Jason's Notebook

Mean-Shift Clustering

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INFO

A non-parametric, iterative clustering algorithm that does not require the pre-specification of the number of clusters.
Identifies dense areas in the feature space by shifting data points toward regions of higher density

  • Developed by: Yizong Cheng (1995)
  • Core Principle: Uses kernel density estimation to iteratively shift data points toward local maxima in the density function
  • Search Strategy:
    • Estimate density using a Gaussian kernel
    • Shift each point toward the mean of its neighborhood
    • Continue until points converge to stable positions

Workflow

  1. Initialization
    • Define bandwidth: radius for neighborhood density estimation
  2. Iterative Shifting
    • Update each point’s position based on local density gradients
    • Points converge to high-density regions, forming clusters

Code Example

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.cluster import MeanShift, estimate_bandwidth
from sklearn.datasets import make_blobs
 
# Generate synthetic customer data (spending, frequency)
np.random.seed(42)
X, _ = make_blobs(n_samples=300, centers=4, cluster_std=1.0, random_state=42)
 
# Estimate the optimal bandwidth
bandwidth = estimate_bandwidth(X, quantile=0.2, n_samples=100)
 
# Apply Mean-Shift clustering
ms = MeanShift(bandwidth=bandwidth)
ms.fit(X)
labels = ms.labels_
cluster_centers = ms.cluster_centers_
 
# Convert to DataFrame for analysis
df = pd.DataFrame(X, columns=["Spending", "Frequency"])
df["Cluster"] = labels
 
# Display cluster statistics
import ace_tools as tools
tools.display_dataframe_to_user(name="Mean-Shift Clustering Results", dataframe=df)
 
# Plot the clusters
plt.figure(figsize=(8, 6))
plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', marker='o', edgecolors='k', alpha=0.7)
plt.scatter(cluster_centers[:, 0], cluster_centers[:, 1], c='red', marker='X', s=200, label='Centroids')
plt.title('Mean-Shift Clustering of Customer Segments')
plt.xlabel('Spending')
plt.ylabel('Frequency')
plt.legend()
plt.show()

Advantages

  • Discovers the optimal number of clusters without prior specification
  • Detects arbitrary shaped clusters
  • Does not assume spherical cluster geometry
  • Avoids local minima due to non-reliance on initialization

Disadvantages

  • High computational complexity
  • Sensitive to bandwidth selection
  • May struggle with high-dimensional data

Graph View

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