umap-learn（乌玛普学习）

UMAP-Learn

Overview

UMAP (Uniform Manifold Approximation and Projection) is a dimensionality reduction technique for visualization and general non-linear dimensionality reduction. Apply this skill for fast, scalable embeddings that preserve local and global structure, supervised learning, and clustering preprocessing.

Quick Start

Installation

# Via conda
conda install -c conda-forge umap-learn

# Via pip
pip install umap-learn

Basic Usage

UMAP follows scikit-learn conventions and can be used as a drop-in replacement for t-SNE or PCA.

import umap
from sklearn.preprocessing import StandardScaler

# Prepare data (standardization is essential)
scaled_data = StandardScaler().fit_transform(data)

# Method 1: Single step (fit and transform)
embedding = umap.UMAP().fit_transform(scaled_data)

# Method 2: Separate steps (for reusing trained model)
reducer = umap.UMAP(random_state=42)
reducer.fit(scaled_data)
embedding = reducer.embedding_  # Access the trained embedding

Critical preprocessing requirement: Always standardize features to comparable scales before applying UMAP to ensure equal weighting across dimensions.

Typical Workflow

import umap
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler

# 1. Preprocess data
scaler = StandardScaler()
scaled_data = scaler.fit_transform(raw_data)

# 2. Create and fit UMAP
reducer = umap.UMAP(
    n_neighbors=15,
    min_dist=0.1,
    n_components=2,
    metric='euclidean',
    random_state=42
)
embedding = reducer.fit_transform(scaled_data)

# 3. Visualize
plt.scatter(embedding[:, 0], embedding[:, 1], c=labels, cmap='Spectral', s=5)
plt.colorbar()
plt.title('UMAP Embedding')
plt.show()

Parameter Tuning Guide

UMAP has four primary parameters that control the embedding behavior. Understanding these is crucial for effective usage.

n_neighbors (default: 15)

Purpose: Balances local versus global structure in the embedding.

How it works: Controls the size of the local neighborhood UMAP examines when learning manifold structure.

Effects by value:

• Low values (2-5): Emphasizes fine local detail but may fragment data into disconnected components
• Medium values (15-20): Balanced view of both local structure and global relationships (recommended starting point)
• High values (50-200): Prioritizes broad topological structure at the expense of fine-grained details

Recommendation: Start with 15 and adjust based on results. Increase for more global structure, decrease for more local detail.

min_dist (default: 0.1)

Purpose: Controls how tightly points cluster in the low-dimensional space.

How it works: Sets the minimum distance apart that points are allowed to be in the output representation.

Effects by value:

• Low values (0.0-0.1): Creates clumped embeddings useful for clustering; reveals fine topological details
• High values (0.5-0.99): Prevents tight packing; emphasizes broad topological preservation over local structure

Recommendation: Use 0.0 for clustering applications, 0.1-0.3 for visualization, 0.5+ for loose structure.

n_components (default: 2)

Purpose: Determines the dimensionality of the embedded output space.

Key feature: Unlike t-SNE, UMAP scales well in the embedding dimension, enabling use beyond visualization.

Common uses:

• 2-3 dimensions: Visualization
• 5-10 dimensions: Clustering preprocessing (better preserves density than 2D)
• 10-50 dimensions: Feature engineering for downstream ML models

Recommendation: Use 2 for visualization, 5-10 for clustering, higher for ML pipelines.

metric (default: 'euclidean')

Purpose: Specifies how distance is calculated between input data points.

Supported metrics:

• Minkowski variants: euclidean, manhattan, chebyshev
• Spatial metrics: canberra, braycurtis, haversine
• Correlation metrics: cosine, correlation (good for text/document embeddings)
• Binary data metrics: hamming, jaccard, dice, russellrao, kulsinski, rogerstanimoto, sokalmichener, sokalsneath, yule
• Custom metrics: User-defined distance functions via Numba

Recommendation: Use euclidean for numeric data, cosine for text/document vectors, hamming for binary data.

Parameter Tuning Example

# For visualization with emphasis on local structure
umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, metric='euclidean')

# For clustering preprocessing
umap.UMAP(n_neighbors=30, min_dist=0.0, n_components=10, metric='euclidean')

# For document embeddings
umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, metric='cosine')

# For preserving global structure
umap.UMAP(n_neighbors=100, min_dist=0.5, n_components=2, metric='euclidean')

Supervised and Semi-Supervised Dimension Reduction

UMAP supports incorporating label information to guide the embedding process, enabling class separation while preserving internal structure.

Supervised UMAP

Pass target labels via the y parameter when fitting:

# Supervised dimension reduction
embedding = umap.UMAP().fit_transform(data, y=labels)

Key benefits:

• Achieves cleanly separated classes
• Preserves internal structure within each class
• Maintains global relationships between classes

When to use: When you have labeled data and want to separate known classes while keeping meaningful point embeddings.

Semi-Supervised UMAP

For partial labels, mark unlabeled points with -1 following scikit-learn convention:

# Create semi-supervised labels
semi_labels = labels.copy()
semi_labels[unlabeled_indices] = -1

# Fit with partial labels
embedding = umap.UMAP().fit_transform(data, y=semi_labels)

When to use: When labeling is expensive or you have more data than labels available.

Metric Learning with UMAP

Train a supervised embedding on labeled data, then apply to new unlabeled data:

# Train on labeled data
mapper = umap.UMAP().fit(train_data, train_labels)

# Transform unlabeled test data
test_embedding = mapper.transform(test_data)

# Use as feature engineering for downstream classifier
from sklearn.svm import SVC
clf = SVC().fit(mapper.embedding_, train_labels)
predictions = clf.predict(test_embedding)

When to use: For supervised feature engineering in machine learning pipelines.

UMAP for Clustering

UMAP serves as effective preprocessing for density-based clustering algorithms like HDBSCAN, overcoming the curse of dimensionality.

Best Practices for Clustering

Key principle: Configure UMAP differently for clustering than for visualization.

Recommended parameters:

• n_neighbors: Increase to ~30 (default 15 is too local and can create artificial fine-grained clusters)
• min_dist: Set to 0.0 (pack points densely within clusters for clearer boundaries)
• n_components: Use 5-10 dimensions (maintains performance while improving density preservation vs. 2D)

Clustering Workflow

import umap
import hdbscan
from sklearn.preprocessing import StandardScaler

# 1. Preprocess data
scaled_data = StandardScaler().fit_transform(data)

# 2. UMAP with clustering-optimized parameters
reducer = umap.UMAP(
    n_neighbors=30,
    min_dist=0.0,
    n_components=10,  # Higher than 2 for better density preservation
    metric='euclidean',
    random_state=42
)
embedding = reducer.fit_transform(scaled_data)

# 3. Apply HDBSCAN clustering
clusterer = hdbscan.HDBSCAN(
    min_cluster_size=15,
    min_samples=5,
    metric='euclidean'
)
labels = clusterer.fit_predict(embedding)

# 4. Evaluate
from sklearn.metrics import adjusted_rand_score
score = adjusted_rand_score(true_labels, labels)
print(f"Adjusted Rand Score: {score:.3f}")
print(f"Number of clusters: {len(set(labels)) - (1 if -1 in labels else 0)}")
print(f"Noise points: {sum(labels == -1)}")

Visualization After Clustering

# Create 2D embedding for visualization (separate from clustering)
vis_reducer = umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, random_state=42)
vis_embedding = vis_reducer.fit_transform(scaled_data)

# Plot with cluster labels
import matplotlib.pyplot as plt
plt.scatter(vis_embedding[:, 0], vis_embedding[:, 1], c=labels, cmap='Spectral', s=5)
plt.colorbar()
plt.title('UMAP Visualization with HDBSCAN Clusters')
plt.show()

Important caveat: UMAP does not completely preserve density and can create artificial cluster divisions. Always validate and explore resulting clusters.

Transforming New Data

UMAP enables preprocessing of new data through its transform() method, allowing trained models to project unseen data into the learned embedding space.

Basic Transform Usage

# Train on training data
trans = umap.UMAP(n_neighbors=15, random_state=42).fit(X_train)

# Transform test data
test_embedding = trans.transform(X_test)

Integration with Machine Learning Pipelines

from sklearn.svm import SVC
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import umap

# Split data
X_train, X_test, y_train, y_test = train_test_split(data, labels, test_size=0.2)

# Preprocess
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

# Train UMAP
reducer = umap.UMAP(n_components=10, random_state=42)
X_train_embedded = reducer.fit_transform(X_train_scaled)
X_test_embedded = reducer.transform(X_test_scaled)

# Train classifier on embeddings
clf = SVC()
clf.fit(X_train_embedded, y_train)
accuracy = clf.score(X_test_embedded, y_test)
print(f"Test accuracy: {accuracy:.3f}")

Important Considerations

Data consistency: The transform method assumes the overall distribution in the higher-dimensional space is consistent between training and test data. When this assumption fails, consider using Parametric UMAP instead.

Performance: Transform operations are efficient (typically <1 second), though initial calls may be slower due to Numba JIT compilation.

Scikit-learn compatibility: UMAP follows standard sklearn conventions and works seamlessly in pipelines:

from sklearn.pipeline import Pipeline

pipeline = Pipeline([
    ('scaler', StandardScaler()),
    ('umap', umap.UMAP(n_components=10)),
    ('classifier', SVC())
])

pipeline.fit(X_train, y_train)
predictions = pipeline.predict(X_test)

Advanced Features

Parametric UMAP

Parametric UMAP replaces direct embedding optimization with a learned neural network mapping function.

Key differences from standard UMAP:

• Uses TensorFlow/Keras to train encoder networks
• Enables efficient transformation of new data
• Supports reconstruction via decoder networks (inverse transform)
• Allows custom architectures (CNNs for images, RNNs for sequences)

Installation:

pip install umap-learn[parametric_umap]
# Requires TensorFlow 2.x

Basic usage:

from umap.parametric_umap import ParametricUMAP

# Default architecture (3-layer 100-neuron fully-connected network)
embedder = ParametricUMAP()
embedding = embedder.fit_transform(data)

# Transform new data efficiently
new_embedding = embedder.transform(new_data)

Custom architecture:

import tensorflow as tf

# Define custom encoder
encoder = tf.keras.Sequential([
    tf.keras.layers.InputLayer(input_shape=(input_dim,)),
    tf.keras.layers.Dense(128, activation='relu'),
    tf.keras.layers.Dense(64, activation='relu'),
    tf.keras.layers.Dense(2)  # Output dimension
])

embedder = ParametricUMAP(encoder=encoder, dims=(input_dim,))
embedding = embedder.fit_transform(data)

When to use Parametric UMAP:

• Need efficient transformation of new data after training
• Require reconstruction capabilities (inverse transforms)
• Want to combine UMAP with autoencoders
• Working with complex data types (images, sequences) benefiting from specialized architectures

When to use standard UMAP:

• Need simplicity and quick prototyping
• Dataset is small and computational efficiency isn't critical
• Don't require learned transformations for future data

Inverse Transforms

Inverse transforms enable reconstruction of high-dimensional data from low-dimensional embeddings.

Basic usage:

reducer = umap.UMAP()
embedding = reducer.fit_transform(data)

# Reconstruct high-dimensional data from embedding coordinates
reconstructed = reducer.inverse_transform(embedding)

Important limitations:

• Computationally expensive operation
• Works poorly outside the convex hull of the embedding
• Accuracy decreases in regions with gaps between clusters

Use cases:

• Understanding structure of embedded data
• Visualizing smooth transitions between clusters
• Exploring interpolations between data points
• Generating synthetic samples in embedding space

Example: Exploring embedding space:

import numpy as np

# Create grid of points in embedding space
x = np.linspace(embedding[:, 0].min(), embedding[:, 0].max(), 10)
y = np.linspace(embedding[:, 1].min(), embedding[:, 1].max(), 10)
xx, yy = np.meshgrid(x, y)
grid_points = np.c_[xx.ravel(), yy.ravel()]

# Reconstruct samples from grid
reconstructed_samples = reducer.inverse_transform(grid_points)

AlignedUMAP

For analyzing temporal or related datasets (e.g., time-series experiments, batch data):

from umap import AlignedUMAP

# List of related datasets
datasets = [day1_data, day2_data, day3_data]

# Create aligned embeddings
mapper = AlignedUMAP().fit(datasets)
aligned_embeddings = mapper.embeddings_  # List of embeddings

When to use: Comparing embeddings across related datasets while maintaining consistent coordinate systems.

Reproducibility

To ensure reproducible results, always set the random_state parameter:

reducer = umap.UMAP(random_state=42)

UMAP uses stochastic optimization, so results will vary slightly between runs without a fixed random state.

Common Issues and Solutions

Issue: Disconnected components or fragmented clusters

• Solution: Increase n_neighbors to emphasize more global structure

Issue: Clusters too spread out or not well separated

• Solution: Decrease min_dist to allow tighter packing

Issue: Poor clustering results

• Solution: Use clustering-specific parameters (n_neighbors=30, min_dist=0.0, n_components=5-10)

Issue: Transform results differ significantly from training

• Solution: Ensure test data distribution matches training, or use Parametric UMAP

Issue: Slow performance on large datasets

• Solution: Set low_memory=True (default), or consider dimensionality reduction with PCA first

Issue: All points collapsed to single cluster

• Solution: Check data preprocessing (ensure proper scaling), increase min_dist

Resources

references/

Contains detailed API documentation:

• api_reference.md: Complete UMAP class parameters and methods

Load these references when detailed parameter information or advanced method usage is needed.