umap-learn — Снижение размерности данных с сохранением структуры

--- name: umap-learn description: UMAP dimensionality reduction. Fast nonlinear manifold learning for 2D/3D visualization, clustering preprocessing (HDBSCAN), supervised/parametric UMAP, for high-dimensional data. license: BSD-3-Clause license metadata: skill-author: K-Dense Inc. --- # 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 ```bash 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. ```python 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 ```python 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 ```python # 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: ```python # 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: ```python # 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: ```python # 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 ```python 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 ```python # 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 ```python # 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 ```python 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: ```python 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:** ```bash uv pip install umap-learn[parametric_umap] # Requires TensorFlow 2.x ``` **Basic usage:** ```python 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:** ```python 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:** ```python 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:** ```python 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): ```python 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: ```python 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.