# -*- coding: utf-8 -*-
"""
====================================
Demo of HDBSCAN clustering algorithm
====================================
.. currentmodule:: sklearn
In this demo we will take a look at :class:`cluster.HDBSCAN` from the
perspective of generalizing the :class:`cluster.DBSCAN` algorithm.
We'll compare both algorithms on specific datasets. Finally we'll evaluate
HDBSCAN's sensitivity to certain hyperparameters.
We first define a couple utility functions for convenience.
"""
# %%
import matplotlib.pyplot as plt
import numpy as np
from sklearn.cluster import DBSCAN, HDBSCAN
from sklearn.datasets import make_blobs
def plot(X, labels, probabilities=None, parameters=None, ground_truth=False, ax=None):
if ax is None:
_, ax = plt.subplots(figsize=(10, 4))
labels = labels if labels is not None else np.ones(X.shape[0])
probabilities = probabilities if probabilities is not None else np.ones(X.shape[0])
# Black removed and is used for noise instead.
unique_labels = set(labels)
colors = [plt.cm.Spectral(each) for each in np.linspace(0, 1, len(unique_labels))]
# The probability of a point belonging to its labeled cluster determines
# the size of its marker
proba_map = {idx: probabilities[idx] for idx in range(len(labels))}
for k, col in zip(unique_labels, colors):
if k == -1:
# Black used for noise.
col = [0, 0, 0, 1]
class_index = np.where(labels == k)[0]
for ci in class_index:
ax.plot(
X[ci, 0],
X[ci, 1],
"x" if k == -1 else "o",
markerfacecolor=tuple(col),
markeredgecolor="k",
markersize=4 if k == -1 else 1 + 5 * proba_map[ci],
)
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)
preamble = "True" if ground_truth else "Estimated"
title = f"{preamble} number of clusters: {n_clusters_}"
if parameters is not None:
parameters_str = ", ".join(f"{k}={v}" for k, v in parameters.items())
title += f" | {parameters_str}"
ax.set_title(title)
plt.tight_layout()
# %%
# Generate sample data
# --------------------
# One of the greatest advantages of HDBSCAN over DBSCAN is its out-of-the-box
# robustness. It's especially remarkable on heterogeneous mixtures of data.
# Like DBSCAN, it can model arbitrary shapes and distributions, however unlike
# DBSCAN it does not require specification of an arbitrary and sensitive
# `eps` hyperparameter.
#
# For example, below we generate a dataset from a mixture of three bi-dimensional
# and isotropic Gaussian distributions.
centers = [[1, 1], [-1, -1], [1.5, -1.5]]
X, labels_true = make_blobs(
n_samples=750, centers=centers, cluster_std=[0.4, 0.1, 0.75], random_state=0
)
plot(X, labels=labels_true, ground_truth=True)
# %%
# Scale Invariance
# -----------------
# It's worth remembering that, while DBSCAN provides a default value for `eps`
# parameter, it hardly has a proper default value and must be tuned for the
# specific dataset at use.
#
# As a simple demonstration, consider the clustering for a `eps` value tuned
# for one dataset, and clustering obtained with the same value but applied to
# rescaled versions of the dataset.
fig, axes = plt.subplots(3, 1, figsize=(10, 12))
dbs = DBSCAN(eps=0.3)
for idx, scale in enumerate([1, 0.5, 3]):
dbs.fit(X * scale)
plot(X * scale, dbs.labels_, parameters={"scale": scale, "eps": 0.3}, ax=axes[idx])
# %%
# Indeed, in order to maintain the same results we would have to scale `eps` by
# the same factor.
fig, axis = plt.subplots(1, 1, figsize=(12, 5))
dbs = DBSCAN(eps=0.9).fit(3 * X)
plot(3 * X, dbs.labels_, parameters={"scale": 3, "eps": 0.9}, ax=axis)
# %%
# While standardizing data (e.g. using
# :class:`sklearn.preprocessing.StandardScaler`) helps mitigate this problem,
# great care must be taken to select the appropriate value for `eps`.
#
# HDBSCAN is much more robust in this sense: HDBSCAN can be seen as
# clustering over all possible values of `eps` and extracting the best
# clusters from all possible clusters (see :ref:`User Guide `).
# One immediate advantage is that HDBSCAN is scale-invariant.
fig, axes = plt.subplots(3, 1, figsize=(10, 12))
hdb = HDBSCAN()
for idx, scale in enumerate([1, 0.5, 3]):
hdb.fit(X * scale)
plot(
X * scale,
hdb.labels_,
hdb.probabilities_,
ax=axes[idx],
parameters={"scale": scale},
)
# %%
# Multi-Scale Clustering
# ----------------------
# HDBSCAN is much more than scale invariant though -- it is capable of
# multi-scale clustering, which accounts for clusters with varying density.
# Traditional DBSCAN assumes that any potential clusters are homogeneous in
# density. HDBSCAN is free from such constraints. To demonstrate this we
# consider the following dataset
centers = [[-0.85, -0.85], [-0.85, 0.85], [3, 3], [3, -3]]
X, labels_true = make_blobs(
n_samples=750, centers=centers, cluster_std=[0.2, 0.35, 1.35, 1.35], random_state=0
)
plot(X, labels=labels_true, ground_truth=True)
# %%
# This dataset is more difficult for DBSCAN due to the varying densities and
# spatial separation:
#
# - If `eps` is too large then we risk falsely clustering the two dense
# clusters as one since their mutual reachability will extend
# clusters.
# - If `eps` is too small, then we risk fragmenting the sparser clusters
# into many false clusters.
#
# Not to mention this requires manually tuning choices of `eps` until we
# find a tradeoff that we are comfortable with.
fig, axes = plt.subplots(2, 1, figsize=(10, 8))
params = {"eps": 0.7}
dbs = DBSCAN(**params).fit(X)
plot(X, dbs.labels_, parameters=params, ax=axes[0])
params = {"eps": 0.3}
dbs = DBSCAN(**params).fit(X)
plot(X, dbs.labels_, parameters=params, ax=axes[1])
# %%
# To properly cluster the two dense clusters, we would need a smaller value of
# epsilon, however at `eps=0.3` we are already fragmenting the sparse clusters,
# which would only become more severe as we decrease epsilon. Indeed it seems
# that DBSCAN is incapable of simultaneously separating the two dense clusters
# while preventing the sparse clusters from fragmenting. Let's compare with
# HDBSCAN.
hdb = HDBSCAN().fit(X)
plot(X, hdb.labels_, hdb.probabilities_)
# %%
# HDBSCAN is able to adapt to the multi-scale structure of the dataset without
# requiring parameter tuning. While any sufficiently interesting dataset will
# require tuning, this case demonstrates that HDBSCAN can yield qualitatively
# better classes of clusterings without users' intervention which are
# inaccessible via DBSCAN.
# %%
# Hyperparameter Robustness
# -------------------------
# Ultimately tuning will be an important step in any real world application, so
# let's take a look at some of the most important hyperparameters for HDBSCAN.
# While HDBSCAN is free from the `eps` parameter of DBSCAN, it does still have
# some hyperparameters like `min_cluster_size` and `min_samples` which tune its
# results regarding density. We will however see that HDBSCAN is relatively robust
# to various real world examples thanks to those parameters whose clear meaning
# helps tuning them.
#
# `min_cluster_size`
# ^^^^^^^^^^^^^^^^^^
# `min_cluster_size` is the minimum number of samples in a group for that
# group to be considered a cluster.
#
# Clusters smaller than the ones of this size will be left as noise.
# The default value is 5. This parameter is generally tuned to
# larger values as needed. Smaller values will likely to lead to results with
# fewer points labeled as noise. However values which too small will lead to
# false sub-clusters being picked up and preferred. Larger values tend to be
# more robust with respect to noisy datasets, e.g. high-variance clusters with
# significant overlap.
PARAM = ({"min_cluster_size": 5}, {"min_cluster_size": 3}, {"min_cluster_size": 25})
fig, axes = plt.subplots(3, 1, figsize=(10, 12))
for i, param in enumerate(PARAM):
hdb = HDBSCAN(**param).fit(X)
labels = hdb.labels_
plot(X, labels, hdb.probabilities_, param, ax=axes[i])
# %%
# `min_samples`
# ^^^^^^^^^^^^^
# `min_samples` is the number of samples in a neighborhood for a point to
# be considered as a core point, including the point itself.
# `min_samples` defaults to `min_cluster_size`.
# Similarly to `min_cluster_size`, larger values for `min_samples` increase
# the model's robustness to noise, but risks ignoring or discarding
# potentially valid but small clusters.
# `min_samples` better be tuned after finding a good value for `min_cluster_size`.
PARAM = (
{"min_cluster_size": 20, "min_samples": 5},
{"min_cluster_size": 20, "min_samples": 3},
{"min_cluster_size": 20, "min_samples": 25},
)
fig, axes = plt.subplots(3, 1, figsize=(10, 12))
for i, param in enumerate(PARAM):
hdb = HDBSCAN(**param).fit(X)
labels = hdb.labels_
plot(X, labels, hdb.probabilities_, param, ax=axes[i])
# %%
# `dbscan_clustering`
# ^^^^^^^^^^^^^^^^^^^
# During `fit`, `HDBSCAN` builds a single-linkage tree which encodes the
# clustering of all points across all values of :class:`~cluster.DBSCAN`'s
# `eps` parameter.
# We can thus plot and evaluate these clusterings efficiently without fully
# recomputing intermediate values such as core-distances, mutual-reachability,
# and the minimum spanning tree. All we need to do is specify the `cut_distance`
# (equivalent to `eps`) we want to cluster with.
PARAM = (
{"cut_distance": 0.1},
{"cut_distance": 0.5},
{"cut_distance": 1.0},
)
hdb = HDBSCAN()
hdb.fit(X)
fig, axes = plt.subplots(len(PARAM), 1, figsize=(10, 12))
for i, param in enumerate(PARAM):
labels = hdb.dbscan_clustering(**param)
plot(X, labels, hdb.probabilities_, param, ax=axes[i])