0; i < npoints_; i++) { // initialize as 1-1 mapping. (*clusters_)[i] = points_[i]->Copy(); (*assignments_)[i] = i; } } void BottomUpClusterer::SetInitialDistances() { for (int32 i = 0; i < npoints_; i++) { for (int32 j = 0; j < i; j++) { BaseFloat dist = (*clusters_)[i]->Distance(*((*clusters_)[j])); dist_vec_[(i * (i - 1)) / 2 + j] = dist; if (dist <= max_merge_thresh_) queue_.push(std::make_pair(dist, std::make_pair(static_cast<uint_smaller>(i), static_cast<uint_smaller>(j)))); } } } bool BottomUpClusterer::CanMerge(int32 i, int32 j, BaseFloat dist) { KALDI_ASSERT(i != j && i < npoints_ && j < npoints_); if ((*clusters_)[i] == NULL || (*clusters_)[j] == NULL) return false; BaseFloat cached_dist = dist_vec_[(i * (i - 1)) / 2 + j]; return (std::fabs(cached_dist - dist) <= 1.0e-05 * std::fabs(dist)); } void BottomUpClusterer::MergeClusters(int32 i, int32 j) { KALDI_ASSERT(i != j && i < npoints_ && j < npoints_); (*clusters_)[i]->Add(*((*clusters_)[j])); delete (*clusters_)[j]; (*clusters_)[j] = NULL; // note that we may have to follow the chain within "assignment_" to get // final assignments. (*assignments_)[j] = i; // subtract negated objective function change, i.e. add objective function // change. ans_ -= dist_vec_[(i * (i - 1)) / 2 + j]; nclusters_--; // Now update "distances". for (int32 k = 0; k < npoints_; k++) { if (k != i && (*clusters_)[k] != NULL) { if (k < i) SetDistance(i, k); // SetDistance requires k < i. else SetDistance(k, i); } } } void BottomUpClusterer::ReconstructQueue() { // empty queue [since there is no clear()] { QueueType tmp; std::swap(tmp, queue_); } for (int32 i = 0; i < npoints_; i++) { if ((*clusters_)[i] != NULL) { for (int32 j = 0; j < i; j++) { if ((*clusters_)[j] != NULL) { BaseFloat dist = dist_vec_[(i * (i - 1)) / 2 + j]; if (dist <= max_merge_thresh_) { queue_.push(std::make_pair(dist, std::make_pair( static_cast<uint_smaller>(i), static_cast<uint_smaller>(j)))); } } } } } } void BottomUpClusterer::SetDistance(int32 i, int32 j) { KALDI_ASSERT(i < npoints_ && j < i && (*clusters_)[i] != NULL && (*clusters_)[j] != NULL); BaseFloat dist = (*clusters_)[i]->Distance(*((*clusters_)[j])); dist_vec_[(i * (i - 1)) / 2 + j] = dist; // set the distance in the array. if (dist < max_merge_thresh_) { queue_.push(std::make_pair(dist, std::make_pair(static_cast<uint_smaller>(i), static_cast<uint_smaller>(j)))); } // every time it's at least twice the maximum possible size. if (queue_.size() >= static_cast<size_t> (npoints_ * npoints_)) { // Control memory use by getting rid of orphaned queue entries ReconstructQueue(); } } BaseFloat ClusterBottomUp(const std::vector<Clusterable*> &points, BaseFloat max_merge_thresh, int32 min_clust, std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out) { KALDI_ASSERT(max_merge_thresh >= 0.0 && min_clust >= 0); KALDI_ASSERT(!ContainsNullPointers(points)); int32 npoints = points.size(); // make sure fits in uint_smaller and does not hit the -1 which is reserved. KALDI_ASSERT(sizeof(uint_smaller)==sizeof(uint32) || npoints < static_cast<int32>(static_cast<uint_smaller>(-1))); KALDI_VLOG(2) << "Initializing clustering object."; BottomUpClusterer bc(points, max_merge_thresh, min_clust, clusters_out, assignments_out); BaseFloat ans = bc.Cluster(); if (clusters_out) KALDI_ASSERT(!ContainsNullPointers(*clusters_out)); return ans; } // ============================================================================ // Compartmentalized bottom-up clustering routines // ============================================================================ struct CompBotClustElem { BaseFloat dist; int32 compartment, point1, point2; CompBotClustElem(BaseFloat d, int32 comp, int32 i, int32 j) : dist(d), compartment(comp), point1(i), point2(j) {} }; bool operator > (const CompBotClustElem &a, const CompBotClustElem &b) { return a.dist > b.dist; } class CompartmentalizedBottomUpClusterer { public: CompartmentalizedBottomUpClusterer( const vector< vector<Clusterable*> > &points, BaseFloat max_merge_thresh, int32 min_clust) : points_(points), max_merge_thresh_(max_merge_thresh), min_clust_(min_clust) { ncompartments_ = points.size(); nclusters_ = 0; npoints_.resize(ncompartments_); for (int32 comp = 0; comp < ncompartments_; comp++) { npoints_[comp] = points[comp].size(); nclusters_ += npoints_[comp]; } } BaseFloat Cluster(vector< vector<Clusterable*> > *clusters_out, vector< vector<int32> > *assignments_out); ~CompartmentalizedBottomUpClusterer() { for (vector< vector<Clusterable*> >::iterator itr = clusters_.begin(), end = clusters_.end(); itr != end; ++itr) DeletePointers(&(*itr)); } private: // Renumbers to make clusters contiguously numbered. Called after clustering. // Also processes assignments_ to remove chains of references. void Renumber(int32 compartment); void InitializeAssignments(); void SetInitialDistances(); ///< Sets up distances and queue. /// CanMerge returns true if i and j are existing clusters, and the distance /// (negated objf-change) "dist" is accurate (i.e. not outdated). bool CanMerge(int32 compartment, int32 i, int32 j, BaseFloat dist); /// Merge j into i and delete j. Returns obj function change. BaseFloat MergeClusters(int32 compartment, int32 i, int32 j); /// Reconstructs the priority queue from the distances. void ReconstructQueue(); void SetDistance(int32 compartment, int32 i, int32 j); const vector< vector<Clusterable*> > &points_; BaseFloat max_merge_thresh_; int32 min_clust_; vector< vector<Clusterable*> > clusters_; vector< vector<int32> > assignments_; vector< vector<BaseFloat> > dist_vec_; int32 ncompartments_, nclusters_; vector<int32> npoints_; // Priority queue using greater (lowest distances are highest priority). typedef std::priority_queue< CompBotClustElem, std::vector<CompBotClustElem>, std::greater<CompBotClustElem> > QueueType; QueueType queue_; }; BaseFloat CompartmentalizedBottomUpClusterer::Cluster( vector< vector<Clusterable*> > *clusters_out, vector< vector<int32> > *assignments_out) { InitializeAssignments(); SetInitialDistances(); BaseFloat total_obj_change = 0; while (nclusters_ > min_clust_ && !queue_.empty()) { CompBotClustElem qelem = queue_.top(); queue_.pop(); if (CanMerge(qelem.compartment, qelem.point1, qelem.point2, qelem.dist)) total_obj_change += MergeClusters(qelem.compartment, qelem.point1, qelem.point2); } for (int32 comp = 0; comp < ncompartments_; comp++) Renumber(comp); if (clusters_out != NULL) clusters_out->swap(clusters_); if (assignments_out != NULL) assignments_out->swap(assignments_); return total_obj_change; } void CompartmentalizedBottomUpClusterer::Renumber(int32 comp) { // first free up memory by getting rid of queue. this is a special trick // to force STL to free memory. { QueueType tmp; std::swap(tmp, queue_); } // First find the number of surviving clusters in the compartment. int32 clusts_in_compartment = 0; for (int32 i = 0; i < npoints_[comp]; i++) { if (clusters_[comp][i] != NULL) clusts_in_compartment++; } KALDI_ASSERT(clusts_in_compartment <= nclusters_); // mapping from intermediate to final clusters. vector<uint_smaller> mapping(npoints_[comp], static_cast<uint_smaller> (-1)); vector<Clusterable*> new_clusters(clusts_in_compartment); // Now copy the surviving clusters in a fresh array. clusts_in_compartment = 0; for (int32 i = 0; i < npoints_[comp]; i++) { if (clusters_[comp][i] != NULL) { new_clusters[clusts_in_compartment] = clusters_[comp][i]; mapping[i] = clusts_in_compartment; clusts_in_compartment++; } } // Next, process the assignments. std::vector<int32> new_assignments(npoints_[comp]); for (int32 i = 0; i < npoints_[comp]; i++) { int32 ii = i; while (assignments_[comp][ii] != ii) ii = assignments_[comp][ii]; // follow the chain. // cannot assign to nonexistent cluster. KALDI_ASSERT(clusters_[comp][ii] != NULL); KALDI_ASSERT(mapping[ii] != static_cast<uint_smaller>(-1)); new_assignments[i] = mapping[ii]; } clusters_[comp].swap(new_clusters); assignments_[comp].swap(new_assignments); } void CompartmentalizedBottomUpClusterer::InitializeAssignments() { clusters_.resize(ncompartments_); assignments_.resize(ncompartments_); for (int32 comp = 0; comp < ncompartments_; comp++) { clusters_[comp].resize(npoints_[comp]); assignments_[comp].resize(npoints_[comp]); for (int32 i = 0; i < npoints_[comp]; i++) { // initialize as 1-1 mapping. clusters_[comp][i] = points_[comp][i]->Copy(); assignments_[comp][i] = i; } } } void CompartmentalizedBottomUpClusterer::SetInitialDistances() { dist_vec_.resize(ncompartments_); for (int32 comp = 0; comp < ncompartments_; comp++) { dist_vec_[comp].resize((npoints_[comp] * (npoints_[comp] - 1)) / 2); for (int32 i = 0; i < npoints_[comp]; i++) for (int32 j = 0; j < i; j++) SetDistance(comp, i, j); } } bool CompartmentalizedBottomUpClusterer::CanMerge(int32 comp, int32 i, int32 j, BaseFloat dist) { KALDI_ASSERT(comp < ncompartments_ && i < npoints_[comp] && j < i); if (clusters_[comp][i] == NULL || clusters_[comp][j] == NULL) return false; BaseFloat cached_dist = dist_vec_[comp][(i * (i - 1)) / 2 + j]; return (std::fabs(cached_dist - dist) <= 1.0e-05 * std::fabs(dist)); } BaseFloat CompartmentalizedBottomUpClusterer::MergeClusters(int32 comp, int32 i, int32 j) { KALDI_ASSERT(comp < ncompartments_ && i < npoints_[comp] && j < i); clusters_[comp][i]->Add(*(clusters_[comp][j])); delete clusters_[comp][j]; clusters_[comp][j] = NULL; // note that we may have to follow the chain within "assignment_" to get // final assignments. assignments_[comp][j] = i; // objective function change. BaseFloat ans = -dist_vec_[comp][(i * (i - 1)) / 2 + j]; nclusters_--; // Now update "distances". for (int32 k = 0; k < npoints_[comp]; k++) { if (k != i && clusters_[comp][k] != NULL) { if (k < i) SetDistance(comp, i, k); // SetDistance requires k < i. else SetDistance(comp, k, i); } } // Control memory use by getting rid of orphaned queue entries every time // it's at least twice the maximum possible size. if (queue_.size() >= static_cast<size_t> (nclusters_ * nclusters_)) { ReconstructQueue(); } return ans; } void CompartmentalizedBottomUpClusterer::ReconstructQueue() { // empty queue [since there is no clear()] { QueueType tmp; std::swap(tmp, queue_); } for (int32 comp = 0; comp < ncompartments_; comp++) { for (int32 i = 0; i < npoints_[comp]; i++) { if (clusters_[comp][i] == NULL) continue; for (int32 j = 0; j < i; j++) { if (clusters_[comp][j] == NULL) continue; SetDistance(comp, i, j); } } } } void CompartmentalizedBottomUpClusterer::SetDistance(int32 comp, int32 i, int32 j) { KALDI_ASSERT(comp < ncompartments_ && i < npoints_[comp] && j < i); KALDI_ASSERT(clusters_[comp][i] != NULL && clusters_[comp][j] != NULL); BaseFloat dist = clusters_[comp][i]->Distance(*(clusters_[comp][j])); dist_vec_[comp][(i * (i - 1)) / 2 + j] = dist; if (dist < max_merge_thresh_) { queue_.push(CompBotClustElem(dist, comp, static_cast<uint_smaller>(i), static_cast<uint_smaller>(j))); } } BaseFloat ClusterBottomUpCompartmentalized( const std::vector< std::vector<Clusterable*> > &points, BaseFloat thresh, int32 min_clust, std::vector< std::vector<Clusterable*> > *clusters_out, std::vector< std::vector<int32> > *assignments_out) { KALDI_ASSERT(thresh >= 0.0 && min_clust >= 0); int32 npoints = 0, num_non_empty_compartments = 0; for (vector< vector<Clusterable*> >::const_iterator itr = points.begin(), end = points.end(); itr != end; ++itr) { KALDI_ASSERT(!ContainsNullPointers(*itr)); npoints += itr->size(); if (itr->size() > 0) num_non_empty_compartments++; } KALDI_ASSERT(min_clust >= num_non_empty_compartments); // Code does not merge compartments. // make sure fits in uint_smaller and does not hit the -1 which is reserved. KALDI_ASSERT(sizeof(uint_smaller)==sizeof(uint32) || npoints < static_cast<int32>(static_cast<uint_smaller>(-1))); CompartmentalizedBottomUpClusterer bc(points, thresh, min_clust); BaseFloat ans = bc.Cluster(clusters_out, assignments_out); if (clusters_out) { for (vector< vector<Clusterable*> >::iterator itr = clusters_out->begin(), end = clusters_out->end(); itr != end; ++itr) { KALDI_ASSERT(!ContainsNullPointers(*itr)); } } return ans; } // ============================================================================ // Clustering through refinement routines // ============================================================================ class RefineClusterer { public: // size used in point_info structure (we store a lot of these so don't want // to just make it int32). Also used as a time-id (cannot have more moves of // points, than can fit in this time). Must be big enough to store num-clust. typedef int32 LocalInt; typedef uint_smaller ClustIndexInt; RefineClusterer(const std::vector<Clusterable*> &points, std::vector<Clusterable*> *clusters, std::vector<int32> *assignments, RefineClustersOptions cfg) : points_(points), clusters_(clusters), assignments_(assignments), cfg_(cfg) { KALDI_ASSERT(cfg_.top_n >= 2); num_points_ = points_.size(); num_clust_ = static_cast<int32> (clusters->size()); // so can fit clust-id in LocalInt if (cfg_.top_n > (int32) num_clust_) cfg_.top_n = static_cast<int32> (num_clust_); KALDI_ASSERT(cfg_.top_n == static_cast<int32>(static_cast<ClustIndexInt>(cfg_.top_n))); t_ = 0; my_clust_index_.resize(num_points_); // will set all PointInfo's to 0 too (they will be up-to-date). clust_time_.resize(num_clust_, 0); clust_objf_.resize(num_clust_); for (int32 i = 0; i < num_clust_; i++) clust_objf_[i] = (*clusters_)[i]->Objf(); info_.resize(num_points_ * cfg_.top_n); ans_ = 0; InitPoints(); } BaseFloat Refine() { if (cfg_.top_n <= 1) return 0.0; // nothing to do. Iterate(); return ans_; } // at some point check cfg_.top_n > 1 after maxing to num_clust_. private: void InitPoint(int32 point) { // Find closest clusters to this point. // distances are really negated objf changes, ignoring terms that don't vary with the "other" cluster. std::vector<std::pair<BaseFloat, LocalInt> > distances; distances.reserve(num_clust_-1); int32 my_clust = (*assignments_)[point]; Clusterable *point_cl = points_[point]; for (int32 clust = 0;clust < num_clust_;clust++) { if (clust != my_clust) { Clusterable *tmp = (*clusters_)[clust]->Copy(); tmp->Add(*point_cl); BaseFloat other_clust_objf = clust_objf_[clust]; BaseFloat other_clust_plus_me_objf = (*clusters_)[clust]->ObjfPlus(* (points_[point])); BaseFloat distance = other_clust_objf-other_clust_plus_me_objf; // negated delta-objf, with only "varying" terms. distances.push_back(std::make_pair(distance, (LocalInt)clust)); delete tmp; } } if ((cfg_.top_n-1-1) >= 0) { std::nth_element(distances.begin(), distances.begin()+(cfg_.top_n-1-1), distances.end()); } // top_n-1 is the # of elements we want to retain. -1 because we need the iterator // that points to the end of that range (i.e. not potentially off the end of the array). for (int32 index = 0;index < cfg_.top_n-1;index++) { point_info &info = GetInfo(point, index); int32 clust = distances[index].second; info.clust = clust; BaseFloat distance = distances[index].first; BaseFloat other_clust_objf = clust_objf_[clust]; BaseFloat other_clust_plus_me_objf = -(distance - other_clust_objf); info.objf = other_clust_plus_me_objf; info.time = 0; } // now put the last element in, which is my current cluster. point_info &info = GetInfo(point, cfg_.top_n-1); info.clust = my_clust; info.time = 0; info.objf = (*clusters_)[my_clust]->ObjfMinus(*(points_[point])); my_clust_index_[point] = cfg_.top_n-1; } void InitPoints() { // finds, for each point, the closest cfg_.top_n clusters (including its own cluster). // this may be the most time-consuming step of the algorithm. for (int32 p = 0;p < num_points_;p++) InitPoint(p); } void Iterate() { int32 iter, num_iters = cfg_.num_iters; for (iter = 0;iter < num_iters;iter++) { int32 cur_t = t_; for (int32 point = 0;point < num_points_;point++) { if (t_+1 == 0) { KALDI_WARN << "Stopping iterating at int32 moves"; return; // once we use up all time points, must return-- this // should rarely happen as int32 is large. } ProcessPoint(point); } if (t_ == cur_t) break; // nothing changed so we converged. } } void MovePoint(int32 point, int32 new_index) { // move point to a different cluster. t_++; int32 old_index = my_clust_index_[point]; // index into info // array corresponding to current cluster. KALDI_ASSERT(new_index < cfg_.top_n && new_index != old_index); point_info &old_info = GetInfo(point, old_index), &new_info = GetInfo(point, new_index); my_clust_index_[point] = new_index; // update to new index. int32 old_clust = old_info.clust, new_clust = new_info.clust; KALDI_ASSERT( (*assignments_)[point] == old_clust); (*assignments_)[point] = new_clust; (*clusters_)[old_clust]->Sub( *(points_[point]) ); (*clusters_)[new_clust]->Add( *(points_[point]) ); UpdateClust(old_clust); UpdateClust(new_clust); } void UpdateClust(int32 clust) { KALDI_ASSERT(clust < num_clust_); clust_objf_[clust] = (*clusters_)[clust]->Objf(); clust_time_[clust] = t_; } void ProcessPoint(int32 point) { // note: calling code uses the fact // that it only ever increases t_ by one. KALDI_ASSERT(point < num_points_); // (1) Make sure own-cluster like is updated. int32 self_index = my_clust_index_[point]; // index <cfg_.top_n of own cluster. point_info &self_info = GetInfo(point, self_index); int32 self_clust = self_info.clust; // cluster index of own cluster. KALDI_ASSERT(self_index < cfg_.top_n); UpdateInfo(point, self_index); float own_clust_objf = clust_objf_[self_clust]; float own_clust_minus_me_objf = self_info.objf; // objf of own cluster minus self. // Now check the other "close" clusters and see if we want to move there. for (int32 index = 0;index < cfg_.top_n;index++) { if (index != self_index) { UpdateInfo(point, index); point_info &other_info = GetInfo(point, index); BaseFloat other_clust_objf = clust_objf_[other_info.clust]; BaseFloat other_clust_plus_me_objf = other_info.objf; BaseFloat impr = other_clust_plus_me_objf + own_clust_minus_me_objf - other_clust_objf - own_clust_objf; if (impr > 0) { // better to switch... ans_ += impr; MovePoint(point, index); return; // the stuff we precomputed at the top is invalidated now, and it's // easiest just to wait till next time we visit this point. } } } } void UpdateInfo(int32 point, int32 idx) { point_info &pinfo = GetInfo(point, idx); if (pinfo.time < clust_time_[pinfo.clust]) { // it's not up-to-date... Clusterable *tmp_cl = (*clusters_)[pinfo.clust]->Copy(); if (idx == my_clust_index_[point]) { tmp_cl->Sub( *(points_[point]) ); } else{ tmp_cl->Add( *(points_[point]) ); } pinfo.time = t_; pinfo.objf = tmp_cl->Objf(); delete tmp_cl; } } typedef struct { LocalInt clust; LocalInt time; BaseFloat objf; // Objf of this cluster plus this point (or minus, if own cluster). } point_info; point_info &GetInfo(int32 point, int32 idx) { KALDI_ASSERT(point < num_points_ && idx < cfg_.top_n); int32 i = point*cfg_.top_n + idx; KALDI_PARANOID_ASSERT(i < static_cast<int32>(info_.size())); return info_[i]; } const std::vector<Clusterable*> &points_; std::vector<Clusterable*> *clusters_; std::vector<int32> *assignments_; std::vector<point_info> info_; // size is [num_points_ * cfg_.top_n]. std::vector<ClustIndexInt> my_clust_index_; // says for each point, which index 0...cfg_.top_n-1 currently // corresponds to its own cluster. std::vector<LocalInt> clust_time_; // Modification time of cluster. std::vector<BaseFloat> clust_objf_; // [clust], objf for cluster. BaseFloat ans_; // objf improvement. int32 num_clust_; int32 num_points_; int32 t_; RefineClustersOptions cfg_; // note, we change top_n in config; don't make this member a reference member. }; BaseFloat RefineClusters(const std::vector<Clusterable*> &points, std::vector<Clusterable*> *clusters, std::vector<int32> *assignments, RefineClustersOptions cfg) { #ifndef KALDI_PARANOID // don't do this check in "paranoid" mode as we want to expose bugs. if (cfg.num_iters <= 0) { return 0.0; } // nothing to do. #endif KALDI_ASSERT(clusters != NULL && assignments != NULL); KALDI_ASSERT(!ContainsNullPointers(points) && !ContainsNullPointers(*clusters)); RefineClusterer rc(points, clusters, assignments, cfg); BaseFloat ans = rc.Refine(); KALDI_ASSERT(!ContainsNullPointers(*clusters)); return ans; } // ============================================================================ // K-means like clustering routines // ============================================================================ /// ClusterKMeansOnce is called internally by ClusterKMeans; it is equivalent /// to calling ClusterKMeans with cfg.num_tries == 1. It returns the objective /// function improvement versus everything being in one cluster. BaseFloat ClusterKMeansOnce(const std::vector<Clusterable*> &points, int32 num_clust, std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out, ClusterKMeansOptions &cfg) { std::vector<int32> my_assignments; int32 num_points = points.size(); KALDI_ASSERT(clusters_out != NULL); KALDI_ASSERT(num_points != 0); KALDI_ASSERT(num_clust <= num_points); KALDI_ASSERT(clusters_out->empty()); // or we wouldn't know what to do with pointers in there. clusters_out->resize(num_clust, (Clusterable*)NULL); assignments_out->resize(num_points); { // This block assigns points to clusters. // This is done pseudo-randomly using Rand() so that // if we call ClusterKMeans multiple times we get different answers (so we can choose // the best if we want). int32 skip; // randomly choose a "skip" that's coprime to num_points. if (num_points == 1) { skip = 1; } else { skip = 1 + (Rand() % (num_points-1)); // a number between 1 and num_points-1. while (Gcd(skip, num_points) != 1) { // while skip is not coprime to num_points... if (skip == num_points-1) skip = 0; skip++; // skip is now still betweeen 1 and num_points-1. will cycle through // all of 1...num_points-1. } } int32 i, j, count = 0; for (i = 0, j = 0; count != num_points;i = (i+skip)%num_points, j = (j+1)%num_clust, count++) { // i cycles pseudo-randomly through all points; j skips ahead by 1 each time // modulo num_points. // assign point i to cluster j. if ((*clusters_out)[j] == NULL) (*clusters_out)[j] = points[i]->Copy(); else (*clusters_out)[j]->Add(*(points[i])); (*assignments_out)[i] = j; } } BaseFloat normalizer = SumClusterableNormalizer(*clusters_out); BaseFloat ans; { // work out initial value of "ans" (objective function improvement). Clusterable *all_stats = SumClusterable(*clusters_out); ans = SumClusterableObjf(*clusters_out) - all_stats->Objf(); // improvement just from the random // initialization. if (ans < -0.01 && ans < -0.01 * fabs(all_stats->Objf())) { // something bad happend. KALDI_WARN << "ClusterKMeans: objective function after random assignment to clusters is worse than in single cluster: "<< (all_stats->Objf()) << " changed by " << ans << ". Perhaps your stats class has the wrong properties?"; } delete all_stats; } for (int32 iter = 0;iter < cfg.num_iters;iter++) { // Keep refining clusters by reassigning points. BaseFloat objf_before; if (cfg.verbose) objf_before =SumClusterableObjf(*clusters_out); BaseFloat impr = RefineClusters(points, clusters_out, assignments_out, cfg.refine_cfg); BaseFloat objf_after; if (cfg.verbose) objf_after = SumClusterableObjf(*clusters_out); ans += impr; if (cfg.verbose) KALDI_LOG << "ClusterKMeans: on iteration "<<(iter)<<", objf before = "<<(objf_before)<<", impr = "<<(impr)<<", objf after = "<<(objf_after)<<", normalized by "<<(normalizer)<<" = "<<(objf_after/normalizer); if (impr == 0) break; } return ans; } BaseFloat ClusterKMeans(const std::vector<Clusterable*> &points, int32 num_clust, std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out, ClusterKMeansOptions cfg) { if (points.size() == 0) { if (clusters_out) KALDI_ASSERT(clusters_out->empty()); // or we wouldn't know whether to free the pointers. if (assignments_out) assignments_out->clear(); return 0.0; } KALDI_ASSERT(cfg.num_tries>=1 && cfg.num_iters>=1); if (clusters_out) KALDI_ASSERT(clusters_out->empty()); // or we wouldn't know whether to deallocate. if (cfg.num_tries == 1) { std::vector<int32> assignments; return ClusterKMeansOnce(points, num_clust, clusters_out, (assignments_out != NULL?assignments_out:&assignments), cfg); } else { // multiple tries. if (clusters_out) { KALDI_ASSERT(clusters_out->empty()); // we don't know the ownership of any pointers in there, otherwise. } BaseFloat best_ans = 0.0; for (int32 i = 0;i < cfg.num_tries;i++) { std::vector<Clusterable*> clusters_tmp; std::vector<int32> assignments_tmp; BaseFloat ans = ClusterKMeansOnce(points, num_clust, &clusters_tmp, &assignments_tmp, cfg); KALDI_ASSERT(!ContainsNullPointers(clusters_tmp)); if (i == 0 || ans > best_ans) { best_ans = ans; if (clusters_out) { if (clusters_out->size()) DeletePointers(clusters_out); *clusters_out = clusters_tmp; clusters_tmp.clear(); // suppress deletion of pointers. } if (assignments_out) *assignments_out = assignments_tmp; } // delete anything remaining in clusters_tmp (we cleared it if we used // the pointers. DeletePointers(&clusters_tmp); } return best_ans; } } // ============================================================================ // Routines for clustering using a top-down tree // ============================================================================ class TreeClusterer { public: TreeClusterer(const std::vector<Clusterable*> &points, int32 max_clust, TreeClusterOptions cfg): points_(points), max_clust_(max_clust), ans_(0.0), cfg_(cfg) { KALDI_ASSERT(cfg_.branch_factor > 1); Init(); } BaseFloat Cluster(std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out, std::vector<int32> *clust_assignments_out, int32 *num_leaves_out) { while (static_cast<int32>(leaf_nodes_.size()) < max_clust_ && !queue_.empty()) { std::pair<BaseFloat, Node*> pr = queue_.top(); queue_.pop(); ans_ += pr.first; DoSplit(pr.second); } CreateOutput(clusters_out, assignments_out, clust_assignments_out, num_leaves_out); return ans_; } ~TreeClusterer() { for (int32 leaf = 0; leaf < static_cast<int32>(leaf_nodes_.size());leaf++) { delete leaf_nodes_[leaf]->node_total; DeletePointers(&(leaf_nodes_[leaf]->leaf.clusters)); delete leaf_nodes_[leaf]; } for (int32 nonleaf = 0; nonleaf < static_cast<int32>(nonleaf_nodes_.size()); nonleaf++) { delete nonleaf_nodes_[nonleaf]->node_total; delete nonleaf_nodes_[nonleaf]; } } private: struct Node { bool is_leaf; int32 index; // index into leaf_nodes or nonleaf_nodes as applicable. Node *parent; Clusterable *node_total; // sum of all data with this node. struct { std::vector<Clusterable*> points; std::vector<int32> point_indices; BaseFloat best_split; std::vector<Clusterable*> clusters; // [branch_factor]... if we do split. std::vector<int32> assignments; // assignments of points to clusters. } leaf; std::vector<Node*> children; // vector of size branch_factor. if non-leaf. // pointers not owned here but in vectors leaf_nodes_, nonleaf_nodes_. }; void CreateOutput(std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out, std::vector<int32> *clust_assignments_out, int32 *num_leaves_out) { if (num_leaves_out) *num_leaves_out = leaf_nodes_.size(); if (assignments_out) CreateAssignmentsOutput(assignments_out); if (clust_assignments_out) CreateClustAssignmentsOutput(clust_assignments_out); if (clusters_out) CreateClustersOutput(clusters_out); } // This creates the output index corresponding to an index "index" into the array nonleaf_nodes_. // reverse numbering so root node is last. int32 NonleafOutputIndex(int32 index) { return leaf_nodes_.size() + nonleaf_nodes_.size() - 1 - index; } void CreateAssignmentsOutput(std::vector<int32> *assignments_out) { assignments_out->clear(); assignments_out->resize(points_.size(), (int32)(-1)); // fill with -1. for (int32 leaf = 0; leaf < static_cast<int32>(leaf_nodes_.size()); leaf++) { std::vector<int32> &indices = leaf_nodes_[leaf]->leaf.point_indices; for (int32 i = 0; i < static_cast<int32>(indices.size()); i++) { KALDI_ASSERT(static_cast<size_t>(indices[i]) < points_.size()); KALDI_ASSERT((*assignments_out)[indices[i]] == (int32)(-1)); // check we're not assigning twice. (*assignments_out)[indices[i]] = leaf; } } #ifdef KALDI_PARANOID for (size_t i = 0;i<assignments_out->size();i++) KALDI_ASSERT((*assignments_out)[i] != (int32)(-1)); #endif } void CreateClustAssignmentsOutput(std::vector<int32> *clust_assignments_out) { clust_assignments_out->resize(leaf_nodes_.size() + nonleaf_nodes_.size()); for (int32 leaf = 0; leaf < static_cast<int32>(leaf_nodes_.size()); leaf++) { int32 parent_index; if (leaf_nodes_[leaf]->parent == NULL) { // tree with only one node. KALDI_ASSERT(leaf_nodes_.size() == 1&&nonleaf_nodes_.size() == 0 && leaf == 0); parent_index = 0; } else { if (leaf_nodes_[leaf]->parent->is_leaf) parent_index = leaf_nodes_[leaf]->parent->index; else parent_index = NonleafOutputIndex(leaf_nodes_[leaf]->parent->index); } (*clust_assignments_out)[leaf] = parent_index; } for (int32 nonleaf = 0; nonleaf < static_cast<int32>(nonleaf_nodes_.size()); nonleaf++) { int32 index = NonleafOutputIndex(nonleaf); int32 parent_index; if (nonleaf_nodes_[nonleaf]->parent == NULL) parent_index = index; // top node. make it own parent. else { KALDI_ASSERT(! nonleaf_nodes_[nonleaf]->parent->is_leaf); // parent is nonleaf since child is nonleaf. parent_index = NonleafOutputIndex(nonleaf_nodes_[nonleaf]->parent->index); } (*clust_assignments_out)[index] = parent_index; } } void CreateClustersOutput(std::vector<Clusterable*> *clusters_out) { clusters_out->resize(leaf_nodes_.size() + nonleaf_nodes_.size()); for (int32 leaf = 0; leaf < static_cast<int32>(leaf_nodes_.size()); leaf++) { (*clusters_out)[leaf] = leaf_nodes_[leaf]->node_total; leaf_nodes_[leaf]->node_total = NULL; // suppress delete. } for (int32 nonleaf = 0; nonleaf < static_cast<int32>(nonleaf_nodes_.size()); nonleaf++) { int32 index = NonleafOutputIndex(nonleaf); (*clusters_out)[index] = nonleaf_nodes_[nonleaf]->node_total; nonleaf_nodes_[nonleaf]->node_total = NULL; // suppress delete. } } void DoSplit(Node *node) { KALDI_ASSERT(node->is_leaf && node->leaf.best_split > cfg_.thresh*0.999); // 0.999 is to avoid potential floating-point weirdness under compiler optimizations. KALDI_ASSERT(node->children.size() == 0); node->children.resize(cfg_.branch_factor); for (int32 i = 0;i < cfg_.branch_factor;i++) { Node *child = new Node; node->children[i] = child; child->is_leaf = true; child->parent = node; child->node_total = node->leaf.clusters[i]; if (i == 0) { child->index = node->index; // assign node's own index in leaf_nodes_ to 1st child. leaf_nodes_[child->index] = child; } else { child->index = leaf_nodes_.size(); // generate new indices for other children. leaf_nodes_.push_back(child); } } KALDI_ASSERT(node->leaf.assignments.size() == node->leaf.points.size()); KALDI_ASSERT(node->leaf.point_indices.size() == node->leaf.points.size()); for (int32 i = 0; i < static_cast<int32>(node->leaf.points.size()); i++) { int32 child_index = node->leaf.assignments[i]; KALDI_ASSERT(child_index < static_cast<int32>(cfg_.branch_factor)); node->children[child_index]->leaf.points.push_back(node->leaf.points[i]); node->children[child_index]->leaf.point_indices.push_back(node->leaf.point_indices[i]); } node->leaf.points.clear(); node->leaf.point_indices.clear(); node->leaf.clusters.clear(); // already assigned pointers to children. node->leaf.assignments.clear(); node->is_leaf = false; node->index = nonleaf_nodes_.size(); // new index at end of nonleaf_nodes_. nonleaf_nodes_.push_back(node); for (int32 i = 0;i < static_cast<int32>(cfg_.branch_factor);i++) FindBestSplit(node->children[i]); } void FindBestSplit(Node *node) { // takes a leaf node that has just been set up, and does ClusterKMeans with k = cfg_branch_factor. KALDI_ASSERT(node->is_leaf); if (node->leaf.points.size() == 0) { KALDI_WARN << "Warning: tree clustering: leaf with no data"; node->leaf.best_split = 0; return; } if (node->leaf.points.size()<=1) { node->leaf.best_split = 0; return; } else { // use kmeans. BaseFloat impr = ClusterKMeans(node->leaf.points, cfg_.branch_factor, &node->leaf.clusters, &node->leaf.assignments, cfg_.kmeans_cfg); node->leaf.best_split = impr; if (impr > cfg_.thresh) queue_.push(std::make_pair(impr, node)); } } void Init() { // Initializes top node. Node *top_node = new Node; top_node->index = leaf_nodes_.size(); // == 0 currently. top_node->parent = NULL; // no parent since root of tree. top_node->is_leaf = true; leaf_nodes_.push_back(top_node); top_node->leaf.points = points_; top_node->node_total = SumClusterable(points_); top_node->leaf.point_indices.resize(points_.size()); for (size_t i = 0;i<points_.size();i++) top_node->leaf.point_indices[i] = i; FindBestSplit(top_node); // this should always be called when new node is created. } std::vector<Node*> leaf_nodes_; std::vector<Node*> nonleaf_nodes_; const std::vector<Clusterable*> &points_; int32 max_clust_; BaseFloat ans_; // objf improvement. std::priority_queue<std::pair<BaseFloat, Node*> > queue_; // contains leaves. TreeClusterOptions cfg_; }; BaseFloat TreeCluster(const std::vector<Clusterable*> &points, int32 max_clust, // this is a max only. std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out, std::vector<int32> *clust_assignments_out, int32 *num_leaves_out, TreeClusterOptions cfg) { if (points.size() == 0) { if (clusters_out) clusters_out->clear(); if (assignments_out) assignments_out->clear(); if (clust_assignments_out) clust_assignments_out->clear(); if (num_leaves_out) *num_leaves_out = 0; return 0.0; } TreeClusterer tc(points, max_clust, cfg); BaseFloat ans = tc.Cluster(clusters_out, assignments_out, clust_assignments_out, num_leaves_out); if (clusters_out) KALDI_ASSERT(!ContainsNullPointers(*clusters_out)); return ans; } BaseFloat ClusterTopDown(const std::vector<Clusterable*> &points, int32 max_clust, // max # of clusters. std::vector<Clusterable*> *clusters_out, std::vector<int32> *assignments_out, TreeClusterOptions cfg) { int32 num_leaves = 0; BaseFloat ans = TreeCluster(points, max_clust, clusters_out, assignments_out, NULL, &num_leaves, cfg); if (clusters_out != NULL) { for (size_t j = num_leaves;j<clusters_out->size();j++) delete (*clusters_out)[j]; clusters_out->resize(num_leaves); // number of leaf-level clusters in tree. } return ans; } void RefineClustersOptions::Write(std::ostream &os, bool binary) const { WriteToken(os, binary, "<RefineClustersOptions>"); WriteBasicType(os, binary, num_iters); WriteBasicType(os, binary, top_n); WriteToken(os, binary, "</RefineClustersOptions>"); } void RefineClustersOptions::Read(std::istream &is, bool binary) { ExpectToken(is, binary, "<RefineClustersOptions>"); ReadBasicType(is, binary, &num_iters); ReadBasicType(is, binary, &top_n); ExpectToken(is, binary, "</RefineClustersOptions>"); } } // end namespace kaldi. |