Note
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Clustering algorithm comparison¶
A comparison of several clustering algorithms on low-dimensional synthetic datasets, adapted to SPD matrices from [1]. The point of this example is to illustrate the nature of clustering of different algorithms, used with different metrics [2]. This should be taken with a grain of salt, as the intuition conveyed by these examples does not necessarily carry over to real datasets.
# Authors: Quentin Barthélemy
#
# License: BSD (3-clause)
from itertools import cycle, islice
from time import time
import matplotlib.pyplot as plt
import numpy as np
from pyriemann.clustering import (
Kmeans,
MeanShift,
GaussianMixture,
)
from pyriemann.datasets import make_matrices, make_gaussian_blobs
def plot_clusterers(metric):
fig = plt.figure(figsize=(12, 10))
fig.suptitle(f"Clustering algorithms with metric='{metric}'", fontsize=16)
i = 1
# iterate over datasets
for i_dataset, X in enumerate(datasets):
print(f"Dataset n°{i_dataset+1}")
x_min, x_max = X[:, 0, 0].min(), X[:, 0, 0].max()
y_min, y_max = X[:, 0, 1].min(), X[:, 0, 1].max()
z_min, z_max = X[:, 1, 1].min(), X[:, 1, 1].max()
# iterate over clusterers
for name, clt in zip(names, clusts):
clt.set_params(**{"metric": metric})
t0 = time()
clt.fit(X)
t1 = time() - t0
if hasattr(clt, "labels_"):
y_pred = clt.labels_.astype(int)
else:
y_pred = clt.predict(X)
print(f" {name}:\n training time={t1:.5f}")
colors = np.array(
list(
islice(
cycle(
[
"#377eb8",
"#ff7f00",
"#4daf4a",
"#f781bf",
"#a65628",
"#984ea3",
"#999999",
"#e41a1c",
"#dede00",
]
),
int(max(y_pred) + 1),
)
)
)
colors = np.append(colors, ["#000000"])
# plot
ax = plt.subplot(n_datasets, n_clusts, i, projection="3d")
ax.scatter(
X[:, 0, 0],
X[:, 0, 1],
X[:, 1, 1],
color=colors[y_pred]
)
if i_dataset == 0:
ax.set_title(name)
ax.set_xlim(x_min, x_max)
ax.set_ylim(y_min, y_max)
ax.set_zlim(z_min, z_max)
ax.set_xticks(())
ax.set_yticks(())
ax.set_zticks(())
if i_dataset <= 1:
ax.view_init(azim=-110)
if i_dataset == 2:
ax.view_init(elev=20, azim=40)
if i_dataset == 3:
ax.view_init(elev=5, azim=100, roll=0)
i += 1
plt.show()
Clustering and Datasets¶
names = [
"k-means\n2 clusters",
"k-means\n3 clusters",
"mean shift\nuniform kernel",
"mean shift\nnormal kernel",
"gaussian mixture\n3 clusters",
]
n_jobs = 4
clusts = [
Kmeans(n_clusters=2, n_jobs=n_jobs),
Kmeans(n_clusters=3, n_jobs=n_jobs),
MeanShift(kernel="uniform", n_jobs=n_jobs),
MeanShift(kernel="normal", n_jobs=n_jobs),
GaussianMixture(n_components=3),
]
n_clusts = len(clusts)
rs = np.random.RandomState(2025)
n_matrices, n_channels = 50, 2
datasets = [
np.concatenate([
make_matrices(
n_matrices, n_channels, "spd", rs,
evals_low=10, evals_high=14, eigvecs_mean=0.0, eigvecs_std=1.0,
),
make_matrices(
n_matrices, n_channels, "spd", rs,
evals_low=14, evals_high=18, eigvecs_mean=5.0, eigvecs_std=2.0,
)
]),
np.concatenate([
make_matrices(
n_matrices, n_channels, "spd", rs,
evals_low=4, evals_high=8, eigvecs_mean=0.0, eigvecs_std=0.5,
),
make_matrices(
n_matrices, n_channels, "spd", rs,
evals_low=9, evals_high=13, eigvecs_mean=2.0, eigvecs_std=1.0,
),
make_matrices(
n_matrices, n_channels, "spd", rs,
evals_low=14, evals_high=18, eigvecs_mean=5.0, eigvecs_std=2.0,
)
]),
make_gaussian_blobs(
2*n_matrices, n_channels, random_state=rs, n_jobs=4,
class_sep=5., class_disp=.5,
)[0],
make_gaussian_blobs(
2*n_matrices, n_channels, random_state=rs, n_jobs=4,
class_sep=2., class_disp=.5,
)[0]
]
n_datasets = len(datasets)
Clustering with affine-invariant Riemannian metric¶
plot_clusterers("riemann")
Dataset n°1
k-means
2 clusters:
training time=0.19248
k-means
3 clusters:
training time=0.15646
MeanShift bandwidth=0.178
mean shift
uniform kernel:
training time=0.37613
MeanShift bandwidth=0.178
mean shift
normal kernel:
training time=0.56284
gaussian mixture
3 clusters:
training time=0.34239
Dataset n°2
k-means
2 clusters:
training time=0.13500
k-means
3 clusters:
training time=0.17886
MeanShift bandwidth=0.384
mean shift
uniform kernel:
training time=0.83654
MeanShift bandwidth=0.384
mean shift
normal kernel:
training time=2.43664
gaussian mixture
3 clusters:
training time=0.68162
Dataset n°3
k-means
2 clusters:
training time=0.18522
k-means
3 clusters:
training time=0.52193
MeanShift bandwidth=0.837
mean shift
uniform kernel:
training time=1.02419
MeanShift bandwidth=0.837
mean shift
normal kernel:
training time=1.27609
gaussian mixture
3 clusters:
training time=0.67676
Dataset n°4
k-means
2 clusters:
training time=0.30173
k-means
3 clusters:
training time=0.59241
MeanShift bandwidth=0.810
mean shift
uniform kernel:
training time=0.98013
MeanShift bandwidth=0.810
mean shift
normal kernel:
training time=1.24276
gaussian mixture
3 clusters:
training time=0.41684
Clustering with Euclidean metric¶
plot_clusterers("euclid")
Dataset n°1
k-means
2 clusters:
training time=0.15995
k-means
3 clusters:
training time=0.03742
MeanShift bandwidth=2.449
mean shift
uniform kernel:
training time=0.16535
MeanShift bandwidth=2.449
mean shift
normal kernel:
training time=0.22860
gaussian mixture
3 clusters:
training time=0.02970
Dataset n°2
k-means
2 clusters:
training time=0.04298
k-means
3 clusters:
training time=0.03388
MeanShift bandwidth=3.290
mean shift
uniform kernel:
training time=0.19735
MeanShift bandwidth=3.290
mean shift
normal kernel:
training time=0.41245
/home/docs/checkouts/readthedocs.org/user_builds/pyriemann/checkouts/latest/pyriemann/clustering.py:849: UserWarning: EM convergence not reached
warnings.warn("EM convergence not reached")
gaussian mixture
3 clusters:
training time=0.16089
Dataset n°3
k-means
2 clusters:
training time=0.03535
k-means
3 clusters:
training time=0.06463
MeanShift bandwidth=2.257
mean shift
uniform kernel:
training time=0.36082
MeanShift bandwidth=2.257
mean shift
normal kernel:
training time=0.73927
gaussian mixture
3 clusters:
training time=0.04282
Dataset n°4
k-means
2 clusters:
training time=0.03586
k-means
3 clusters:
training time=0.06246
MeanShift bandwidth=1.552
mean shift
uniform kernel:
training time=0.48252
MeanShift bandwidth=1.552
mean shift
normal kernel:
training time=0.59518
gaussian mixture
3 clusters:
training time=0.12473
References¶
Total running time of the script: (0 minutes 19.129 seconds)