Distance
Distance is a measure of separation between points or entities in a defined space or context.
Data Without Labels
A distance metric is a distance function that satisfies the metric-space properties, including nonnegativity, symmetry, and the triangle inequality.
- How it is used
- Measures similarity for clustering and helps determine centroid assignments, hierarchical merges, and DBSCAN neighborhoods.
- How deep it goes
- Defines three distance measures with coordinate formulas and applies them in clustering workflows, without developing formal metric-space properties.
- Examples
- Uses two-point coordinate formulas, visual distance comparisons, and SciPy dendrograms with varied linkage rules and cutoffs.
- What you can do after
- Apply it via SciPy hierarchical clustering to compare distance settings and linkage rules, then inspect how a cutoff changes the groups.
Advanced Algorithms and Data Structures
A distance function is a function that assigns a path-cost contribution or distance value to an edge or other argument.
- How it is used
- Supplies comparison values for nearest-neighbor search and clustering, or edge-cost contributions for graph pathfinding.
- How deep it goes
- Works through threshold tests and A* parameter choices, while distinguishing Euclidean requirements from an SS-tree’s more general metric requirements.
- Examples
- Uses warehouse selection, price-and-rating points, canopy thresholds, SS-tree bounding spheres, and weighted versus unit-cost graph edges.
- What you can do after
- Apply it via nearest-neighbor queries, clustering thresholds, SS-tree sphere tests, or an A* edge-cost argument.
Read how Advanced Algorithms and Data Structures explains distance →
Outlier Detection in Python
A function that quantifies dissimilarity or separation between observations in a data space.
- How it is used
- Uses pairwise separation to identify unusual records and represent divergence between related time series.
- How deep it goes
- Compares several distance measures and mixed-data weighting, while cautioning that high dimensionality can undermine distance-based detection.
- Examples
- Illustrates a four-dimensional point unusual in one feature and air-quality series compared through pairwise differences.
- What you can do after
- Evaluate/understand it: compare distance measures and recognize when scaling, mixed-data choices, or dimensionality may affect results.
Natural Language Processing in Action, Second Edition
A distance metric is a function that quantifies dissimilarity between objects while satisfying the mathematical properties of a metric.
- How it is used
- Uses distances between text and feature vectors to compare documents, assess topic representations, and support tasks such as spelling correction.
- How deep it goes
- Names common distance measures and explains vector comparisons, noting that LSA may lose fine-grained proximity.
- Examples
- Contrasts “good” with “okay” and “bad” with “bag,” then compares LSA topic-vector distances with TF–IDF distances.
- What you can do after
- Evaluate whether topic vectors retain document relationships by comparing their distances with those in a higher-dimensional TF–IDF representation.
Read how Natural Language Processing in Action, Second Edition explains distance →
Math for Web Design
Distance is a numerical measure of the separation between two points or geometric objects.
- How it is used
- Drives pointer, touch, animation, and canvas interactions by measuring separation between coordinates.
- How deep it goes
- Explains Pythagorean calculations and applies normalized, clamped, and radius-bounded distances in JavaScript.
- Examples
- Uses hover tilt, a click-chaser dot, photo pinch zoom, and donut-chart slice hit detection.
- What you can do after
- Apply it via JavaScript to normalize hover effects, animate toward targets, scale touch content, and test radial bounds.
Architecture Modernization: Socio-technical alignment of software, strategy, and structure
Distance is the amount of technical and organizational coordination required for related parts to implement a change together.
- How it is used
- Assess the coordination cost of coupling as one factor in estimating its overall pain.
- How deep it goes
- Defines organizational and technical distance and illustrates a scale from variables in one function to separate microservices.
- Examples
- Contrasts variables in one function with classes across codebases, and teams with differing managers or office locations.
- What you can do after
- Evaluate coupling costs by assessing coordination distance alongside strength and volatility.
Geometry for Programmers
Distance is a nonnegative measure of separation between points or between a point and a geometric set.
- How it is used
- Deploys scalar distance fields to describe geometric separation, planes, segments, rectangles, and enclosed shapes.
- How deep it goes
- Explains geometric derivations and Python implementations for points, lines, segments, planes, and rectangles, stopping short of mesh-wide construction.
- Examples
- Uses point-to-plane geometry, a disk SDF, point-to-point and point-to-segment Python functions, and a rectangular SDF.
- What you can do after
- Build it from scratch using vector products, projections, endpoint tests, and edge signs to compute basic distance fields.
Machine Learning Platform Engineering
A distance metric is a function that quantifies separation between vectors in a mathematical space.
- How it is used
- Uses vector distances to find chunks near a query vector during RAG retrieval.
- How deep it goes
- Names L2, cosine, and inner product, and explains cosine’s focus on semantic direction without deriving the metrics.
- Examples
- Uses a query vector and nearby document-chunk vectors to illustrate retrieval, and contrasts cosine with magnitude-sensitive comparison.
- What you can do after
- Evaluate retrieval choices by considering supported distance metrics and cosine’s emphasis on semantic direction.
Read how Machine Learning Platform Engineering explains distance →
Classic Computer Science Problems in Swift: Essential techniques for practicing programmers
A measure of separation between locations or points in a feature space.
- How it is used
- Tracks accumulated route costs to find shortest paths from a starting vertex through a weighted graph.
- How deep it goes
- Explains initialization, priority-queue exploration, and shorter-route updates through a Swift implementation.
- Examples
- Uses a city graph to calculate distances from Los Angeles and trace a route to Boston.
- What you can do after
- Apply Dijkstra’s algorithm to compute shortest distances and recover paths in a weighted graph.
Machine Learning System Design
A function that assigns a numerical measure of separation or dissimilarity between mathematical objects or representations.
- How it is used
- Combines retrieval distances and other signals into a unified relevance score for photo search.
- How deep it goes
- Contrasts a simple sum with a weighted sum, but does not detail how to choose or train the weights.
- Examples
- Combines query-to-image and query-to-description distances with user and document features in a photo-search score.
- What you can do after
- Evaluate whether a simple sum or weighted sum should combine retrieval distances and other features.
Related concepts
- mahalanobis distanceincludes · Mahalanobis distance is a covariance-adjusted measure of separation between observations or between an observation and a reference distribution.
- Euclidean distanceincludes · Euclidean distance is the straight-line distance between two points in Euclidean space, calculated as the square root of the sum of squared differences between corresponding coordinates.
- similarity metricmeasures · A similarity measure is a rule that quantifies or characterizes how alike two objects or representations are according to selected properties.
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