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
uv 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
scaled_data = StandardScaler().fit_transform(data)
embedding = umap.UMAP().fit_transform(scaled_data)
reducer = umap.UMAP(random_state=42)
reducer.fit(scaled_data)
embedding = reducer.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
scaler = StandardScaler()
scaled_data = scaler.fit_transform(raw_data)
reducer = umap.UMAP(
n_neighbors=15,
min_dist=0.1,
n_components=2,
metric='euclidean',
random_state=42
)
embedding = reducer.fit_transform(scaled_data)
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
umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, metric='euclidean')
umap.UMAP(n_neighbors=30, min_dist=0.0, n_components=10, metric='euclidean')
umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, metric='cosine')
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:
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:
semi_labels = labels.copy()
semi_labels[unlabeled_indices] = -1
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:
mapper = umap.UMAP().fit(train_data, train_labels)
test_embedding = mapper.transform(test_data)
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
scaled_data = StandardScaler().fit_transform(data)
reducer = umap.UMAP(
n_neighbors=30,
min_dist=0.0,
n_components=10,
metric='euclidean',
random_state=42
)
embedding = reducer.fit_transform(scaled_data)
clusterer = hdbscan.HDBSCAN(
min_cluster_size=15,
min_samples=5,
metric='euclidean'
)
labels = clusterer.fit_predict(embedding)
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
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)
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
trans = umap.UMAP(n_neighbors=15, random_state=42).fit(X_train)
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
X_train, X_test, y_train, y_test = train_test_split(data, labels, test_size=0.2)
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)
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)
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:
uv pip install umap-learn[parametric_umap]
Basic usage:
from umap.parametric_umap import ParametricUMAP
embedder = ParametricUMAP()
embedding = embedder.fit_transform(data)
new_embedding = embedder.transform(new_data)
Custom architecture:
import tensorflow as tf
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)
])
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)
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
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()]
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
datasets = [day1_data, day2_data, day3_data]
mapper = AlignedUMAP().fit(datasets)
aligned_embeddings = mapper.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.
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