"""Hierarchical Agglomerative Clustering These routines perform some hierarchical agglomerative clustering of some input data. Authors : Vincent Michel, Bertrand Thirion, Alexandre Gramfort, Gael Varoquaux License: BSD 3 clause """ # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import warnings from heapq import heapify, heappop, heappush, heappushpop from numbers import Integral, Real import numpy as np from scipy import sparse from scipy.sparse.csgraph import connected_components from ..base import ( BaseEstimator, ClassNamePrefixFeaturesOutMixin, ClusterMixin, _fit_context, ) from ..metrics import DistanceMetric from ..metrics._dist_metrics import METRIC_MAPPING64 from ..metrics.pairwise import _VALID_METRICS, paired_distances from ..utils import check_array from ..utils._fast_dict import IntFloatDict from ..utils._param_validation import ( HasMethods, Interval, StrOptions, validate_params, ) from ..utils.graph import _fix_connected_components from ..utils.validation import check_memory, validate_data # mypy error: Module 'sklearn.cluster' has no attribute '_hierarchical_fast' from . import _hierarchical_fast as _hierarchical # type: ignore from ._feature_agglomeration import AgglomerationTransform ############################################################################### # For non fully-connected graphs def _fix_connectivity(X, connectivity, affinity): """ Fixes the connectivity matrix. The different steps are: - copies it - makes it symmetric - converts it to LIL if necessary - completes it if necessary. Parameters ---------- X : array-like of shape (n_samples, n_features) Feature matrix representing `n_samples` samples to be clustered. connectivity : sparse matrix, default=None Connectivity matrix. Defines for each sample the neighboring samples following a given structure of the data. The matrix is assumed to be symmetric and only the upper triangular half is used. Default is `None`, i.e, the Ward algorithm is unstructured. affinity : {"euclidean", "precomputed"}, default="euclidean" Which affinity to use. At the moment `precomputed` and ``euclidean`` are supported. `euclidean` uses the negative squared Euclidean distance between points. Returns ------- connectivity : sparse matrix The fixed connectivity matrix. n_connected_components : int The number of connected components in the graph. """ n_samples = X.shape[0] if connectivity.shape[0] != n_samples or connectivity.shape[1] != n_samples: raise ValueError( "Wrong shape for connectivity matrix: %s when X is %s" % (connectivity.shape, X.shape) ) # Make the connectivity matrix symmetric: connectivity = connectivity + connectivity.T # Convert connectivity matrix to LIL if not sparse.issparse(connectivity): connectivity = sparse.lil_matrix(connectivity) # `connectivity` is a sparse matrix at this point if connectivity.format != "lil": connectivity = connectivity.tolil() # Compute the number of nodes n_connected_components, labels = connected_components(connectivity) if n_connected_components > 1: warnings.warn( "the number of connected components of the " "connectivity matrix is %d > 1. Completing it to avoid " "stopping the tree early." % n_connected_components, stacklevel=2, ) # XXX: Can we do without completing the matrix? connectivity = _fix_connected_components( X=X, graph=connectivity, n_connected_components=n_connected_components, component_labels=labels, metric=affinity, mode="connectivity", ) return connectivity, n_connected_components def _single_linkage_tree( connectivity, n_samples, n_nodes, n_clusters, n_connected_components, return_distance, ): """ Perform single linkage clustering on sparse data via the minimum spanning tree from scipy.sparse.csgraph, then using union-find to label. The parent array is then generated by walking through the tree. """ from scipy.sparse.csgraph import minimum_spanning_tree # explicitly cast connectivity to ensure safety connectivity = connectivity.astype(np.float64, copy=False) # Ensure zero distances aren't ignored by setting them to "epsilon" epsilon_value = np.finfo(dtype=connectivity.data.dtype).eps connectivity.data[connectivity.data == 0] = epsilon_value # Use scipy.sparse.csgraph to generate a minimum spanning tree mst = minimum_spanning_tree(connectivity.tocsr()) # Convert the graph to scipy.cluster.hierarchy array format mst = mst.tocoo() # Undo the epsilon values mst.data[mst.data == epsilon_value] = 0 mst_array = np.vstack([mst.row, mst.col, mst.data]).T # Sort edges of the min_spanning_tree by weight mst_array = mst_array[np.argsort(mst_array.T[2], kind="mergesort"), :] # Convert edge list into standard hierarchical clustering format single_linkage_tree = _hierarchical._single_linkage_label(mst_array) children_ = single_linkage_tree[:, :2].astype(int) # Compute parents parent = np.arange(n_nodes, dtype=np.intp) for i, (left, right) in enumerate(children_, n_samples): if n_clusters is not None and i >= n_nodes: break if left < n_nodes: parent[left] = i if right < n_nodes: parent[right] = i if return_distance: distances = single_linkage_tree[:, 2] return children_, n_connected_components, n_samples, parent, distances return children_, n_connected_components, n_samples, parent ############################################################################### # Hierarchical tree building functions @validate_params( { "X": ["array-like"], "connectivity": ["array-like", "sparse matrix", None], "n_clusters": [Interval(Integral, 1, None, closed="left"), None], "return_distance": ["boolean"], }, prefer_skip_nested_validation=True, ) def ward_tree(X, *, connectivity=None, n_clusters=None, return_distance=False): """Ward clustering based on a Feature matrix. Recursively merges the pair of clusters that minimally increases within-cluster variance. The inertia matrix uses a Heapq-based representation. This is the structured version, that takes into account some topological structure between samples. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like of shape (n_samples, n_features) Feature matrix representing `n_samples` samples to be clustered. connectivity : {array-like, sparse matrix}, default=None Connectivity matrix. Defines for each sample the neighboring samples following a given structure of the data. The matrix is assumed to be symmetric and only the upper triangular half is used. Default is None, i.e, the Ward algorithm is unstructured. n_clusters : int, default=None `n_clusters` should be less than `n_samples`. Stop early the construction of the tree at `n_clusters.` This is useful to decrease computation time if the number of clusters is not small compared to the number of samples. In this case, the complete tree is not computed, thus the 'children' output is of limited use, and the 'parents' output should rather be used. This option is valid only when specifying a connectivity matrix. return_distance : bool, default=False If `True`, return the distance between the clusters. Returns ------- children : ndarray of shape (n_nodes-1, 2) The children of each non-leaf node. Values less than `n_samples` correspond to leaves of the tree which are the original samples. A node `i` greater than or equal to `n_samples` is a non-leaf node and has children `children_[i - n_samples]`. Alternatively at the i-th iteration, children[i][0] and children[i][1] are merged to form node `n_samples + i`. n_connected_components : int The number of connected components in the graph. n_leaves : int The number of leaves in the tree. parents : ndarray of shape (n_nodes,) or None The parent of each node. Only returned when a connectivity matrix is specified, elsewhere 'None' is returned. distances : ndarray of shape (n_nodes-1,) Only returned if `return_distance` is set to `True` (for compatibility). The distances between the centers of the nodes. `distances[i]` corresponds to a weighted Euclidean distance between the nodes `children[i, 1]` and `children[i, 2]`. If the nodes refer to leaves of the tree, then `distances[i]` is their unweighted Euclidean distance. Distances are updated in the following way (from scipy.hierarchy.linkage): The new entry :math:`d(u,v)` is computed as follows, .. math:: d(u,v) = \\sqrt{\\frac{|v|+|s|} {T}d(v,s)^2 + \\frac{|v|+|t|} {T}d(v,t)^2 - \\frac{|v|} {T}d(s,t)^2} where :math:`u` is the newly joined cluster consisting of clusters :math:`s` and :math:`t`, :math:`v` is an unused cluster in the forest, :math:`T=|v|+|s|+|t|`, and :math:`|*|` is the cardinality of its argument. This is also known as the incremental algorithm. Examples -------- >>> import numpy as np >>> from sklearn.cluster import ward_tree >>> X = np.array([[1, 2], [1, 4], [1, 0], ... [4, 2], [4, 4], [4, 0]]) >>> children, n_connected_components, n_leaves, parents = ward_tree(X) >>> children array([[0, 1], [3, 5], [2, 6], [4, 7], [8, 9]]) >>> n_connected_components 1 >>> n_leaves 6 """ X = np.asarray(X) if X.ndim == 1: X = np.reshape(X, (-1, 1)) n_samples, n_features = X.shape if connectivity is None: from scipy.cluster import hierarchy # imports PIL if n_clusters is not None: warnings.warn( ( "Partial build of the tree is implemented " "only for structured clustering (i.e. with " "explicit connectivity). The algorithm " "will build the full tree and only " "retain the lower branches required " "for the specified number of clusters" ), stacklevel=2, ) X = np.require(X, requirements="W") out = hierarchy.ward(X) children_ = out[:, :2].astype(np.intp) if return_distance: distances = out[:, 2] return children_, 1, n_samples, None, distances else: return children_, 1, n_samples, None connectivity, n_connected_components = _fix_connectivity( X, connectivity, affinity="euclidean" ) if n_clusters is None: n_nodes = 2 * n_samples - 1 else: if n_clusters > n_samples: raise ValueError( "Cannot provide more clusters than samples. " "%i n_clusters was asked, and there are %i " "samples." % (n_clusters, n_samples) ) n_nodes = 2 * n_samples - n_clusters # create inertia matrix coord_row = [] coord_col = [] A = [] for ind, row in enumerate(connectivity.rows): A.append(row) # We keep only the upper triangular for the moments # Generator expressions are faster than arrays on the following row = [i for i in row if i < ind] coord_row.extend( len(row) * [ ind, ] ) coord_col.extend(row) coord_row = np.array(coord_row, dtype=np.intp, order="C") coord_col = np.array(coord_col, dtype=np.intp, order="C") # build moments as a list moments_1 = np.zeros(n_nodes, order="C") moments_1[:n_samples] = 1 moments_2 = np.zeros((n_nodes, n_features), order="C") moments_2[:n_samples] = X inertia = np.empty(len(coord_row), dtype=np.float64, order="C") _hierarchical.compute_ward_dist(moments_1, moments_2, coord_row, coord_col, inertia) inertia = list(zip(inertia, coord_row, coord_col)) heapify(inertia) # prepare the main fields parent = np.arange(n_nodes, dtype=np.intp) used_node = np.ones(n_nodes, dtype=bool) children = [] if return_distance: distances = np.empty(n_nodes - n_samples) not_visited = np.empty(n_nodes, dtype=bool, order="C") # recursive merge loop for k in range(n_samples, n_nodes): # identify the merge while True: inert, i, j = heappop(inertia) if used_node[i] and used_node[j]: break parent[i], parent[j] = k, k children.append((i, j)) used_node[i] = used_node[j] = False if return_distance: # store inertia value distances[k - n_samples] = inert # update the moments moments_1[k] = moments_1[i] + moments_1[j] moments_2[k] = moments_2[i] + moments_2[j] # update the structure matrix A and the inertia matrix coord_col = [] not_visited.fill(1) not_visited[k] = 0 _hierarchical._get_parents(A[i], coord_col, parent, not_visited) _hierarchical._get_parents(A[j], coord_col, parent, not_visited) # List comprehension is faster than a for loop [A[col].append(k) for col in coord_col] A.append(coord_col) coord_col = np.array(coord_col, dtype=np.intp, order="C") coord_row = np.empty(coord_col.shape, dtype=np.intp, order="C") coord_row.fill(k) n_additions = len(coord_row) ini = np.empty(n_additions, dtype=np.float64, order="C") _hierarchical.compute_ward_dist(moments_1, moments_2, coord_row, coord_col, ini) # List comprehension is faster than a for loop [heappush(inertia, (ini[idx], k, coord_col[idx])) for idx in range(n_additions)] # Separate leaves in children (empty lists up to now) n_leaves = n_samples # sort children to get consistent output with unstructured version children = [c[::-1] for c in children] children = np.array(children) # return numpy array for efficient caching if return_distance: # 2 is scaling factor to compare w/ unstructured version distances = np.sqrt(2.0 * distances) return children, n_connected_components, n_leaves, parent, distances else: return children, n_connected_components, n_leaves, parent # single average and complete linkage def linkage_tree( X, connectivity=None, n_clusters=None, linkage="complete", affinity="euclidean", return_distance=False, ): """Linkage agglomerative clustering based on a Feature matrix. The inertia matrix uses a Heapq-based representation. This is the structured version, that takes into account some topological structure between samples. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like of shape (n_samples, n_features) Feature matrix representing `n_samples` samples to be clustered. connectivity : sparse matrix, default=None Connectivity matrix. Defines for each sample the neighboring samples following a given structure of the data. The matrix is assumed to be symmetric and only the upper triangular half is used. Default is `None`, i.e, the Ward algorithm is unstructured. n_clusters : int, default=None Stop early the construction of the tree at `n_clusters`. This is useful to decrease computation time if the number of clusters is not small compared to the number of samples. In this case, the complete tree is not computed, thus the 'children' output is of limited use, and the 'parents' output should rather be used. This option is valid only when specifying a connectivity matrix. linkage : {"average", "complete", "single"}, default="complete" Which linkage criteria to use. The linkage criterion determines which distance to use between sets of observation. - "average" uses the average of the distances of each observation of the two sets. - "complete" or maximum linkage uses the maximum distances between all observations of the two sets. - "single" uses the minimum of the distances between all observations of the two sets. affinity : str or callable, default='euclidean' Which metric to use. Can be 'euclidean', 'manhattan', or any distance known to paired distance (see metric.pairwise). return_distance : bool, default=False Whether or not to return the distances between the clusters. Returns ------- children : ndarray of shape (n_nodes-1, 2) The children of each non-leaf node. Values less than `n_samples` correspond to leaves of the tree which are the original samples. A node `i` greater than or equal to `n_samples` is a non-leaf node and has children `children_[i - n_samples]`. Alternatively at the i-th iteration, children[i][0] and children[i][1] are merged to form node `n_samples + i`. n_connected_components : int The number of connected components in the graph. n_leaves : int The number of leaves in the tree. parents : ndarray of shape (n_nodes, ) or None The parent of each node. Only returned when a connectivity matrix is specified, elsewhere 'None' is returned. distances : ndarray of shape (n_nodes-1,) Returned when `return_distance` is set to `True`. distances[i] refers to the distance between children[i][0] and children[i][1] when they are merged. See Also -------- ward_tree : Hierarchical clustering with ward linkage. """ X = np.asarray(X) if X.ndim == 1: X = np.reshape(X, (-1, 1)) n_samples, n_features = X.shape linkage_choices = { "complete": _hierarchical.max_merge, "average": _hierarchical.average_merge, "single": None, } # Single linkage is handled differently try: join_func = linkage_choices[linkage] except KeyError as e: raise ValueError( "Unknown linkage option, linkage should be one of %s, but %s was given" % (linkage_choices.keys(), linkage) ) from e if affinity == "cosine" and np.any(~np.any(X, axis=1)): raise ValueError("Cosine affinity cannot be used when X contains zero vectors") if connectivity is None: from scipy.cluster import hierarchy # imports PIL if n_clusters is not None: warnings.warn( ( "Partial build of the tree is implemented " "only for structured clustering (i.e. with " "explicit connectivity). The algorithm " "will build the full tree and only " "retain the lower branches required " "for the specified number of clusters" ), stacklevel=2, ) if affinity == "precomputed": # for the linkage function of hierarchy to work on precomputed # data, provide as first argument an ndarray of the shape returned # by sklearn.metrics.pairwise_distances. if X.shape[0] != X.shape[1]: raise ValueError( f"Distance matrix should be square, got matrix of shape {X.shape}" ) i, j = np.triu_indices(X.shape[0], k=1) X = X[i, j] elif affinity == "l2": # Translate to something understood by scipy affinity = "euclidean" elif affinity in ("l1", "manhattan"): affinity = "cityblock" elif callable(affinity): X = affinity(X) i, j = np.triu_indices(X.shape[0], k=1) X = X[i, j] if ( linkage == "single" and affinity != "precomputed" and not callable(affinity) and affinity in METRIC_MAPPING64 ): # We need the fast cythonized metric from neighbors dist_metric = DistanceMetric.get_metric(affinity) # The Cython routines used require contiguous arrays X = np.ascontiguousarray(X, dtype=np.double) mst = _hierarchical.mst_linkage_core(X, dist_metric) # Sort edges of the min_spanning_tree by weight mst = mst[np.argsort(mst.T[2], kind="mergesort"), :] # Convert edge list into standard hierarchical clustering format out = _hierarchical.single_linkage_label(mst) else: out = hierarchy.linkage(X, method=linkage, metric=affinity) children_ = out[:, :2].astype(int, copy=False) if return_distance: distances = out[:, 2] return children_, 1, n_samples, None, distances return children_, 1, n_samples, None connectivity, n_connected_components = _fix_connectivity( X, connectivity, affinity=affinity ) connectivity = connectivity.tocoo() # Put the diagonal to zero diag_mask = connectivity.row != connectivity.col connectivity.row = connectivity.row[diag_mask] connectivity.col = connectivity.col[diag_mask] connectivity.data = connectivity.data[diag_mask] del diag_mask if affinity == "precomputed": distances = X[connectivity.row, connectivity.col].astype(np.float64, copy=False) else: # FIXME We compute all the distances, while we could have only computed # the "interesting" distances distances = paired_distances( X[connectivity.row], X[connectivity.col], metric=affinity ) connectivity.data = distances if n_clusters is None: n_nodes = 2 * n_samples - 1 else: assert n_clusters <= n_samples n_nodes = 2 * n_samples - n_clusters if linkage == "single": return _single_linkage_tree( connectivity, n_samples, n_nodes, n_clusters, n_connected_components, return_distance, ) if return_distance: distances = np.empty(n_nodes - n_samples) # create inertia heap and connection matrix A = np.empty(n_nodes, dtype=object) inertia = list() # LIL seems to the best format to access the rows quickly, # without the numpy overhead of slicing CSR indices and data. connectivity = connectivity.tolil() # We are storing the graph in a list of IntFloatDict for ind, (data, row) in enumerate(zip(connectivity.data, connectivity.rows)): A[ind] = IntFloatDict( np.asarray(row, dtype=np.intp), np.asarray(data, dtype=np.float64) ) # We keep only the upper triangular for the heap # Generator expressions are faster than arrays on the following inertia.extend( _hierarchical.WeightedEdge(d, ind, r) for r, d in zip(row, data) if r < ind ) del connectivity heapify(inertia) # prepare the main fields parent = np.arange(n_nodes, dtype=np.intp) used_node = np.ones(n_nodes, dtype=np.intp) children = [] # recursive merge loop for k in range(n_samples, n_nodes): # identify the merge while True: edge = heappop(inertia) if used_node[edge.a] and used_node[edge.b]: break i = edge.a j = edge.b if return_distance: # store distances distances[k - n_samples] = edge.weight parent[i] = parent[j] = k children.append((i, j)) # Keep track of the number of elements per cluster n_i = used_node[i] n_j = used_node[j] used_node[k] = n_i + n_j used_node[i] = used_node[j] = False # update the structure matrix A and the inertia matrix # a clever 'min', or 'max' operation between A[i] and A[j] coord_col = join_func(A[i], A[j], used_node, n_i, n_j) for col, d in coord_col: A[col].append(k, d) # Here we use the information from coord_col (containing the # distances) to update the heap heappush(inertia, _hierarchical.WeightedEdge(d, k, col)) A[k] = coord_col # Clear A[i] and A[j] to save memory A[i] = A[j] = 0 # Separate leaves in children (empty lists up to now) n_leaves = n_samples # # return numpy array for efficient caching children = np.array(children)[:, ::-1] if return_distance: return children, n_connected_components, n_leaves, parent, distances return children, n_connected_components, n_leaves, parent # Matching names to tree-building strategies def _complete_linkage(*args, **kwargs): kwargs["linkage"] = "complete" return linkage_tree(*args, **kwargs) def _average_linkage(*args, **kwargs): kwargs["linkage"] = "average" return linkage_tree(*args, **kwargs) def _single_linkage(*args, **kwargs): kwargs["linkage"] = "single" return linkage_tree(*args, **kwargs) _TREE_BUILDERS = dict( ward=ward_tree, complete=_complete_linkage, average=_average_linkage, single=_single_linkage, ) ############################################################################### # Functions for cutting hierarchical clustering tree def _hc_cut(n_clusters, children, n_leaves): """Function cutting the ward tree for a given number of clusters. Parameters ---------- n_clusters : int or ndarray The number of clusters to form. children : ndarray of shape (n_nodes-1, 2) The children of each non-leaf node. Values less than `n_samples` correspond to leaves of the tree which are the original samples. A node `i` greater than or equal to `n_samples` is a non-leaf node and has children `children_[i - n_samples]`. Alternatively at the i-th iteration, children[i][0] and children[i][1] are merged to form node `n_samples + i`. n_leaves : int Number of leaves of the tree. Returns ------- labels : array [n_samples] Cluster labels for each point. """ if n_clusters > n_leaves: raise ValueError( "Cannot extract more clusters than samples: " f"{n_clusters} clusters were given for a tree with {n_leaves} leaves." ) # In this function, we store nodes as a heap to avoid recomputing # the max of the nodes: the first element is always the smallest # We use negated indices as heaps work on smallest elements, and we # are interested in largest elements # children[-1] is the root of the tree nodes = [-(max(children[-1]) + 1)] for _ in range(n_clusters - 1): # As we have a heap, nodes[0] is the smallest element these_children = children[-nodes[0] - n_leaves] # Insert the 2 children and remove the largest node heappush(nodes, -these_children[0]) heappushpop(nodes, -these_children[1]) label = np.zeros(n_leaves, dtype=np.intp) for i, node in enumerate(nodes): label[_hierarchical._hc_get_descendent(-node, children, n_leaves)] = i return label ############################################################################### class AgglomerativeClustering(ClusterMixin, BaseEstimator): """ Agglomerative Clustering. Recursively merges pair of clusters of sample data; uses linkage distance. Read more in the :ref:`User Guide `. Parameters ---------- n_clusters : int or None, default=2 The number of clusters to find. It must be ``None`` if ``distance_threshold`` is not ``None``. metric : str or callable, default="euclidean" Metric used to compute the linkage. Can be "euclidean", "l1", "l2", "manhattan", "cosine", or "precomputed". If linkage is "ward", only "euclidean" is accepted. If "precomputed", a distance matrix is needed as input for the fit method. If connectivity is None, linkage is "single" and affinity is not "precomputed" any valid pairwise distance metric can be assigned. .. versionadded:: 1.2 memory : str or object with the joblib.Memory interface, default=None Used to cache the output of the computation of the tree. By default, no caching is done. If a string is given, it is the path to the caching directory. connectivity : array-like, sparse matrix, or callable, default=None Connectivity matrix. Defines for each sample the neighboring samples following a given structure of the data. This can be a connectivity matrix itself or a callable that transforms the data into a connectivity matrix, such as derived from `kneighbors_graph`. Default is ``None``, i.e, the hierarchical clustering algorithm is unstructured. For an example of connectivity matrix using :class:`~sklearn.neighbors.kneighbors_graph`, see :ref:`sphx_glr_auto_examples_cluster_plot_agglomerative_clustering.py`. compute_full_tree : 'auto' or bool, default='auto' Stop early the construction of the tree at ``n_clusters``. This is useful to decrease computation time if the number of clusters is not small compared to the number of samples. This option is useful only when specifying a connectivity matrix. Note also that when varying the number of clusters and using caching, it may be advantageous to compute the full tree. It must be ``True`` if ``distance_threshold`` is not ``None``. By default `compute_full_tree` is "auto", which is equivalent to `True` when `distance_threshold` is not `None` or that `n_clusters` is inferior to the maximum between 100 or `0.02 * n_samples`. Otherwise, "auto" is equivalent to `False`. linkage : {'ward', 'complete', 'average', 'single'}, default='ward' Which linkage criterion to use. The linkage criterion determines which distance to use between sets of observation. The algorithm will merge the pairs of cluster that minimize this criterion. - 'ward' minimizes the variance of the clusters being merged. - 'average' uses the average of the distances of each observation of the two sets. - 'complete' or 'maximum' linkage uses the maximum distances between all observations of the two sets. - 'single' uses the minimum of the distances between all observations of the two sets. .. versionadded:: 0.20 Added the 'single' option For examples comparing different `linkage` criteria, see :ref:`sphx_glr_auto_examples_cluster_plot_linkage_comparison.py`. distance_threshold : float, default=None The linkage distance threshold at or above which clusters will not be merged. If not ``None``, ``n_clusters`` must be ``None`` and ``compute_full_tree`` must be ``True``. .. versionadded:: 0.21 compute_distances : bool, default=False Computes distances between clusters even if `distance_threshold` is not used. This can be used to make dendrogram visualization, but introduces a computational and memory overhead. .. versionadded:: 0.24 For an example of dendrogram visualization, see :ref:`sphx_glr_auto_examples_cluster_plot_agglomerative_dendrogram.py`. Attributes ---------- n_clusters_ : int The number of clusters found by the algorithm. If ``distance_threshold=None``, it will be equal to the given ``n_clusters``. labels_ : ndarray of shape (n_samples) Cluster labels for each point. n_leaves_ : int Number of leaves in the hierarchical tree. n_connected_components_ : int The estimated number of connected components in the graph. .. versionadded:: 0.21 ``n_connected_components_`` was added to replace ``n_components_``. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 children_ : array-like of shape (n_samples-1, 2) The children of each non-leaf node. Values less than `n_samples` correspond to leaves of the tree which are the original samples. A node `i` greater than or equal to `n_samples` is a non-leaf node and has children `children_[i - n_samples]`. Alternatively at the i-th iteration, children[i][0] and children[i][1] are merged to form node `n_samples + i`. distances_ : array-like of shape (n_nodes-1,) Distances between nodes in the corresponding place in `children_`. Only computed if `distance_threshold` is used or `compute_distances` is set to `True`. See Also -------- FeatureAgglomeration : Agglomerative clustering but for features instead of samples. ward_tree : Hierarchical clustering with ward linkage. Examples -------- >>> from sklearn.cluster import AgglomerativeClustering >>> import numpy as np >>> X = np.array([[1, 2], [1, 4], [1, 0], ... [4, 2], [4, 4], [4, 0]]) >>> clustering = AgglomerativeClustering().fit(X) >>> clustering AgglomerativeClustering() >>> clustering.labels_ array([1, 1, 1, 0, 0, 0]) """ _parameter_constraints: dict = { "n_clusters": [Interval(Integral, 1, None, closed="left"), None], "metric": [ StrOptions(set(_VALID_METRICS) | {"precomputed"}), callable, ], "memory": [str, HasMethods("cache"), None], "connectivity": ["array-like", "sparse matrix", callable, None], "compute_full_tree": [StrOptions({"auto"}), "boolean"], "linkage": [StrOptions(set(_TREE_BUILDERS.keys()))], "distance_threshold": [Interval(Real, 0, None, closed="left"), None], "compute_distances": ["boolean"], } def __init__( self, n_clusters=2, *, metric="euclidean", memory=None, connectivity=None, compute_full_tree="auto", linkage="ward", distance_threshold=None, compute_distances=False, ): self.n_clusters = n_clusters self.distance_threshold = distance_threshold self.memory = memory self.connectivity = connectivity self.compute_full_tree = compute_full_tree self.linkage = linkage self.metric = metric self.compute_distances = compute_distances @_fit_context(prefer_skip_nested_validation=True) def fit(self, X, y=None): """Fit the hierarchical clustering from features, or distance matrix. Parameters ---------- X : array-like, shape (n_samples, n_features) or \ (n_samples, n_samples) Training instances to cluster, or distances between instances if ``metric='precomputed'``. y : Ignored Not used, present here for API consistency by convention. Returns ------- self : object Returns the fitted instance. """ X = validate_data(self, X, ensure_min_samples=2) return self._fit(X) def _fit(self, X): """Fit without validation Parameters ---------- X : ndarray of shape (n_samples, n_features) or (n_samples, n_samples) Training instances to cluster, or distances between instances if ``metric='precomputed'``. Returns ------- self : object Returns the fitted instance. """ memory = check_memory(self.memory) if not ((self.n_clusters is None) ^ (self.distance_threshold is None)): raise ValueError( "Exactly one of n_clusters and " "distance_threshold has to be set, and the other " "needs to be None." ) if self.distance_threshold is not None and not self.compute_full_tree: raise ValueError( "compute_full_tree must be True if distance_threshold is set." ) if self.linkage == "ward" and self.metric != "euclidean": raise ValueError( f"{self.metric} was provided as metric. Ward can only " "work with euclidean distances." ) tree_builder = _TREE_BUILDERS[self.linkage] connectivity = self.connectivity if self.connectivity is not None: if callable(self.connectivity): connectivity = self.connectivity(X) connectivity = check_array( connectivity, accept_sparse=["csr", "coo", "lil"] ) n_samples = len(X) compute_full_tree = self.compute_full_tree if self.connectivity is None: compute_full_tree = True if compute_full_tree == "auto": if self.distance_threshold is not None: compute_full_tree = True else: # Early stopping is likely to give a speed up only for # a large number of clusters. The actual threshold # implemented here is heuristic compute_full_tree = self.n_clusters < max(100, 0.02 * n_samples) n_clusters = self.n_clusters if compute_full_tree: n_clusters = None # Construct the tree kwargs = {} if self.linkage != "ward": kwargs["linkage"] = self.linkage kwargs["affinity"] = self.metric distance_threshold = self.distance_threshold return_distance = (distance_threshold is not None) or self.compute_distances out = memory.cache(tree_builder)( X, connectivity=connectivity, n_clusters=n_clusters, return_distance=return_distance, **kwargs, ) (self.children_, self.n_connected_components_, self.n_leaves_, parents) = out[ :4 ] if return_distance: self.distances_ = out[-1] if self.distance_threshold is not None: # distance_threshold is used self.n_clusters_ = ( np.count_nonzero(self.distances_ >= distance_threshold) + 1 ) else: # n_clusters is used self.n_clusters_ = self.n_clusters # Cut the tree if compute_full_tree: self.labels_ = _hc_cut(self.n_clusters_, self.children_, self.n_leaves_) else: labels = _hierarchical.hc_get_heads(parents, copy=False) # copy to avoid holding a reference on the original array labels = np.copy(labels[:n_samples]) # Reassign cluster numbers self.labels_ = np.searchsorted(np.unique(labels), labels) return self def fit_predict(self, X, y=None): """Fit and return the result of each sample's clustering assignment. In addition to fitting, this method also return the result of the clustering assignment for each sample in the training set. Parameters ---------- X : array-like of shape (n_samples, n_features) or \ (n_samples, n_samples) Training instances to cluster, or distances between instances if ``affinity='precomputed'``. y : Ignored Not used, present here for API consistency by convention. Returns ------- labels : ndarray of shape (n_samples,) Cluster labels. """ return super().fit_predict(X, y) class FeatureAgglomeration( ClassNamePrefixFeaturesOutMixin, AgglomerationTransform, AgglomerativeClustering ): """Agglomerate features. Recursively merges pair of clusters of features. Refer to :ref:`sphx_glr_auto_examples_cluster_plot_feature_agglomeration_vs_univariate_selection.py` for an example comparison of :class:`FeatureAgglomeration` strategy with a univariate feature selection strategy (based on ANOVA). Read more in the :ref:`User Guide `. Parameters ---------- n_clusters : int or None, default=2 The number of clusters to find. It must be ``None`` if ``distance_threshold`` is not ``None``. metric : str or callable, default="euclidean" Metric used to compute the linkage. Can be "euclidean", "l1", "l2", "manhattan", "cosine", or "precomputed". If linkage is "ward", only "euclidean" is accepted. If "precomputed", a distance matrix is needed as input for the fit method. .. versionadded:: 1.2 memory : str or object with the joblib.Memory interface, default=None Used to cache the output of the computation of the tree. By default, no caching is done. If a string is given, it is the path to the caching directory. connectivity : array-like, sparse matrix, or callable, default=None Connectivity matrix. Defines for each feature the neighboring features following a given structure of the data. This can be a connectivity matrix itself or a callable that transforms the data into a connectivity matrix, such as derived from `kneighbors_graph`. Default is `None`, i.e, the hierarchical clustering algorithm is unstructured. compute_full_tree : 'auto' or bool, default='auto' Stop early the construction of the tree at `n_clusters`. This is useful to decrease computation time if the number of clusters is not small compared to the number of features. This option is useful only when specifying a connectivity matrix. Note also that when varying the number of clusters and using caching, it may be advantageous to compute the full tree. It must be ``True`` if ``distance_threshold`` is not ``None``. By default `compute_full_tree` is "auto", which is equivalent to `True` when `distance_threshold` is not `None` or that `n_clusters` is inferior to the maximum between 100 or `0.02 * n_samples`. Otherwise, "auto" is equivalent to `False`. linkage : {"ward", "complete", "average", "single"}, default="ward" Which linkage criterion to use. The linkage criterion determines which distance to use between sets of features. The algorithm will merge the pairs of cluster that minimize this criterion. - "ward" minimizes the variance of the clusters being merged. - "complete" or maximum linkage uses the maximum distances between all features of the two sets. - "average" uses the average of the distances of each feature of the two sets. - "single" uses the minimum of the distances between all features of the two sets. pooling_func : callable, default=np.mean This combines the values of agglomerated features into a single value, and should accept an array of shape [M, N] and the keyword argument `axis=1`, and reduce it to an array of size [M]. distance_threshold : float, default=None The linkage distance threshold at or above which clusters will not be merged. If not ``None``, ``n_clusters`` must be ``None`` and ``compute_full_tree`` must be ``True``. .. versionadded:: 0.21 compute_distances : bool, default=False Computes distances between clusters even if `distance_threshold` is not used. This can be used to make dendrogram visualization, but introduces a computational and memory overhead. .. versionadded:: 0.24 Attributes ---------- n_clusters_ : int The number of clusters found by the algorithm. If ``distance_threshold=None``, it will be equal to the given ``n_clusters``. labels_ : array-like of (n_features,) Cluster labels for each feature. n_leaves_ : int Number of leaves in the hierarchical tree. n_connected_components_ : int The estimated number of connected components in the graph. .. versionadded:: 0.21 ``n_connected_components_`` was added to replace ``n_components_``. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 children_ : array-like of shape (n_nodes-1, 2) The children of each non-leaf node. Values less than `n_features` correspond to leaves of the tree which are the original samples. A node `i` greater than or equal to `n_features` is a non-leaf node and has children `children_[i - n_features]`. Alternatively at the i-th iteration, children[i][0] and children[i][1] are merged to form node `n_features + i`. distances_ : array-like of shape (n_nodes-1,) Distances between nodes in the corresponding place in `children_`. Only computed if `distance_threshold` is used or `compute_distances` is set to `True`. See Also -------- AgglomerativeClustering : Agglomerative clustering samples instead of features. ward_tree : Hierarchical clustering with ward linkage. Examples -------- >>> import numpy as np >>> from sklearn import datasets, cluster >>> digits = datasets.load_digits() >>> images = digits.images >>> X = np.reshape(images, (len(images), -1)) >>> agglo = cluster.FeatureAgglomeration(n_clusters=32) >>> agglo.fit(X) FeatureAgglomeration(n_clusters=32) >>> X_reduced = agglo.transform(X) >>> X_reduced.shape (1797, 32) """ _parameter_constraints: dict = { "n_clusters": [Interval(Integral, 1, None, closed="left"), None], "metric": [ StrOptions(set(_VALID_METRICS) | {"precomputed"}), callable, ], "memory": [str, HasMethods("cache"), None], "connectivity": ["array-like", "sparse matrix", callable, None], "compute_full_tree": [StrOptions({"auto"}), "boolean"], "linkage": [StrOptions(set(_TREE_BUILDERS.keys()))], "pooling_func": [callable], "distance_threshold": [Interval(Real, 0, None, closed="left"), None], "compute_distances": ["boolean"], } def __init__( self, n_clusters=2, *, metric="euclidean", memory=None, connectivity=None, compute_full_tree="auto", linkage="ward", pooling_func=np.mean, distance_threshold=None, compute_distances=False, ): super().__init__( n_clusters=n_clusters, memory=memory, connectivity=connectivity, compute_full_tree=compute_full_tree, linkage=linkage, metric=metric, distance_threshold=distance_threshold, compute_distances=compute_distances, ) self.pooling_func = pooling_func @_fit_context(prefer_skip_nested_validation=True) def fit(self, X, y=None): """Fit the hierarchical clustering on the data. Parameters ---------- X : array-like of shape (n_samples, n_features) The data. y : Ignored Not used, present here for API consistency by convention. Returns ------- self : object Returns the transformer. """ X = validate_data(self, X, ensure_min_features=2) super()._fit(X.T) self._n_features_out = self.n_clusters_ return self @property def fit_predict(self): """Fit and return the result of each sample's clustering assignment.""" raise AttributeError