Mean-shift clustering

Mean-Shift is a density-based models: These models define clusters by their density in the data space. Areas with a high density of data points will become clusters, which are typically separated from one another by low-density areas.

The algorithm works by modeling the data points as a distribution function, where high-density areas (high concentration of data points) represent high peaks. Then, the general idea is to shift each data point until it reaches its nearest peak, which becomes a cluster.

Importing libraries and packages

# Mathematical operations and data manipulation
import pandas as pd

# Model
from sklearn.cluster import MeanShift
from sklearn.metrics import silhouette_score
from sklearn.metrics import calinski_harabasz_score

# Plotting
import matplotlib.pyplot as plt

# Warnings
import warnings

warnings.filterwarnings("ignore")

%matplotlib inline

Set paths

# Path to datasets directory
data_path = "./datasets"
# Path to assets directory (for saving results to)
assets_path = "./assets"

Loading dataset

dataset = pd.read_csv(f"{data_path}/circles.csv")

Exploring dataset

# Shape of the dataset
print("Shape of the dataset: ", dataset.shape)
# Head
dataset

Shape of the dataset:  (1500, 2)

	0	1
0	0.393992	-0.416376
1	0.528243	-0.828242
2	-0.740158	0.607730
3	-0.971016	0.316821
4	0.018693	-0.605288
...	...	...
1495	0.085197	-0.463028
1496	0.890820	0.003483
1497	0.223768	-0.419122
1498	0.221189	-0.510314
1499	0.544376	0.049358

1500 rows × 2 columns

plt.scatter(dataset.iloc[:, 0], dataset.iloc[:, 1])
plt.show()

# Using slicing to select the feature
plt.hist(dataset.iloc[:, 0])
plt.show()

<a id=”mean-shift>

Mean-Shift

# The mean-shift algorithm does not the number of clusters specified.
# Bandwith can be fine-tuned to get the best performance. Train the
# model with a bandwidth of 0.5 - chosen after trying out 0.1 and 0.9.
est_meanshift = MeanShift(bandwidth=0.5)
# Fit to the data
est_meanshift.fit(dataset)
# Using the model to assign a cluster to each data point
pred_meanshift = est_meanshift.predict(dataset)

# Plot the data points into clusters
plt.scatter(dataset.iloc[:, 0], dataset.iloc[:, 1], c=pred_meanshift)
plt.savefig(f"{assets_path}/circles-mean-shift.png", bbox_inches="tight")
plt.show()

Metrics

# Silhouette
meanshift_silhouette_score = silhouette_score(
    dataset, pred_meanshift, metric="euclidean"
)
print(meanshift_silhouette_score)

0.3705351315933256

# Calinski_harabasz
meanshift_calinski_harabasz_score = calinski_harabasz_score(
    dataset, pred_meanshift
)
print(meanshift_calinski_harabasz_score)

1305.1425653034062