UMAP dimensionality reduction. Fast nonlinear manifold learning for 2D/3D visualization, clustering preprocessing (HDBSCAN), supervised/parametric UMAP, for high-dimensional data.
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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.
uv pip install umap-learn
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.
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()
UMAP has four primary parameters that control the embedding behavior. Understanding these is crucial for effective usage.
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:
Recommendation: Start with 15 and adjust based on results. Increase for more global structure, decrease for more local detail.
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:
Recommendation: Use 0.0 for clustering applications, 0.1-0.3 for visualization, 0.5+ for loose structure.
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:
Recommendation: Use 2 for visualization, 5-10 for clustering, higher for ML pipelines.
Purpose: Specifies how distance is calculated between input data points.
Supported metrics:
Recommendation: Use euclidean for numeric data, cosine for text/document vectors, hamming for binary data.
# 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')
UMAP supports incorporating label information to guide the embedding process, enabling class separation while preserving internal structure.
Pass target labels via the y parameter when fitting:
# Supervised dimension reduction
embedding = umap.UMAP().fit_transform(data, y=labels)
Key benefits:
When to use: When you have labeled data and want to separate known classes while keeping meaningful point embeddings.
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.
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 serves as effective preprocessing for density-based clustering algorithms like HDBSCAN, overcoming the curse of dimensionality.
Key principle: Configure UMAP differently for clustering than for visualization.
Recommended parameters:
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)}")
# 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.
UMAP enables preprocessing of new data through its transform() method, allowing trained models to project unseen data into the learned embedding space.
# 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)
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}")
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)
Parametric UMAP replaces direct embedding optimization with a learned neural network mapping function.
Key differences from standard UMAP:
Installation:
uv 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:
When to use standard UMAP:
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:
Use cases:
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)
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.
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.
Issue: Disconnected components or fragmented clusters
n_neighbors to emphasize more global structureIssue: Clusters too spread out or not well separated
min_dist to allow tighter packingIssue: Poor clustering results
Issue: Transform results differ significantly from training
Issue: Slow performance on large datasets
low_memory=True (default), or consider dimensionality reduction with PCA firstIssue: All points collapsed to single cluster
min_distContains detailed API documentation:
api_reference.md: Complete UMAP class parameters and methodsLoad these references when detailed parameter information or advanced method usage is needed.
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Set up and use 1Password CLI (op). Use when installing the CLI, enabling desktop app integration, signing in (single or multi-account), or reading/injecting/running secrets via op.
CLI to manage emails via IMAP/SMTP. Use `himalaya` to list, read, write, reply, forward, search, and organize emails from the terminal. Supports multiple accounts and message composition with MML (MIME Meta Language).