Dimension
A dimension is an independent coordinate, measurable axis, or descriptive attribute used to represent, locate, or analyze something.
D3.js in Action, Third Edition
A chart axis is a reference line with a scale, ticks, and often labels that communicates values or categories in a chart.
- How it is used
- Provides readable references for values and categories in line charts, histograms, scatterplots, and other visualizations.
- How deep it goes
- Builds axes from scales, positions and formats them, and also manually renders their SVG lines, ticks, and labels in React.
- Examples
- Uses temperature by month, salary histograms, salary box plots, and retention-versus-user-count scatterplots.
- What you can do after
- Build it from scratch with D3 generators or React SVG components, placing and formatting bottom and left axes.
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Advanced Algorithms and Data Structures
A dimension is an independent coordinate axis or degree of freedom needed to specify a point in a space.
- How it is used
- Organizes points and similarity data by representing each entry across multiple coordinate axes.
- How deep it goes
- Explains coordinate representation and partitioning consequences, then applies dimensionality to k-d tree deletion and SS-tree structures.
- Examples
- Uses ℝ², complex numbers, Cartesian-plane partitions, k-d tree points, and SS-tree k-dimensional tuples.
- What you can do after
- Evaluate how ignoring coordinates affects spatial partitioning and represent dimensionality in multidimensional index structures.
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Everyday Data Visualization
The blue-yellow axis is a color-space dimension whose opposing directions represent blue and yellow.
- How it is used
- Supports selecting and tweaking visualization color sets through CIELAB coordinates.
- How deep it goes
- Defines b* by direction and common range, without deriving its underlying mathematics.
- Examples
- Compares CIELAB color-space slices at L* = 75 and L* = 25.
- What you can do after
- Apply it to tweak colors toward blue or yellow when working across color spaces.
Build Python Web Apps with Streamlit
A dimension is a categorical or descriptive attribute by which data can be grouped, filtered, or analyzed.
- How it is used
- Uses dimensions to group, filter, and compare dashboard metrics across products, demographics, geography, and time.
- How deep it goes
- Explains dimensions through dashboard requirements and grouped chart data, then stops short of broader data-modeling theory.
- Examples
- Demonstrates product, category, segment, gender, age group, state, and date using sales-dashboard CSV rows and pie-chart groupings.
- What you can do after
- Apply it via pandas grouping to prepare dimension-level values for Plotly and Streamlit dashboard charts.
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Grokking AI Algorithms, Second Edition
Embedding size is the number of numerical dimensions in each learned vector representation.
- How it is used
- Uses dimension to describe feature coordinates, search-space complexity, and Transformer embedding width.
- How deep it goes
- Explains dimensions through concrete examples and defines embedding width, but does not detail vector operations or representation learning.
- Examples
- Illustrates dimension with pepper attributes, diamond measurements, and toy and real-world Transformer widths.
- What you can do after
- Evaluate embedding width and recognize how added features expand datasets or optimization search spaces.
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Math for Web Design
An axis is a reference direction in a coordinate system along which a component or position is measured.
- How it is used
- Explains how CSS and JavaScript measure positions, size elements, place grid content, and represent colors.
- How deep it goes
- Defines axes through viewport, grid, color, and vector examples, but stops short of a general mathematical treatment.
- Examples
- Uses viewport positioning, CSS Grid cells, LAB color axes, viewport-sized heroes, and two-dimensional movement vectors.
- What you can do after
- Apply it via CSS and JavaScript to reason about positions, responsive sizes, grid placement, colors, and movement.
Math and Architectures of Deep Learning
The number of independent coordinates in an input space, used here to distinguish one-dimensional from two-dimensional constructions.
- How it is used
- Frames vectors, model inputs, outputs, and geometric transformations as points in spaces of varying dimension.
- How deep it goes
- Defines dimensions geometrically and extends them to hyperellipses, stopping short of a broader dimensionality treatment.
- Examples
- Uses plane coordinates, a page-corner vector, and a two-dimensional hyperellipse implemented with PyTorch.
- What you can do after
- Evaluate/understand how coordinate counts determine vector spaces and how two-dimensional constructions extend to multiple dimensions.
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Data Without Labels
A dimension is an independent feature or coordinate axis describing each observation in a data representation.
- How it is used
- Supports clustering and dimensionality reduction by representing observations with manageable numerical or derived features.
- How deep it goes
- Explains dimension reduction through selection, mathematical transformation, categorical encoding, and worked variable-combination formulas.
- Examples
- Uses city categories, retail transactions, and monthly telecom call minutes to demonstrate expanded, combined, and aggregated dimensions.
- What you can do after
- Apply selection, encoding, aggregation, and derived-variable construction to reduce or restructure dataset dimensions.
Related concepts
- coordinate systempart of · A coordinate system is a framework for specifying the positions of points or other geometric entities using numerical coordinates relative to defined references, such as an origin and axes.
- embeddingused by · A numerical vector representation of an item or input that encodes features or relationships useful for computational tasks.
- visualizationpart of · Visualization is the representation of data, information, or concepts in visual form to support inspection, interpretation, analysis, or communication.
- hyperplaneincludes · A hyperplane is a flat affine subspace with dimension one less than its ambient space, capable of dividing that space into regions.
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