Local neighborhood
A local neighborhood is a set of elements considered near a specified element according to a defined spatial, topological, distance-based, or relational criterion.
Advanced Algorithms and Data Structures
An epsilon-neighborhood is the set of points within epsilon distance of a specified point.
- How it is used
- Defines which nearby points count when identifying DBSCAN core points and preserving their classifications across data shards.
- How deep it goes
- Works through the consequences of split neighborhoods and ε-wide shard overlap, without deriving a general neighborhood-search algorithm.
- Examples
- Illustrates extended grid cells and a four-cell MapReduce DBSCAN run with overlapping margins.
- What you can do after
- Apply it via MR-DBSCAN to design overlapping shards that retain boundary points’ neighbors for local clustering.
Read how Advanced Algorithms and Data Structures explains local neighborhood →
Data Without Labels
A neighborhood is the region around a point containing points at a specified distance from that point, represented as an n-sphere in n-dimensional space.
- How it is used
- Defines which observations count as nearby when density-based clustering identifies dense regions and separates sparse ones.
- How deep it goes
- Defines ε-neighborhood geometry, relates radius to point counts and density, and applies the definition to DBSCAN’s core-point threshold.
- Examples
- Uses a vector-space circle, connected core points, and Python plots of nearest-neighbor distances and clusters.
- What you can do after
- Apply it via scikit-learn’s NearestNeighbors and DBSCAN to inspect radius choices and cluster standardized observations.
Graph Neural Networks in Action
A node neighborhood is the set of nodes connected to a particular graph node, typically within a specified number of hops.
- How it is used
- Provides the graph-based window for convolution and the nearby feature context used to update node representations.
- How deep it goes
- Defines one-hop membership and explains order-independent aggregation, then shows configurable layers without deriving their mathematics.
- Examples
- Compares an image grid with a graph and configures aggregation in a two-layer GraphSAGE model.
- What you can do after
- Apply it via PyTorch Geometric SAGEConv to choose an aggregation and preserve neighbor context during masked training.
Read how Graph Neural Networks in Action explains local neighborhood →
Optimization Algorithms: AI techniques for design, planning, and control problems
The set of candidate solutions reachable from a current solution by permitted local moves.
- How it is used
- Supports tabu search by restricting each iteration to locally reachable candidate solutions.
- How deep it goes
- Defines neighborhoods through pairwise exchanges and counts candidates, then applies feasibility and objective evaluation.
- Examples
- Uses six-task permutations, pairwise exchanges, precedence diagrams, cycle time, workloads, and smoothing-index evaluations.
- What you can do after
- Apply it via tabu-search procedures to generate, filter, and evaluate candidate solutions for assembly-line balancing.
Related concepts
- graphletused by · A graphlet is a node position within a distinctly connected subgraph consisting of a specified number of nodes.
- graph machine learningused by · Graph machine learning comprises machine-learning methods that learn representations, predictions, or patterns from graph-structured data and relationships.
- pairwise exchangeimplemented by · A pairwise exchange is a neighborhood move that swaps the positions or assignments of two tasks.
- neural message passingused by · Neural message passing is a graph-learning technique that iteratively updates node representations by aggregating information from neighboring nodes.
- data aggregationuses · Data aggregation is the combination of multiple values, records, observations, or results into a consolidated or summarized output.
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