332 lines
10 KiB
Cython
332 lines
10 KiB
Cython
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# Author: Peter Prettenhofer <peter.prettenhofer@gmail.com>
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# Olivier Grisel <olivier.grisel@ensta.org>
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# Lars Buitinck
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#
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# License: BSD 3 clause
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import numpy as np
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from cython cimport floating
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from cython.parallel cimport prange
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from libc.math cimport sqrt
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from ..utils.extmath import row_norms
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# Number of samples per data chunk defined as a global constant.
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CHUNK_SIZE = 256
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cdef floating _euclidean_dense_dense(
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const floating* a, # IN
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const floating* b, # IN
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int n_features,
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bint squared
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) noexcept nogil:
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"""Euclidean distance between a dense and b dense"""
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cdef:
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int i
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int n = n_features // 4
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int rem = n_features % 4
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floating result = 0
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# We manually unroll the loop for better cache optimization.
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for i in range(n):
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result += (
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(a[0] - b[0]) * (a[0] - b[0]) +
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(a[1] - b[1]) * (a[1] - b[1]) +
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(a[2] - b[2]) * (a[2] - b[2]) +
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(a[3] - b[3]) * (a[3] - b[3])
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)
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a += 4
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b += 4
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for i in range(rem):
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result += (a[i] - b[i]) * (a[i] - b[i])
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return result if squared else sqrt(result)
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def _euclidean_dense_dense_wrapper(
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const floating[::1] a,
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const floating[::1] b,
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bint squared
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):
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"""Wrapper of _euclidean_dense_dense for testing purpose"""
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return _euclidean_dense_dense(&a[0], &b[0], a.shape[0], squared)
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cdef floating _euclidean_sparse_dense(
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const floating[::1] a_data, # IN
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const int[::1] a_indices, # IN
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const floating[::1] b, # IN
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floating b_squared_norm,
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bint squared
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) noexcept nogil:
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"""Euclidean distance between a sparse and b dense"""
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cdef:
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int nnz = a_indices.shape[0]
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int i
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floating tmp, bi
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floating result = 0.0
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for i in range(nnz):
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bi = b[a_indices[i]]
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tmp = a_data[i] - bi
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result += tmp * tmp - bi * bi
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result += b_squared_norm
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if result < 0:
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result = 0.0
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return result if squared else sqrt(result)
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def _euclidean_sparse_dense_wrapper(
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const floating[::1] a_data,
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const int[::1] a_indices,
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const floating[::1] b,
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floating b_squared_norm,
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bint squared
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):
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"""Wrapper of _euclidean_sparse_dense for testing purpose"""
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return _euclidean_sparse_dense(
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a_data, a_indices, b, b_squared_norm, squared)
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cpdef floating _inertia_dense(
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const floating[:, ::1] X, # IN
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const floating[::1] sample_weight, # IN
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const floating[:, ::1] centers, # IN
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const int[::1] labels, # IN
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int n_threads,
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int single_label=-1,
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):
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"""Compute inertia for dense input data
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Sum of squared distance between each sample and its assigned center.
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If single_label is >= 0, the inertia is computed only for that label.
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"""
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cdef:
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int n_samples = X.shape[0]
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int n_features = X.shape[1]
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int i, j
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floating sq_dist = 0.0
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floating inertia = 0.0
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for i in prange(n_samples, nogil=True, num_threads=n_threads,
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schedule='static'):
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j = labels[i]
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if single_label < 0 or single_label == j:
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sq_dist = _euclidean_dense_dense(&X[i, 0], ¢ers[j, 0],
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n_features, True)
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inertia += sq_dist * sample_weight[i]
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return inertia
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cpdef floating _inertia_sparse(
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X, # IN
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const floating[::1] sample_weight, # IN
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const floating[:, ::1] centers, # IN
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const int[::1] labels, # IN
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int n_threads,
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int single_label=-1,
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):
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"""Compute inertia for sparse input data
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Sum of squared distance between each sample and its assigned center.
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If single_label is >= 0, the inertia is computed only for that label.
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"""
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cdef:
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floating[::1] X_data = X.data
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int[::1] X_indices = X.indices
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int[::1] X_indptr = X.indptr
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int n_samples = X.shape[0]
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int i, j
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floating sq_dist = 0.0
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floating inertia = 0.0
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floating[::1] centers_squared_norms = row_norms(centers, squared=True)
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for i in prange(n_samples, nogil=True, num_threads=n_threads,
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schedule='static'):
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j = labels[i]
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if single_label < 0 or single_label == j:
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sq_dist = _euclidean_sparse_dense(
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X_data[X_indptr[i]: X_indptr[i + 1]],
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X_indices[X_indptr[i]: X_indptr[i + 1]],
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centers[j], centers_squared_norms[j], True)
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inertia += sq_dist * sample_weight[i]
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return inertia
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cpdef void _relocate_empty_clusters_dense(
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const floating[:, ::1] X, # IN
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const floating[::1] sample_weight, # IN
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const floating[:, ::1] centers_old, # IN
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floating[:, ::1] centers_new, # INOUT
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floating[::1] weight_in_clusters, # INOUT
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const int[::1] labels # IN
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):
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"""Relocate centers which have no sample assigned to them."""
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cdef:
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int[::1] empty_clusters = np.where(np.equal(weight_in_clusters, 0))[0].astype(np.int32)
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int n_empty = empty_clusters.shape[0]
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if n_empty == 0:
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return
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cdef:
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int n_features = X.shape[1]
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floating[::1] distances = ((np.asarray(X) - np.asarray(centers_old)[labels])**2).sum(axis=1)
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int[::1] far_from_centers = np.argpartition(distances, -n_empty)[:-n_empty-1:-1].astype(np.int32)
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int new_cluster_id, old_cluster_id, far_idx, idx, k
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floating weight
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if np.max(distances) == 0:
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# Happens when there are more clusters than non-duplicate samples. Relocating
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# is pointless in this case.
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return
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for idx in range(n_empty):
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new_cluster_id = empty_clusters[idx]
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far_idx = far_from_centers[idx]
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weight = sample_weight[far_idx]
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old_cluster_id = labels[far_idx]
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for k in range(n_features):
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centers_new[old_cluster_id, k] -= X[far_idx, k] * weight
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centers_new[new_cluster_id, k] = X[far_idx, k] * weight
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weight_in_clusters[new_cluster_id] = weight
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weight_in_clusters[old_cluster_id] -= weight
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cpdef void _relocate_empty_clusters_sparse(
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const floating[::1] X_data, # IN
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const int[::1] X_indices, # IN
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const int[::1] X_indptr, # IN
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const floating[::1] sample_weight, # IN
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const floating[:, ::1] centers_old, # IN
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floating[:, ::1] centers_new, # INOUT
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floating[::1] weight_in_clusters, # INOUT
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const int[::1] labels # IN
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):
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"""Relocate centers which have no sample assigned to them."""
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cdef:
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int[::1] empty_clusters = np.where(np.equal(weight_in_clusters, 0))[0].astype(np.int32)
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int n_empty = empty_clusters.shape[0]
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if n_empty == 0:
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return
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cdef:
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int n_samples = X_indptr.shape[0] - 1
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int i, j, k
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floating[::1] distances = np.zeros(n_samples, dtype=X_data.base.dtype)
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floating[::1] centers_squared_norms = row_norms(centers_old, squared=True)
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for i in range(n_samples):
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j = labels[i]
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distances[i] = _euclidean_sparse_dense(
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X_data[X_indptr[i]: X_indptr[i + 1]],
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X_indices[X_indptr[i]: X_indptr[i + 1]],
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centers_old[j], centers_squared_norms[j], True)
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if np.max(distances) == 0:
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# Happens when there are more clusters than non-duplicate samples. Relocating
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# is pointless in this case.
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return
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cdef:
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int[::1] far_from_centers = np.argpartition(distances, -n_empty)[:-n_empty-1:-1].astype(np.int32)
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int new_cluster_id, old_cluster_id, far_idx, idx
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floating weight
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for idx in range(n_empty):
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new_cluster_id = empty_clusters[idx]
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far_idx = far_from_centers[idx]
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weight = sample_weight[far_idx]
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old_cluster_id = labels[far_idx]
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for k in range(X_indptr[far_idx], X_indptr[far_idx + 1]):
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centers_new[old_cluster_id, X_indices[k]] -= X_data[k] * weight
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centers_new[new_cluster_id, X_indices[k]] = X_data[k] * weight
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weight_in_clusters[new_cluster_id] = weight
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weight_in_clusters[old_cluster_id] -= weight
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cdef void _average_centers(
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floating[:, ::1] centers, # INOUT
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const floating[::1] weight_in_clusters # IN
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):
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"""Average new centers wrt weights."""
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cdef:
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int n_clusters = centers.shape[0]
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int n_features = centers.shape[1]
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int j, k
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floating alpha
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int argmax_weight = np.argmax(weight_in_clusters)
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for j in range(n_clusters):
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if weight_in_clusters[j] > 0:
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alpha = 1.0 / weight_in_clusters[j]
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for k in range(n_features):
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centers[j, k] *= alpha
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else:
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# For convenience, we avoid setting empty clusters at the origin but place
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# them at the location of the biggest cluster.
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for k in range(n_features):
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centers[j, k] = centers[argmax_weight, k]
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cdef void _center_shift(
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const floating[:, ::1] centers_old, # IN
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const floating[:, ::1] centers_new, # IN
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floating[::1] center_shift # OUT
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):
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"""Compute shift between old and new centers."""
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cdef:
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int n_clusters = centers_old.shape[0]
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int n_features = centers_old.shape[1]
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int j
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for j in range(n_clusters):
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center_shift[j] = _euclidean_dense_dense(
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¢ers_new[j, 0], ¢ers_old[j, 0], n_features, False)
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def _is_same_clustering(
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const int[::1] labels1,
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const int[::1] labels2,
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n_clusters
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):
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"""Check if two arrays of labels are the same up to a permutation of the labels"""
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cdef int[::1] mapping = np.full(fill_value=-1, shape=(n_clusters,), dtype=np.int32)
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cdef int i
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for i in range(labels1.shape[0]):
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if mapping[labels1[i]] == -1:
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mapping[labels1[i]] = labels2[i]
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elif mapping[labels1[i]] != labels2[i]:
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return False
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return True
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