Dimensionality reduction

As explained in Graph Algorithms for Data Science

Dimensionality reduction is a technique that represents data with fewer numerical dimensions while preserving selected structure or information.

Dimensionality reduction represents data with fewer features while retaining a strong correlation with the problem being analyzed. Node embedding models apply this idea to generate compact vectors for graph nodes automatically. section 9.0

BMI as a compact feature

Obesity could be described using height, weight, body-fat percentage, muscle content, and waist circumference. BMI compresses this information into one feature based on height and weight, reducing measurement needs while remaining an imperfect proxy: muscular rugby players may be classified as obese. section 9.0

In graph analysis, dimensionality reduction replaces handcrafted node features with automatically generated representation vectors. These embeddings can support downstream machine-learning tasks, while methods such as node2vec explore different structural and neighborhood-based representations. section 9.0

Figure 9.1 Body mass index chart

Use the BMI chart to connect a familiar single-feature estimate with the idea of compact data representation. section 9.0

How Graph Algorithms for Data Science covers it

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 it assumes

Builds from vector representations and handcrafted node features before introducing automatically generated embeddings.

What you can do after

Apply it via node embedding models to produce compact node vectors for downstream machine-learning tasks.

How it connects

Connects dimensionality reduction with feature engineering, node embeddings, node2vec, and downstream machine learning.

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Also explained in

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  Inside Deep Learning: Math, Algorithms, ModelsThe process of mapping data from a higher-dimensional space into a lower-dimensional representation while retaining important structure.

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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.
• unsupervised learningkind of · Unsupervised learning is a machine-learning approach that discovers patterns, structure, or representations in data without labeled target outputs.
• embeddinguses · A numerical vector representation of an item or input that encodes features or relationships useful for computational tasks.

This explainer was generated by Manning's knowledge graph from the text of Graph Algorithms for Data Science. The section links point to the parts of the book it draws on.