Jason's Notebook

Uniform Manifold Approximation and Projection (UMAP)

2 min read

INFO

State-of-the-art dimensionality reduction technique for visualizing high-dimensional data while preserving its structure

  • Developed by: Leland McInnes, John Healy, and James Melville (2018)
  • Core Principle: Uses topological data analysis and manifold learning to construct a high-dimensional graph and optimize a low-dimensional representation
  • Search Strategy:
    • Build a fuzzy topological graph from high-dimensional data
    • Optimize a low-dimensional graph to approximate the original structure
    • Preserves both global and local relationships

Workflow

  1. Graph Construction
    • Define number of neighbors and minimum distance
    • Build high-dimensional graph representing data topology
  2. Low-Dimensional Optimization
    • Embed data in 2D or 3D space
    • Optimize layout using stochastic gradient descent

Code Example

import numpy as np
import pandas as pd
import umap
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.preprocessing import StandardScaler
 
# Generate synthetic customer data
np.random.seed(42)
X, y = make_classification(n_samples=500, n_features=10, n_classes=4, n_informative=5, random_state=42)
 
# Standardize the data
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
 
# Apply UMAP
umap_reducer = umap.UMAP(n_components=2, random_state=42)
X_umap = umap_reducer.fit_transform(X_scaled)
 
# Convert results to DataFrame
df_umap = pd.DataFrame(X_umap, columns=['UMAP1', 'UMAP2'])
df_umap['Cluster'] = y
 
# Plot the UMAP results
plt.figure(figsize=(10, 6))
scatter = plt.scatter(df_umap['UMAP1'], df_umap['UMAP2'], c=df_umap['Cluster'], cmap='viridis', alpha=0.7)
plt.colorbar(scatter, label="Cluster")
plt.xlabel('UMAP Dimension 1')
plt.ylabel('UMAP Dimension 2')
plt.title('UMAP Projection of Customer Data')
plt.show()

Advantages

  • Preserves local and global structure in high-dimensional data
  • Computationally efficient and scalable
  • Useful as a preprocessing step for clustering
  • Supports both supervised and unsupervised learning

Disadvantages

  • Highly sensitive to hyperparameters
    • Number of neighbors
    • Minimum distance
  • Does not provide explicit feature importance or variance explained

Graph View

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