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"""
HDBSCAN: Hierarchical Density-Based Spatial Clustering
of Applications with Noise
"""
# Authors: Leland McInnes <leland.mcinnes@gmail.com>
# Steve Astels <sastels@gmail.com>
# John Healy <jchealy@gmail.com>
# Meekail Zain <zainmeekail@gmail.com>
# Copyright (c) 2015, Leland McInnes
# All rights reserved.
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
# 3. Neither the name of the copyright holder nor the names of its contributors
# may be used to endorse or promote products derived from this software without
# specific prior written permission.
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
from numbers import Integral, Real
from warnings import warn
import numpy as np
from scipy.sparse import csgraph, issparse
from ...base import BaseEstimator, ClusterMixin, _fit_context
from ...metrics import pairwise_distances
from ...metrics._dist_metrics import DistanceMetric
from ...neighbors import BallTree, KDTree, NearestNeighbors
from ...utils._param_validation import Interval, StrOptions
from ...utils.validation import _allclose_dense_sparse, _assert_all_finite
from ._linkage import (
MST_edge_dtype,
make_single_linkage,
mst_from_data_matrix,
mst_from_mutual_reachability,
)
from ._reachability import mutual_reachability_graph
from ._tree import HIERARCHY_dtype, labelling_at_cut, tree_to_labels
FAST_METRICS = set(KDTree.valid_metrics + BallTree.valid_metrics)
# Encodings are arbitrary but must be strictly negative.
# The current encodings are chosen as extensions to the -1 noise label.
# Avoided enums so that the end user only deals with simple labels.
_OUTLIER_ENCODING: dict = {
"infinite": {
"label": -2,
# The probability could also be 1, since infinite points are certainly
# infinite outliers, however 0 is convention from the HDBSCAN library
# implementation.
"prob": 0,
},
"missing": {
"label": -3,
# A nan probability is chosen to emphasize the fact that the
# corresponding data was not considered in the clustering problem.
"prob": np.nan,
},
}
def _brute_mst(mutual_reachability, min_samples):
"""
Builds a minimum spanning tree (MST) from the provided mutual-reachability
values. This function dispatches to a custom Cython implementation for
dense arrays, and `scipy.sparse.csgraph.minimum_spanning_tree` for sparse
arrays/matrices.
Parameters
----------
mututal_reachability_graph: {ndarray, sparse matrix} of shape \
(n_samples, n_samples)
Weighted adjacency matrix of the mutual reachability graph.
min_samples : int, default=None
The number of samples in a neighborhood for a point
to be considered as a core point. This includes the point itself.
Returns
-------
mst : ndarray of shape (n_samples - 1,), dtype=MST_edge_dtype
The MST representation of the mutual-reachability graph. The MST is
represented as a collection of edges.
"""
if not issparse(mutual_reachability):
return mst_from_mutual_reachability(mutual_reachability)
# Check if the mutual reachability matrix has any rows which have
# less than `min_samples` non-zero elements.
indptr = mutual_reachability.indptr
num_points = mutual_reachability.shape[0]
if any((indptr[i + 1] - indptr[i]) < min_samples for i in range(num_points)):
raise ValueError(
f"There exists points with fewer than {min_samples} neighbors. Ensure"
" your distance matrix has non-zero values for at least"
f" `min_sample`={min_samples} neighbors for each points (i.e. K-nn"
" graph), or specify a `max_distance` in `metric_params` to use when"
" distances are missing."
)
# Check connected component on mutual reachability.
# If more than one connected component is present,
# it means that the graph is disconnected.
n_components = csgraph.connected_components(
mutual_reachability, directed=False, return_labels=False
)
if n_components > 1:
raise ValueError(
f"Sparse mutual reachability matrix has {n_components} connected"
" components. HDBSCAN cannot be perfomed on a disconnected graph. Ensure"
" that the sparse distance matrix has only one connected component."
)
# Compute the minimum spanning tree for the sparse graph
sparse_min_spanning_tree = csgraph.minimum_spanning_tree(mutual_reachability)
rows, cols = sparse_min_spanning_tree.nonzero()
mst = np.rec.fromarrays(
[rows, cols, sparse_min_spanning_tree.data],
dtype=MST_edge_dtype,
)
return mst
def _process_mst(min_spanning_tree):
"""
Builds a single-linkage tree (SLT) from the provided minimum spanning tree
(MST). The MST is first sorted then processed by a custom Cython routine.
Parameters
----------
min_spanning_tree : ndarray of shape (n_samples - 1,), dtype=MST_edge_dtype
The MST representation of the mutual-reachability graph. The MST is
represented as a collection of edges.
Returns
-------
single_linkage : ndarray of shape (n_samples - 1,), dtype=HIERARCHY_dtype
The single-linkage tree tree (dendrogram) built from the MST.
"""
# Sort edges of the min_spanning_tree by weight
row_order = np.argsort(min_spanning_tree["distance"])
min_spanning_tree = min_spanning_tree[row_order]
# Convert edge list into standard hierarchical clustering format
return make_single_linkage(min_spanning_tree)
def _hdbscan_brute(
X,
min_samples=5,
alpha=None,
metric="euclidean",
n_jobs=None,
copy=False,
**metric_params,
):
"""
Builds a single-linkage tree (SLT) from the input data `X`. If
`metric="precomputed"` then `X` must be a symmetric array of distances.
Otherwise, the pairwise distances are calculated directly and passed to
`mutual_reachability_graph`.
Parameters
----------
X : ndarray of shape (n_samples, n_features) or (n_samples, n_samples)
Either the raw data from which to compute the pairwise distances,
or the precomputed distances.
min_samples : int, default=None
The number of samples in a neighborhood for a point
to be considered as a core point. This includes the point itself.
alpha : float, default=1.0
A distance scaling parameter as used in robust single linkage.
metric : str or callable, default='euclidean'
The metric to use when calculating distance between instances in a
feature array.
- If metric is a string or callable, it must be one of
the options allowed by :func:`~sklearn.metrics.pairwise_distances`
for its metric parameter.
- If metric is "precomputed", X is assumed to be a distance matrix and
must be square.
n_jobs : int, default=None
The number of jobs to use for computing the pairwise distances. This
works by breaking down the pairwise matrix into n_jobs even slices and
computing them in parallel. This parameter is passed directly to
:func:`~sklearn.metrics.pairwise_distances`.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
copy : bool, default=False
If `copy=True` then any time an in-place modifications would be made
that would overwrite `X`, a copy will first be made, guaranteeing that
the original data will be unchanged. Currently, it only applies when
`metric="precomputed"`, when passing a dense array or a CSR sparse
array/matrix.
metric_params : dict, default=None
Arguments passed to the distance metric.
Returns
-------
single_linkage : ndarray of shape (n_samples - 1,), dtype=HIERARCHY_dtype
The single-linkage tree tree (dendrogram) built from the MST.
"""
if metric == "precomputed":
if X.shape[0] != X.shape[1]:
raise ValueError(
"The precomputed distance matrix is expected to be symmetric, however"
f" it has shape {X.shape}. Please verify that the"
" distance matrix was constructed correctly."
)
if not _allclose_dense_sparse(X, X.T):
raise ValueError(
"The precomputed distance matrix is expected to be symmetric, however"
" its values appear to be asymmetric. Please verify that the distance"
" matrix was constructed correctly."
)
distance_matrix = X.copy() if copy else X
else:
distance_matrix = pairwise_distances(
X, metric=metric, n_jobs=n_jobs, **metric_params
)
distance_matrix /= alpha
max_distance = metric_params.get("max_distance", 0.0)
if issparse(distance_matrix) and distance_matrix.format != "csr":
# we need CSR format to avoid a conversion in `_brute_mst` when calling
# `csgraph.connected_components`
distance_matrix = distance_matrix.tocsr()
# Note that `distance_matrix` is manipulated in-place, however we do not
# need it for anything else past this point, hence the operation is safe.
mutual_reachability_ = mutual_reachability_graph(
distance_matrix, min_samples=min_samples, max_distance=max_distance
)
min_spanning_tree = _brute_mst(mutual_reachability_, min_samples=min_samples)
# Warn if the MST couldn't be constructed around the missing distances
if np.isinf(min_spanning_tree["distance"]).any():
warn(
(
"The minimum spanning tree contains edge weights with value "
"infinity. Potentially, you are missing too many distances "
"in the initial distance matrix for the given neighborhood "
"size."
),
UserWarning,
)
return _process_mst(min_spanning_tree)
def _hdbscan_prims(
X,
algo,
min_samples=5,
alpha=1.0,
metric="euclidean",
leaf_size=40,
n_jobs=None,
**metric_params,
):
"""
Builds a single-linkage tree (SLT) from the input data `X`. If
`metric="precomputed"` then `X` must be a symmetric array of distances.
Otherwise, the pairwise distances are calculated directly and passed to
`mutual_reachability_graph`.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
The raw data.
min_samples : int, default=None
The number of samples in a neighborhood for a point
to be considered as a core point. This includes the point itself.
alpha : float, default=1.0
A distance scaling parameter as used in robust single linkage.
metric : str or callable, default='euclidean'
The metric to use when calculating distance between instances in a
feature array. `metric` must be one of the options allowed by
:func:`~sklearn.metrics.pairwise_distances` for its metric
parameter.
n_jobs : int, default=None
The number of jobs to use for computing the pairwise distances. This
works by breaking down the pairwise matrix into n_jobs even slices and
computing them in parallel. This parameter is passed directly to
:func:`~sklearn.metrics.pairwise_distances`.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
copy : bool, default=False
If `copy=True` then any time an in-place modifications would be made
that would overwrite `X`, a copy will first be made, guaranteeing that
the original data will be unchanged. Currently, it only applies when
`metric="precomputed"`, when passing a dense array or a CSR sparse
array/matrix.
metric_params : dict, default=None
Arguments passed to the distance metric.
Returns
-------
single_linkage : ndarray of shape (n_samples - 1,), dtype=HIERARCHY_dtype
The single-linkage tree tree (dendrogram) built from the MST.
"""
# The Cython routines used require contiguous arrays
X = np.asarray(X, order="C")
# Get distance to kth nearest neighbour
nbrs = NearestNeighbors(
n_neighbors=min_samples,
algorithm=algo,
leaf_size=leaf_size,
metric=metric,
metric_params=metric_params,
n_jobs=n_jobs,
p=None,
).fit(X)
neighbors_distances, _ = nbrs.kneighbors(X, min_samples, return_distance=True)
core_distances = np.ascontiguousarray(neighbors_distances[:, -1])
dist_metric = DistanceMetric.get_metric(metric, **metric_params)
# Mutual reachability distance is implicit in mst_from_data_matrix
min_spanning_tree = mst_from_data_matrix(X, core_distances, dist_metric, alpha)
return _process_mst(min_spanning_tree)
def remap_single_linkage_tree(tree, internal_to_raw, non_finite):
"""
Takes an internal single_linkage_tree structure and adds back in a set of points
that were initially detected as non-finite and returns that new tree.
These points will all be merged into the final node at np.inf distance and
considered noise points.
Parameters
----------
tree : ndarray of shape (n_samples - 1,), dtype=HIERARCHY_dtype
The single-linkage tree tree (dendrogram) built from the MST.
internal_to_raw: dict
A mapping from internal integer index to the raw integer index
non_finite : ndarray
Boolean array of which entries in the raw data are non-finite
"""
finite_count = len(internal_to_raw)
outlier_count = len(non_finite)
for i, _ in enumerate(tree):
left = tree[i]["left_node"]
right = tree[i]["right_node"]
if left < finite_count:
tree[i]["left_node"] = internal_to_raw[left]
else:
tree[i]["left_node"] = left + outlier_count
if right < finite_count:
tree[i]["right_node"] = internal_to_raw[right]
else:
tree[i]["right_node"] = right + outlier_count
outlier_tree = np.zeros(len(non_finite), dtype=HIERARCHY_dtype)
last_cluster_id = max(
tree[tree.shape[0] - 1]["left_node"], tree[tree.shape[0] - 1]["right_node"]
)
last_cluster_size = tree[tree.shape[0] - 1]["cluster_size"]
for i, outlier in enumerate(non_finite):
outlier_tree[i] = (outlier, last_cluster_id + 1, np.inf, last_cluster_size + 1)
last_cluster_id += 1
last_cluster_size += 1
tree = np.concatenate([tree, outlier_tree])
return tree
def _get_finite_row_indices(matrix):
"""
Returns the indices of the purely finite rows of a
sparse matrix or dense ndarray
"""
if issparse(matrix):
row_indices = np.array(
[i for i, row in enumerate(matrix.tolil().data) if np.all(np.isfinite(row))]
)
else:
(row_indices,) = np.isfinite(matrix.sum(axis=1)).nonzero()
return row_indices
class HDBSCAN(ClusterMixin, BaseEstimator):
"""Cluster data using hierarchical density-based clustering.
HDBSCAN - Hierarchical Density-Based Spatial Clustering of Applications
with Noise. Performs :class:`~sklearn.cluster.DBSCAN` over varying epsilon
values and integrates the result to find a clustering that gives the best
stability over epsilon.
This allows HDBSCAN to find clusters of varying densities (unlike
:class:`~sklearn.cluster.DBSCAN`), and be more robust to parameter selection.
Read more in the :ref:`User Guide <hdbscan>`.
For an example of how to use HDBSCAN, as well as a comparison to
:class:`~sklearn.cluster.DBSCAN`, please see the :ref:`plotting demo
<sphx_glr_auto_examples_cluster_plot_hdbscan.py>`.
.. versionadded:: 1.3
Parameters
----------
min_cluster_size : int, default=5
The minimum number of samples in a group for that group to be
considered a cluster; groupings smaller than this size will be left
as noise.
min_samples : int, default=None
The number of samples in a neighborhood for a point
to be considered as a core point. This includes the point itself.
When `None`, defaults to `min_cluster_size`.
cluster_selection_epsilon : float, default=0.0
A distance threshold. Clusters below this value will be merged.
See [5]_ for more information.
max_cluster_size : int, default=None
A limit to the size of clusters returned by the `"eom"` cluster
selection algorithm. There is no limit when `max_cluster_size=None`.
Has no effect if `cluster_selection_method="leaf"`.
metric : str or callable, default='euclidean'
The metric to use when calculating distance between instances in a
feature array.
- If metric is a string or callable, it must be one of
the options allowed by :func:`~sklearn.metrics.pairwise_distances`
for its metric parameter.
- If metric is "precomputed", X is assumed to be a distance matrix and
must be square.
metric_params : dict, default=None
Arguments passed to the distance metric.
alpha : float, default=1.0
A distance scaling parameter as used in robust single linkage.
See [3]_ for more information.
algorithm : {"auto", "brute", "kd_tree", "ball_tree"}, default="auto"
Exactly which algorithm to use for computing core distances; By default
this is set to `"auto"` which attempts to use a
:class:`~sklearn.neighbors.KDTree` tree if possible, otherwise it uses
a :class:`~sklearn.neighbors.BallTree` tree. Both `"kd_tree"` and
`"ball_tree"` algorithms use the
:class:`~sklearn.neighbors.NearestNeighbors` estimator.
If the `X` passed during `fit` is sparse or `metric` is invalid for
both :class:`~sklearn.neighbors.KDTree` and
:class:`~sklearn.neighbors.BallTree`, then it resolves to use the
`"brute"` algorithm.
.. deprecated:: 1.4
The `'kdtree'` option was deprecated in version 1.4,
and will be renamed to `'kd_tree'` in 1.6.
.. deprecated:: 1.4
The `'balltree'` option was deprecated in version 1.4,
and will be renamed to `'ball_tree'` in 1.6.
leaf_size : int, default=40
Leaf size for trees responsible for fast nearest neighbour queries when
a KDTree or a BallTree are used as core-distance algorithms. A large
dataset size and small `leaf_size` may induce excessive memory usage.
If you are running out of memory consider increasing the `leaf_size`
parameter. Ignored for `algorithm="brute"`.
n_jobs : int, default=None
Number of jobs to run in parallel to calculate distances.
`None` means 1 unless in a :obj:`joblib.parallel_backend` context.
`-1` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
cluster_selection_method : {"eom", "leaf"}, default="eom"
The method used to select clusters from the condensed tree. The
standard approach for HDBSCAN* is to use an Excess of Mass (`"eom"`)
algorithm to find the most persistent clusters. Alternatively you can
instead select the clusters at the leaves of the tree -- this provides
the most fine grained and homogeneous clusters.
allow_single_cluster : bool, default=False
By default HDBSCAN* will not produce a single cluster, setting this
to True will override this and allow single cluster results in
the case that you feel this is a valid result for your dataset.
store_centers : str, default=None
Which, if any, cluster centers to compute and store. The options are:
- `None` which does not compute nor store any centers.
- `"centroid"` which calculates the center by taking the weighted
average of their positions. Note that the algorithm uses the
euclidean metric and does not guarantee that the output will be
an observed data point.
- `"medoid"` which calculates the center by taking the point in the
fitted data which minimizes the distance to all other points in
the cluster. This is slower than "centroid" since it requires
computing additional pairwise distances between points of the
same cluster but guarantees the output is an observed data point.
The medoid is also well-defined for arbitrary metrics, and does not
depend on a euclidean metric.
- `"both"` which computes and stores both forms of centers.
copy : bool, default=False
If `copy=True` then any time an in-place modifications would be made
that would overwrite data passed to :term:`fit`, a copy will first be
made, guaranteeing that the original data will be unchanged.
Currently, it only applies when `metric="precomputed"`, when passing
a dense array or a CSR sparse matrix and when `algorithm="brute"`.
Attributes
----------
labels_ : ndarray of shape (n_samples,)
Cluster labels for each point in the dataset given to :term:`fit`.
Outliers are labeled as follows:
- Noisy samples are given the label -1.
- Samples with infinite elements (+/- np.inf) are given the label -2.
- Samples with missing data are given the label -3, even if they
also have infinite elements.
probabilities_ : ndarray of shape (n_samples,)
The strength with which each sample is a member of its assigned
cluster.
- Clustered samples have probabilities proportional to the degree that
they persist as part of the cluster.
- Noisy samples have probability zero.
- Samples with infinite elements (+/- np.inf) have probability 0.
- Samples with missing data have probability `np.nan`.
n_features_in_ : int
Number of features seen during :term:`fit`.
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.
centroids_ : ndarray of shape (n_clusters, n_features)
A collection containing the centroid of each cluster calculated under
the standard euclidean metric. The centroids may fall "outside" their
respective clusters if the clusters themselves are non-convex.
Note that `n_clusters` only counts non-outlier clusters. That is to
say, the `-1, -2, -3` labels for the outlier clusters are excluded.
medoids_ : ndarray of shape (n_clusters, n_features)
A collection containing the medoid of each cluster calculated under
the whichever metric was passed to the `metric` parameter. The
medoids are points in the original cluster which minimize the average
distance to all other points in that cluster under the chosen metric.
These can be thought of as the result of projecting the `metric`-based
centroid back onto the cluster.
Note that `n_clusters` only counts non-outlier clusters. That is to
say, the `-1, -2, -3` labels for the outlier clusters are excluded.
See Also
--------
DBSCAN : Density-Based Spatial Clustering of Applications
with Noise.
OPTICS : Ordering Points To Identify the Clustering Structure.
Birch : Memory-efficient, online-learning algorithm.
References
----------
.. [1] :doi:`Campello, R. J., Moulavi, D., & Sander, J. Density-based clustering
based on hierarchical density estimates.
<10.1007/978-3-642-37456-2_14>`
.. [2] :doi:`Campello, R. J., Moulavi, D., Zimek, A., & Sander, J.
Hierarchical density estimates for data clustering, visualization,
and outlier detection.<10.1145/2733381>`
.. [3] `Chaudhuri, K., & Dasgupta, S. Rates of convergence for the
cluster tree.
<https://papers.nips.cc/paper/2010/hash/
b534ba68236ba543ae44b22bd110a1d6-Abstract.html>`_
.. [4] `Moulavi, D., Jaskowiak, P.A., Campello, R.J., Zimek, A. and
Sander, J. Density-Based Clustering Validation.
<https://www.dbs.ifi.lmu.de/~zimek/publications/SDM2014/DBCV.pdf>`_
.. [5] :arxiv:`Malzer, C., & Baum, M. "A Hybrid Approach To Hierarchical
Density-based Cluster Selection."<1911.02282>`.
Examples
--------
>>> from sklearn.cluster import HDBSCAN
>>> from sklearn.datasets import load_digits
>>> X, _ = load_digits(return_X_y=True)
>>> hdb = HDBSCAN(min_cluster_size=20)
>>> hdb.fit(X)
HDBSCAN(min_cluster_size=20)
>>> hdb.labels_
array([ 2, 6, -1, ..., -1, -1, -1])
"""
_parameter_constraints = {
"min_cluster_size": [Interval(Integral, left=2, right=None, closed="left")],
"min_samples": [Interval(Integral, left=1, right=None, closed="left"), None],
"cluster_selection_epsilon": [
Interval(Real, left=0, right=None, closed="left")
],
"max_cluster_size": [
None,
Interval(Integral, left=1, right=None, closed="left"),
],
"metric": [StrOptions(FAST_METRICS | {"precomputed"}), callable],
"metric_params": [dict, None],
"alpha": [Interval(Real, left=0, right=None, closed="neither")],
# TODO(1.6): Remove "kdtree" and "balltree" option
"algorithm": [
StrOptions(
{"auto", "brute", "kd_tree", "ball_tree", "kdtree", "balltree"},
deprecated={"kdtree", "balltree"},
),
],
"leaf_size": [Interval(Integral, left=1, right=None, closed="left")],
"n_jobs": [Integral, None],
"cluster_selection_method": [StrOptions({"eom", "leaf"})],
"allow_single_cluster": ["boolean"],
"store_centers": [None, StrOptions({"centroid", "medoid", "both"})],
"copy": ["boolean"],
}
def __init__(
self,
min_cluster_size=5,
min_samples=None,
cluster_selection_epsilon=0.0,
max_cluster_size=None,
metric="euclidean",
metric_params=None,
alpha=1.0,
algorithm="auto",
leaf_size=40,
n_jobs=None,
cluster_selection_method="eom",
allow_single_cluster=False,
store_centers=None,
copy=False,
):
self.min_cluster_size = min_cluster_size
self.min_samples = min_samples
self.alpha = alpha
self.max_cluster_size = max_cluster_size
self.cluster_selection_epsilon = cluster_selection_epsilon
self.metric = metric
self.metric_params = metric_params
self.algorithm = algorithm
self.leaf_size = leaf_size
self.n_jobs = n_jobs
self.cluster_selection_method = cluster_selection_method
self.allow_single_cluster = allow_single_cluster
self.store_centers = store_centers
self.copy = copy
@_fit_context(
# HDBSCAN.metric is not validated yet
prefer_skip_nested_validation=False
)
def fit(self, X, y=None):
"""Find clusters based on hierarchical density-based clustering.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features), or \
ndarray of shape (n_samples, n_samples)
A feature array, or array of distances between samples if
`metric='precomputed'`.
y : None
Ignored.
Returns
-------
self : object
Returns self.
"""
if self.metric == "precomputed" and self.store_centers is not None:
raise ValueError(
"Cannot store centers when using a precomputed distance matrix."
)
self._metric_params = self.metric_params or {}
if self.metric != "precomputed":
# Non-precomputed matrices may contain non-finite values.
X = self._validate_data(
X,
accept_sparse=["csr", "lil"],
force_all_finite=False,
dtype=np.float64,
)
self._raw_data = X
all_finite = True
try:
_assert_all_finite(X.data if issparse(X) else X)
except ValueError:
all_finite = False
if not all_finite:
# Pass only the purely finite indices into hdbscan
# We will later assign all non-finite points their
# corresponding labels, as specified in `_OUTLIER_ENCODING`
# Reduce X to make the checks for missing/outlier samples more
# convenient.
reduced_X = X.sum(axis=1)
# Samples with missing data are denoted by the presence of
# `np.nan`
missing_index = np.isnan(reduced_X).nonzero()[0]
# Outlier samples are denoted by the presence of `np.inf`
infinite_index = np.isinf(reduced_X).nonzero()[0]
# Continue with only finite samples
finite_index = _get_finite_row_indices(X)
internal_to_raw = {x: y for x, y in enumerate(finite_index)}
X = X[finite_index]
elif issparse(X):
# Handle sparse precomputed distance matrices separately
X = self._validate_data(
X,
accept_sparse=["csr", "lil"],
dtype=np.float64,
)
else:
# Only non-sparse, precomputed distance matrices are handled here
# and thereby allowed to contain numpy.inf for missing distances
# Perform data validation after removing infinite values (numpy.inf)
# from the given distance matrix.
X = self._validate_data(X, force_all_finite=False, dtype=np.float64)
if np.isnan(X).any():
# TODO: Support np.nan in Cython implementation for precomputed
# dense HDBSCAN
raise ValueError("np.nan values found in precomputed-dense")
if X.shape[0] == 1:
raise ValueError("n_samples=1 while HDBSCAN requires more than one sample")
self._min_samples = (
self.min_cluster_size if self.min_samples is None else self.min_samples
)
if self._min_samples > X.shape[0]:
raise ValueError(
f"min_samples ({self._min_samples}) must be at most the number of"
f" samples in X ({X.shape[0]})"
)
# TODO(1.6): Remove
if self.algorithm == "kdtree":
warn(
(
"`algorithm='kdtree'`has been deprecated in 1.4 and will be renamed"
" to'kd_tree'`in 1.6. To keep the past behaviour, set"
" `algorithm='kd_tree'`."
),
FutureWarning,
)
self.algorithm = "kd_tree"
# TODO(1.6): Remove
if self.algorithm == "balltree":
warn(
(
"`algorithm='balltree'`has been deprecated in 1.4 and will be"
" renamed to'ball_tree'`in 1.6. To keep the past behaviour, set"
" `algorithm='ball_tree'`."
),
FutureWarning,
)
self.algorithm = "ball_tree"
mst_func = None
kwargs = dict(
X=X,
min_samples=self._min_samples,
alpha=self.alpha,
metric=self.metric,
n_jobs=self.n_jobs,
**self._metric_params,
)
if self.algorithm == "kd_tree" and self.metric not in KDTree.valid_metrics:
raise ValueError(
f"{self.metric} is not a valid metric for a KDTree-based algorithm."
" Please select a different metric."
)
elif (
self.algorithm == "ball_tree" and self.metric not in BallTree.valid_metrics
):
raise ValueError(
f"{self.metric} is not a valid metric for a BallTree-based algorithm."
" Please select a different metric."
)
if self.algorithm != "auto":
if (
self.metric != "precomputed"
and issparse(X)
and self.algorithm != "brute"
):
raise ValueError("Sparse data matrices only support algorithm `brute`.")
if self.algorithm == "brute":
mst_func = _hdbscan_brute
kwargs["copy"] = self.copy
elif self.algorithm == "kd_tree":
mst_func = _hdbscan_prims
kwargs["algo"] = "kd_tree"
kwargs["leaf_size"] = self.leaf_size
else:
mst_func = _hdbscan_prims
kwargs["algo"] = "ball_tree"
kwargs["leaf_size"] = self.leaf_size
else:
if issparse(X) or self.metric not in FAST_METRICS:
# We can't do much with sparse matrices ...
mst_func = _hdbscan_brute
kwargs["copy"] = self.copy
elif self.metric in KDTree.valid_metrics:
# TODO: Benchmark KD vs Ball Tree efficiency
mst_func = _hdbscan_prims
kwargs["algo"] = "kd_tree"
kwargs["leaf_size"] = self.leaf_size
else:
# Metric is a valid BallTree metric
mst_func = _hdbscan_prims
kwargs["algo"] = "ball_tree"
kwargs["leaf_size"] = self.leaf_size
self._single_linkage_tree_ = mst_func(**kwargs)
self.labels_, self.probabilities_ = tree_to_labels(
self._single_linkage_tree_,
self.min_cluster_size,
self.cluster_selection_method,
self.allow_single_cluster,
self.cluster_selection_epsilon,
self.max_cluster_size,
)
if self.metric != "precomputed" and not all_finite:
# Remap indices to align with original data in the case of
# non-finite entries. Samples with np.inf are mapped to -1 and
# those with np.nan are mapped to -2.
self._single_linkage_tree_ = remap_single_linkage_tree(
self._single_linkage_tree_,
internal_to_raw,
# There may be overlap for points w/ both `np.inf` and `np.nan`
non_finite=set(np.hstack([infinite_index, missing_index])),
)
new_labels = np.empty(self._raw_data.shape[0], dtype=np.int32)
new_labels[finite_index] = self.labels_
new_labels[infinite_index] = _OUTLIER_ENCODING["infinite"]["label"]
new_labels[missing_index] = _OUTLIER_ENCODING["missing"]["label"]
self.labels_ = new_labels
new_probabilities = np.zeros(self._raw_data.shape[0], dtype=np.float64)
new_probabilities[finite_index] = self.probabilities_
# Infinite outliers have probability 0 by convention, though this
# is arbitrary.
new_probabilities[infinite_index] = _OUTLIER_ENCODING["infinite"]["prob"]
new_probabilities[missing_index] = _OUTLIER_ENCODING["missing"]["prob"]
self.probabilities_ = new_probabilities
if self.store_centers:
self._weighted_cluster_center(X)
return self
def fit_predict(self, X, y=None):
"""Cluster X and return the associated cluster labels.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features), or \
ndarray of shape (n_samples, n_samples)
A feature array, or array of distances between samples if
`metric='precomputed'`.
y : None
Ignored.
Returns
-------
y : ndarray of shape (n_samples,)
Cluster labels.
"""
self.fit(X)
return self.labels_
def _weighted_cluster_center(self, X):
"""Calculate and store the centroids/medoids of each cluster.
This requires `X` to be a raw feature array, not precomputed
distances. Rather than return outputs directly, this helper method
instead stores them in the `self.{centroids, medoids}_` attributes.
The choice for which attributes are calculated and stored is mediated
by the value of `self.store_centers`.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
The feature array that the estimator was fit with.
"""
# Number of non-noise clusters
n_clusters = len(set(self.labels_) - {-1, -2})
mask = np.empty((X.shape[0],), dtype=np.bool_)
make_centroids = self.store_centers in ("centroid", "both")
make_medoids = self.store_centers in ("medoid", "both")
if make_centroids:
self.centroids_ = np.empty((n_clusters, X.shape[1]), dtype=np.float64)
if make_medoids:
self.medoids_ = np.empty((n_clusters, X.shape[1]), dtype=np.float64)
# Need to handle iteratively seen each cluster may have a different
# number of samples, hence we can't create a homogeneous 3D array.
for idx in range(n_clusters):
mask = self.labels_ == idx
data = X[mask]
strength = self.probabilities_[mask]
if make_centroids:
self.centroids_[idx] = np.average(data, weights=strength, axis=0)
if make_medoids:
# TODO: Implement weighted argmin PWD backend
dist_mat = pairwise_distances(
data, metric=self.metric, **self._metric_params
)
dist_mat = dist_mat * strength
medoid_index = np.argmin(dist_mat.sum(axis=1))
self.medoids_[idx] = data[medoid_index]
return
def dbscan_clustering(self, cut_distance, min_cluster_size=5):
"""Return clustering given by DBSCAN without border points.
Return clustering that would be equivalent to running DBSCAN* for a
particular cut_distance (or epsilon) DBSCAN* can be thought of as
DBSCAN without the border points. As such these results may differ
slightly from `cluster.DBSCAN` due to the difference in implementation
over the non-core points.
This can also be thought of as a flat clustering derived from constant
height cut through the single linkage tree.
This represents the result of selecting a cut value for robust single linkage
clustering. The `min_cluster_size` allows the flat clustering to declare noise
points (and cluster smaller than `min_cluster_size`).
Parameters
----------
cut_distance : float
The mutual reachability distance cut value to use to generate a
flat clustering.
min_cluster_size : int, default=5
Clusters smaller than this value with be called 'noise' and remain
unclustered in the resulting flat clustering.
Returns
-------
labels : ndarray of shape (n_samples,)
An array of cluster labels, one per datapoint.
Outliers are labeled as follows:
- Noisy samples are given the label -1.
- Samples with infinite elements (+/- np.inf) are given the label -2.
- Samples with missing data are given the label -3, even if they
also have infinite elements.
"""
labels = labelling_at_cut(
self._single_linkage_tree_, cut_distance, min_cluster_size
)
# Infer indices from labels generated during `fit`
infinite_index = self.labels_ == _OUTLIER_ENCODING["infinite"]["label"]
missing_index = self.labels_ == _OUTLIER_ENCODING["missing"]["label"]
# Overwrite infinite/missing outlier samples (otherwise simple noise)
labels[infinite_index] = _OUTLIER_ENCODING["infinite"]["label"]
labels[missing_index] = _OUTLIER_ENCODING["missing"]["label"]
return labels
def _more_tags(self):
return {"allow_nan": self.metric != "precomputed"}