Dimensionality reduction
Dimensionality reduction is the transformation of data into a representation with fewer dimensions while retaining selected information, structure, or relationships.
Data Without Labels
Dimensionality reduction is the transformation of data into fewer dimensions while retaining important structure or information.
- How it is used
- Prepares high-dimensional data for visualization, clustering, and machine-learning models by reducing variables or transforming them into fewer components.
- How deep it goes
- Works through manual choices and a Python SVD workflow, including cleaning, scaling, explained variance, and plotting; places supporting matrix mathematics in an appendix.
- Examples
- Uses retail transaction ratios, rainfall predictors, subscriber attributes, and an encoded mushroom dataset with explained-variance and class-colored plots.
- What you can do after
- Apply it via NumPy SVD and data-preparation tools to inspect explained variance and visualize a lower-dimensional dataset.
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Math and Architectures of Deep Learning
The reduction of the effective number of dimensions in a representation by a transformation such as a singular weight matrix.
- How it is used
- Uses PCA or learned latent vectors to simplify feature representations while preserving their main information.
- How deep it goes
- Derives geometric PCA intuition, recaps its SVD workflow, and implements projection and approximate reconstruction in PyTorch.
- Examples
- Illustrates correlated document terms, 2D points near a line, 3D points near a plane, and synthetic correlated versus uncorrelated data.
- What you can do after
- Apply it via PyTorch by centering data, using SVD, selecting principal directions, projecting inputs, and reconstructing approximations.
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Natural Language Processing in Action, Second Edition
Dimension reduction is the transformation of data into a representation with fewer features or dimensions while retaining relevant information.
- How it is used
- Turns high-dimensional text vectors into more compact topic representations for comparing documents and supporting semantic search.
- How deep it goes
- Defines the transformation through a geometric analogy and practical motivations, then names PCA without deriving its algorithm.
- Examples
- Uses a sofa’s 2D shadow, sparse TF–IDF matrices, stemmed word forms, and embeddings too large for pgvector.
- What you can do after
- Apply it via PCA when embeddings exceed pgvector’s dense-vector limit.
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Outlier Detection in Python
Dimensionality reduction is the transformation of data into fewer dimensions while retaining relevant information.
- How it is used
- Uses fewer dimensions to make many-feature outlier detection more tractable and enable low-dimensional visualization.
- How deep it goes
- Works through PCA transformations and timed detector comparisons, but does not develop the internals of t-SNE, UMAP, or auto-encoders.
- Examples
- Tests correlated and independent 100,000-row datasets with planted outliers, PCA component subsets, and six PyOD detectors.
- What you can do after
- Apply it via scikit-learn PCA and PyOD detectors, comparing outlier ranks and runtime before choosing components.
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Grokking Machine Learning
A technique that simplifies data by reducing or combining features while preserving as much information as possible.
- How it is used
- Simplifies data by combining similar features, sometimes as preprocessing before supervised learning.
- How deep it goes
- Defines feature reduction and illustrates fewer columns, but does not detail an algorithm.
- Examples
- Uses a housing dataset with many features to illustrate reducing features while retaining much of the information.
- What you can do after
- Understand how reducing columns can simplify a dataset while retaining much of its information.
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Graph Neural Networks in Action
Dimensionality reduction is the transformation of data into a representation with fewer numerical dimensions while retaining selected information or structure.
- How it is used
- Uses fewer dimensions to visualize graph embeddings and expose patterns for clustering or classification.
- How deep it goes
- Explains projection workflows, direct 2D alternatives, and autoencoder latent spaces, but defers technical theory and mathematical derivations.
- Examples
- Demonstrates Political Books embeddings, UMAP plots, direct two-dimensional Node2Vec, synthetic data, and graph autoencoder representations.
- What you can do after
- Apply it via UMAP or Node2Vec to create two-dimensional embedding visualizations and interpret relative clustering.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI
Dimensionality reduction transforms data with many variables into a lower-dimensional representation while attempting to preserve important structure or information.
- How it is used
- Uses lower-dimensional projections to validate tabular data and visually identify patterns, clusters, and anomalies.
- How deep it goes
- Explains projection choices, preprocessing, plotting, and interpretation caveats, but stops short of mathematical derivations.
- Examples
- Demonstrates a two-dimensional t-SNE scatter plot built from numeric and ordinal tabular features.
- What you can do after
- Diagnose patterns and anomalies by generating and interpreting low-dimensional exploratory plots.
Cyber Threat Hunting
Dimensionality reduction transforms data into a representation with fewer features while retaining important information.
- How it is used
- Prepares correlated features for supervised machine-learning models and makes reduced data easier to visualize.
- How deep it goes
- Explains PCA operationally through scaling, variance-based component selection, transformation, and two-dimensional plots, while deferring mathematics.
- Examples
- Uses DNS-derived FQDN features, Pearson-correlation heat maps, four principal components, and class-colored PC1–PC2 and PC3–PC4 plots.
- What you can do after
- Apply it via scikit-learn by scaling training features, selecting components from explained variance, and transforming data with PCA.
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Graph Algorithms for Data Science
Dimensionality reduction is a technique that represents data with fewer numerical dimensions while preserving selected structure or information.
- How it is used
- Supports automatic node representation and downstream machine-learning tasks.
- How deep it goes
- Explains feature compression through BMI and introduces node embeddings, but stops short of detailed algorithm internals.
- Examples
- Uses BMI, obesity assessment, adjacency matrices, and node2vec embeddings as concrete examples.
- What you can do after
- Apply it via node embedding models to produce compact node vectors for downstream machine-learning tasks.
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Delivering Machine Learning Projects: From design to deployment
Dimensionality reduction is the transformation of data into fewer dimensions while attempting to preserve informative structure.
- How it is used
- Supports exploratory analysis of unstructured data by making embedding distributions and relationships easier to inspect.
- How deep it goes
- Explains the visualization workflow and information-loss risk, but does not develop the underlying algorithms mathematically.
- Examples
- Uses embedded Shakespeare sentences, FAISS neighbor queries, and heatmaps comparing plays.
- What you can do after
- Evaluate unstructured-data structure by projecting embeddings or querying their nearest neighbors.
Inside Deep Learning: Math, Algorithms, Models
The process of mapping data from a higher-dimensional space into a lower-dimensional representation while retaining important structure.
- How it is used
- Compresses feature vectors for visualization and motivates autoencoders as alternatives to PCA.
- How deep it goes
- Defines PCA through encoder-decoder notation, weight sharing, reconstruction loss, and constraints, then extends the idea to multilayer bottleneck networks.
- Examples
- Uses D-dimensional feature vectors, bottleneck representations z, symmetric networks, and reconstruction-error thresholds.
- What you can do after
- Apply via PCA or an autoencoder, and diagnose unusual inputs through reconstruction error.
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Related concepts
- principal component analysisincludes · Principal component analysis is a linear dimensionality-reduction technique that transforms data into orthogonal components ordered by the variance they capture.
- UMAPincludes · UMAP, or Uniform Manifold Approximation and Projection, is a nonlinear manifold-learning technique that embeds high-dimensional data in a lower-dimensional space while preserving important neighborhood and structural relationships.
- t-SNEincludes · t-SNE is a nonlinear dimensionality-reduction technique that maps high-dimensional data to a lower-dimensional space while emphasizing local similarities or neighborhood relationships.
- curse of dimensionalityaddresses · The curse of dimensionality is the set of statistical, geometric, and computational difficulties that tend to increase as the number of dimensions grows.
- embeddinguses · A numerical vector representation of an item or input that encodes features or relationships useful for computational tasks.
- unsupervised learningkind of · Unsupervised learning is a machine-learning approach that discovers patterns, structure, or representations in data without labeled target outputs.
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