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# Author: Andreas Mueller # # Licence: BSD 3 clause from cython cimport floating from cython.parallel import prange, parallel from libc.stdlib cimport calloc, free from libc.string cimport memset from ..utils._openmp_helpers cimport omp_lock_t from ..utils._openmp_helpers cimport omp_init_lock from ..utils._openmp_helpers cimport omp_destroy_lock from ..utils._openmp_helpers cimport omp_set_lock from ..utils._openmp_helpers cimport omp_unset_lock from ..utils.extmath import row_norms from ._k_means_common import CHUNK_SIZE from ._k_means_common cimport _relocate_empty_clusters_dense from ._k_means_common cimport _relocate_empty_clusters_sparse from ._k_means_common cimport _euclidean_dense_dense from ._k_means_common cimport _euclidean_sparse_dense from ._k_means_common cimport _average_centers from ._k_means_common cimport _center_shift def init_bounds_dense( const floating[:, ::1] X, # IN const floating[:, ::1] centers, # IN const floating[:, ::1] center_half_distances, # IN int[::1] labels, # OUT floating[::1] upper_bounds, # OUT floating[:, ::1] lower_bounds, # OUT int n_threads): """Initialize upper and lower bounds for each sample for dense input data. Given X, centers and the pairwise distances divided by 2.0 between the centers this calculates the upper bounds and lower bounds for each sample. The upper bound for each sample is set to the distance between the sample and the closest center. The lower bound for each sample is a one-dimensional array of n_clusters. For each sample i assume that the previously assigned cluster is c1 and the previous closest distance is dist, for a new cluster c2, the lower_bound[i][c2] is set to distance between the sample and this new cluster, if and only if dist > center_half_distances[c1][c2]. This prevents computation of unnecessary distances for each sample to the clusters that it is unlikely to be assigned to. Parameters ---------- X : ndarray of shape (n_samples, n_features), dtype=floating The input data. centers : ndarray of shape (n_clusters, n_features), dtype=floating The cluster centers. center_half_distances : ndarray of shape (n_clusters, n_clusters), \ dtype=floating The half of the distance between any 2 clusters centers. labels : ndarray of shape(n_samples), dtype=int The label for each sample. This array is modified in place. upper_bounds : ndarray of shape(n_samples,), dtype=floating The upper bound on the distance between each sample and its closest cluster center. This array is modified in place. lower_bounds : ndarray, of shape(n_samples, n_clusters), dtype=floating The lower bound on the distance between each sample and each cluster center. This array is modified in place. n_threads : int The number of threads to be used by openmp. """ cdef: int n_samples = X.shape[0] int n_clusters = centers.shape[0] int n_features = X.shape[1] floating min_dist, dist int best_cluster, i, j for i in prange( n_samples, num_threads=n_threads, schedule='static', nogil=True ): best_cluster = 0 min_dist = _euclidean_dense_dense(&X[i, 0], &centers[0, 0], n_features, False) lower_bounds[i, 0] = min_dist for j in range(1, n_clusters): if min_dist > center_half_distances[best_cluster, j]: dist = _euclidean_dense_dense(&X[i, 0], &centers[j, 0], n_features, False) lower_bounds[i, j] = dist if dist < min_dist: min_dist = dist best_cluster = j labels[i] = best_cluster upper_bounds[i] = min_dist def init_bounds_sparse( X, # IN const floating[:, ::1] centers, # IN const floating[:, ::1] center_half_distances, # IN int[::1] labels, # OUT floating[::1] upper_bounds, # OUT floating[:, ::1] lower_bounds, # OUT int n_threads): """Initialize upper and lower bounds for each sample for sparse input data. Given X, centers and the pairwise distances divided by 2.0 between the centers this calculates the upper bounds and lower bounds for each sample. The upper bound for each sample is set to the distance between the sample and the closest center. The lower bound for each sample is a one-dimensional array of n_clusters. For each sample i assume that the previously assigned cluster is c1 and the previous closest distance is dist, for a new cluster c2, the lower_bound[i][c2] is set to distance between the sample and this new cluster, if and only if dist > center_half_distances[c1][c2]. This prevents computation of unnecessary distances for each sample to the clusters that it is unlikely to be assigned to. Parameters ---------- X : sparse matrix of shape (n_samples, n_features), dtype=floating The input data. Must be in CSR format. centers : ndarray of shape (n_clusters, n_features), dtype=floating The cluster centers. center_half_distances : ndarray of shape (n_clusters, n_clusters), \ dtype=floating The half of the distance between any 2 clusters centers. labels : ndarray of shape(n_samples), dtype=int The label for each sample. This array is modified in place. upper_bounds : ndarray of shape(n_samples,), dtype=floating The upper bound on the distance between each sample and its closest cluster center. This array is modified in place. lower_bounds : ndarray of shape(n_samples, n_clusters), dtype=floating The lower bound on the distance between each sample and each cluster center. This array is modified in place. n_threads : int The number of threads to be used by openmp. """ cdef: int n_samples = X.shape[0] int n_clusters = centers.shape[0] floating[::1] X_data = X.data int[::1] X_indices = X.indices int[::1] X_indptr = X.indptr floating min_dist, dist int best_cluster, i, j floating[::1] centers_squared_norms = row_norms(centers, squared=True) for i in prange( n_samples, num_threads=n_threads, schedule='static', nogil=True ): best_cluster = 0 min_dist = _euclidean_sparse_dense( X_data[X_indptr[i]: X_indptr[i + 1]], X_indices[X_indptr[i]: X_indptr[i + 1]], centers[0], centers_squared_norms[0], False) lower_bounds[i, 0] = min_dist for j in range(1, n_clusters): if min_dist > center_half_distances[best_cluster, j]: dist = _euclidean_sparse_dense( X_data[X_indptr[i]: X_indptr[i + 1]], X_indices[X_indptr[i]: X_indptr[i + 1]], centers[j], centers_squared_norms[j], False) lower_bounds[i, j] = dist if dist < min_dist: min_dist = dist best_cluster = j labels[i] = best_cluster upper_bounds[i] = min_dist def elkan_iter_chunked_dense( const floating[:, ::1] X, # IN const floating[::1] sample_weight, # IN const floating[:, ::1] centers_old, # IN floating[:, ::1] centers_new, # OUT floating[::1] weight_in_clusters, # OUT const floating[:, ::1] center_half_distances, # IN const floating[::1] distance_next_center, # IN floating[::1] upper_bounds, # INOUT floating[:, ::1] lower_bounds, # INOUT int[::1] labels, # INOUT floating[::1] center_shift, # OUT int n_threads, bint update_centers=True): """Single iteration of K-means Elkan algorithm with dense input. Update labels and centers (inplace), for one iteration, distributed over data chunks. Parameters ---------- X : ndarray of shape (n_samples, n_features), dtype=floating The observations to cluster. sample_weight : ndarray of shape (n_samples,), dtype=floating The weights for each observation in X. centers_old : ndarray of shape (n_clusters, n_features), dtype=floating Centers before previous iteration, placeholder for the centers after previous iteration. centers_new : ndarray of shape (n_clusters, n_features), dtype=floating Centers after previous iteration, placeholder for the new centers computed during this iteration. weight_in_clusters : ndarray of shape (n_clusters,), dtype=floating Placeholder for the sums of the weights of every observation assigned to each center. center_half_distances : ndarray of shape (n_clusters, n_clusters), \ dtype=floating Half pairwise distances between centers. distance_next_center : ndarray of shape (n_clusters,), dtype=floating Distance between each center its closest center. upper_bounds : ndarray of shape (n_samples,), dtype=floating Upper bound for the distance between each sample and its center, updated inplace. lower_bounds : ndarray of shape (n_samples, n_clusters), dtype=floating Lower bound for the distance between each sample and each center, updated inplace. labels : ndarray of shape (n_samples,), dtype=int labels assignment. center_shift : ndarray of shape (n_clusters,), dtype=floating Distance between old and new centers. n_threads : int The number of threads to be used by openmp. update_centers : bool - If True, the labels and the new centers will be computed, i.e. runs the E-step and the M-step of the algorithm. - If False, only the labels will be computed, i.e runs the E-step of the algorithm. This is useful especially when calling predict on a fitted model. """ cdef: int n_samples = X.shape[0] int n_features = X.shape[1] int n_clusters = centers_new.shape[0] if n_samples == 0: # An empty array was passed, do nothing and return early (before # attempting to compute n_chunks). This can typically happen when # calling the prediction function of a bisecting k-means model with a # large fraction of outiers. return cdef: # hard-coded number of samples per chunk. Splitting in chunks is # necessary to get parallelism. Chunk size chosen to be same as lloyd's int n_samples_chunk = CHUNK_SIZE if n_samples > CHUNK_SIZE else n_samples int n_chunks = n_samples // n_samples_chunk int n_samples_rem = n_samples % n_samples_chunk int chunk_idx int start, end int i, j, k floating centers_new_chunk floating weight_in_clusters_chunk omp_lock_t lock # count remainder chunk in total number of chunks n_chunks += n_samples != n_chunks * n_samples_chunk # number of threads should not be bigger than number of chunks n_threads = min(n_threads, n_chunks) if update_centers: memset(&centers_new[0, 0], 0, n_clusters * n_features * sizeof(floating)) memset(&weight_in_clusters[0], 0, n_clusters * sizeof(floating)) omp_init_lock(&lock) with nogil, parallel(num_threads=n_threads): # thread local buffers centers_new_chunk = <floating> calloc(n_clusters n_features, sizeof(floating)) weight_in_clusters_chunk = <floating> calloc(n_clusters, sizeof(floating)) for chunk_idx in prange(n_chunks, schedule='static'): start = chunk_idx n_samples_chunk if chunk_idx == n_chunks - 1 and n_samples_rem > 0: end = start + n_samples_rem else: end = start + n_samples_chunk _update_chunk_dense( X[start: end], sample_weight[start: end], centers_old, center_half_distances, distance_next_center, labels[start: end], upper_bounds[start: end], lower_bounds[start: end], centers_new_chunk, weight_in_clusters_chunk, update_centers) # reduction from local buffers. if update_centers: # The lock is necessary to avoid race conditions when aggregating # info from different thread-local buffers. omp_set_lock(&lock) for j in range(n_clusters): weight_in_clusters[j] += weight_in_clusters_chunk[j] for k in range(n_features): centers_new[j, k] += centers_new_chunk[j * n_features + k] omp_unset_lock(&lock) free(centers_new_chunk) free(weight_in_clusters_chunk) if update_centers: omp_destroy_lock(&lock) _relocate_empty_clusters_dense(X, sample_weight, centers_old, centers_new, weight_in_clusters, labels) _average_centers(centers_new, weight_in_clusters) _center_shift(centers_old, centers_new, center_shift) # update lower and upper bounds for i in range(n_samples): upper_bounds[i] += center_shift[labels[i]] for j in range(n_clusters): lower_bounds[i, j] -= center_shift[j] if lower_bounds[i, j] < 0: lower_bounds[i, j] = 0 cdef void _update_chunk_dense( const floating[:, ::1] X, # IN const floating[::1] sample_weight, # IN const floating[:, ::1] centers_old, # IN const floating[:, ::1] center_half_distances, # IN const floating[::1] distance_next_center, # IN int[::1] labels, # INOUT floating[::1] upper_bounds, # INOUT floating[:, ::1] lower_bounds, # INOUT floating centers_new, # OUT floating weight_in_clusters, # OUT bint update_centers) noexcept nogil: """K-means combined EM step for one dense data chunk. Compute the partial contribution of a single data chunk to the labels and centers. """ cdef: int n_samples = labels.shape[0] int n_clusters = centers_old.shape[0] int n_features = centers_old.shape[1] floating upper_bound, distance int i, j, k, label for i in range(n_samples): upper_bound = upper_bounds[i] bounds_tight = 0 label = labels[i] # Next center is not far away from the currently assigned center. # Sample might need to be assigned to another center. if not distance_next_center[label] >= upper_bound: for j in range(n_clusters): # If this holds, then center_index is a good candidate for the # sample to be relabelled, and we need to confirm this by # recomputing the upper and lower bounds. if ( j != label and (upper_bound > lower_bounds[i, j]) and (upper_bound > center_half_distances[label, j]) ): # Recompute upper bound by calculating the actual distance # between the sample and its current assigned center. if not bounds_tight: upper_bound = _euclidean_dense_dense( &X[i, 0], &centers_old[label, 0], n_features, False) lower_bounds[i, label] = upper_bound bounds_tight = 1 # If the condition still holds, then compute the actual # distance between the sample and center. If this is less # than the previous distance, reassign label. if ( upper_bound > lower_bounds[i, j] or (upper_bound > center_half_distances[label, j]) ): distance = _euclidean_dense_dense( &X[i, 0], &centers_old[j, 0], n_features, False) lower_bounds[i, j] = distance if distance < upper_bound: label = j upper_bound = distance labels[i] = label upper_bounds[i] = upper_bound if update_centers: weight_in_clusters[label] += sample_weight[i] for k in range(n_features): centers_new[label * n_features + k] += X[i, k] * sample_weight[i] def elkan_iter_chunked_sparse( X, # IN const floating[::1] sample_weight, # IN const floating[:, ::1] centers_old, # IN floating[:, ::1] centers_new, # OUT floating[::1] weight_in_clusters, # OUT const floating[:, ::1] center_half_distances, # IN const floating[::1] distance_next_center, # IN floating[::1] upper_bounds, # INOUT floating[:, ::1] lower_bounds, # INOUT int[::1] labels, # INOUT floating[::1] center_shift, # OUT int n_threads, bint update_centers=True): """Single iteration of K-means Elkan algorithm with sparse input. Update labels and centers (inplace), for one iteration, distributed over data chunks. Parameters ---------- X : sparse matrix of shape (n_samples, n_features) The observations to cluster. Must be in CSR format. sample_weight : ndarray of shape (n_samples,), dtype=floating The weights for each observation in X. centers_old : ndarray of shape (n_clusters, n_features), dtype=floating Centers before previous iteration, placeholder for the centers after previous iteration. centers_new : ndarray of shape (n_clusters, n_features), dtype=floating Centers after previous iteration, placeholder for the new centers computed during this iteration. weight_in_clusters : ndarray of shape (n_clusters,), dtype=floating Placeholder for the sums of the weights of every observation assigned to each center. center_half_distances : ndarray of shape (n_clusters, n_clusters), \ dtype=floating Half pairwise distances between centers. distance_next_center : ndarray of shape (n_clusters,), dtype=floating Distance between each center its closest center. upper_bounds : ndarray of shape (n_samples,), dtype=floating Upper bound for the distance between each sample and its center, updated inplace. lower_bounds : ndarray of shape (n_samples, n_clusters), dtype=floating Lower bound for the distance between each sample and each center, updated inplace. labels : ndarray of shape (n_samples,), dtype=int labels assignment. center_shift : ndarray of shape (n_clusters,), dtype=floating Distance between old and new centers. n_threads : int The number of threads to be used by openmp. update_centers : bool - If True, the labels and the new centers will be computed, i.e. runs the E-step and the M-step of the algorithm. - If False, only the labels will be computed, i.e runs the E-step of the algorithm. This is useful especially when calling predict on a fitted model. """ cdef: int n_samples = X.shape[0] int n_features = X.shape[1] int n_clusters = centers_new.shape[0] if n_samples == 0: # An empty array was passed, do nothing and return early (before # attempting to compute n_chunks). This can typically happen when # calling the prediction function of a bisecting k-means model with a # large fraction of outiers. return cdef: floating[::1] X_data = X.data int[::1] X_indices = X.indices int[::1] X_indptr = X.indptr # hard-coded number of samples per chunk. Splitting in chunks is # necessary to get parallelism. Chunk size chosen to be same as lloyd's int n_samples_chunk = CHUNK_SIZE if n_samples > CHUNK_SIZE else n_samples int n_chunks = n_samples // n_samples_chunk int n_samples_rem = n_samples % n_samples_chunk int chunk_idx int start, end int i, j, k floating[::1] centers_squared_norms = row_norms(centers_old, squared=True) floating centers_new_chunk floating weight_in_clusters_chunk omp_lock_t lock # count remainder chunk in total number of chunks n_chunks += n_samples != n_chunks * n_samples_chunk # number of threads should not be bigger than number of chunks n_threads = min(n_threads, n_chunks) if update_centers: memset(&centers_new[0, 0], 0, n_clusters * n_features * sizeof(floating)) memset(&weight_in_clusters[0], 0, n_clusters * sizeof(floating)) omp_init_lock(&lock) with nogil, parallel(num_threads=n_threads): # thread local buffers centers_new_chunk = <floating> calloc(n_clusters n_features, sizeof(floating)) weight_in_clusters_chunk = <floating> calloc(n_clusters, sizeof(floating)) for chunk_idx in prange(n_chunks, schedule='static'): start = chunk_idx n_samples_chunk if chunk_idx == n_chunks - 1 and n_samples_rem > 0: end = start + n_samples_rem else: end = start + n_samples_chunk _update_chunk_sparse( X_data[X_indptr[start]: X_indptr[end]], X_indices[X_indptr[start]: X_indptr[end]], X_indptr[start: end+1], sample_weight[start: end], centers_old, centers_squared_norms, center_half_distances, distance_next_center, labels[start: end], upper_bounds[start: end], lower_bounds[start: end], centers_new_chunk, weight_in_clusters_chunk, update_centers) # reduction from local buffers. if update_centers: # The lock is necessary to avoid race conditions when aggregating # info from different thread-local buffers. omp_set_lock(&lock) for j in range(n_clusters): weight_in_clusters[j] += weight_in_clusters_chunk[j] for k in range(n_features): centers_new[j, k] += centers_new_chunk[j * n_features + k] omp_unset_lock(&lock) free(centers_new_chunk) free(weight_in_clusters_chunk) if update_centers: omp_destroy_lock(&lock) _relocate_empty_clusters_sparse( X_data, X_indices, X_indptr, sample_weight, centers_old, centers_new, weight_in_clusters, labels) _average_centers(centers_new, weight_in_clusters) _center_shift(centers_old, centers_new, center_shift) # update lower and upper bounds for i in range(n_samples): upper_bounds[i] += center_shift[labels[i]] for j in range(n_clusters): lower_bounds[i, j] -= center_shift[j] if lower_bounds[i, j] < 0: lower_bounds[i, j] = 0 cdef void _update_chunk_sparse( const floating[::1] X_data, # IN const int[::1] X_indices, # IN const int[::1] X_indptr, # IN const floating[::1] sample_weight, # IN const floating[:, ::1] centers_old, # IN const floating[::1] centers_squared_norms, # IN const floating[:, ::1] center_half_distances, # IN const floating[::1] distance_next_center, # IN int[::1] labels, # INOUT floating[::1] upper_bounds, # INOUT floating[:, ::1] lower_bounds, # INOUT floating centers_new, # OUT floating weight_in_clusters, # OUT bint update_centers) noexcept nogil: """K-means combined EM step for one sparse data chunk. Compute the partial contribution of a single data chunk to the labels and centers. """ cdef: int n_samples = labels.shape[0] int n_clusters = centers_old.shape[0] int n_features = centers_old.shape[1] floating upper_bound, distance int i, j, k, label int s = X_indptr[0] for i in range(n_samples): upper_bound = upper_bounds[i] bounds_tight = 0 label = labels[i] # Next center is not far away from the currently assigned center. # Sample might need to be assigned to another center. if not distance_next_center[label] >= upper_bound: for j in range(n_clusters): # If this holds, then center_index is a good candidate for the # sample to be relabelled, and we need to confirm this by # recomputing the upper and lower bounds. if ( j != label and (upper_bound > lower_bounds[i, j]) and (upper_bound > center_half_distances[label, j]) ): # Recompute upper bound by calculating the actual distance # between the sample and its current assigned center. if not bounds_tight: upper_bound = _euclidean_sparse_dense( X_data[X_indptr[i] - s: X_indptr[i + 1] - s], X_indices[X_indptr[i] - s: X_indptr[i + 1] - s], centers_old[label], centers_squared_norms[label], False) lower_bounds[i, label] = upper_bound bounds_tight = 1 # If the condition still holds, then compute the actual # distance between the sample and center. If this is less # than the previous distance, reassign label. if ( upper_bound > lower_bounds[i, j] or (upper_bound > center_half_distances[label, j]) ): distance = _euclidean_sparse_dense( X_data[X_indptr[i] - s: X_indptr[i + 1] - s], X_indices[X_indptr[i] - s: X_indptr[i + 1] - s], centers_old[j], centers_squared_norms[j], False) lower_bounds[i, j] = distance if distance < upper_bound: label = j upper_bound = distance labels[i] = label upper_bounds[i] = upper_bound if update_centers: weight_in_clusters[label] += sample_weight[i] for k in range(X_indptr[i] - s, X_indptr[i + 1] - s): centers_new[label * n_features + X_indices[k]] += X_data[k] * sample_weight[i]

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