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DBSCAN
Density-based clustering algorithm that groups sufficiently close points while marking isolated points in low-density regions as outliers.
Epsilon (ε)
Parameter defining the neighborhood radius around a point to determine if it belongs to a cluster, directly influencing clustering granularity.
MinPts
Threshold parameter defining the minimum number of points required in the ε-neighborhood for a point to be considered a core point.
Core Point
Central point of a cluster having at least MinPts points in its ε-neighborhood, serving as an anchor point to form dense clusters.
Border Point
Point located at the periphery of a cluster, not having enough neighbors to be a core point but being reachable from a core point.
Noise Point
Point not belonging to any cluster as it is neither a core point nor reachable from a core point, often considered an anomaly.
ε-Neighborhood
Set of points located at a distance less than or equal to ε from a given point, forming the basis of density calculation in DBSCAN.
Directly Density-Reachable
Relation where a point q is directly reachable from a core point p if q is in the ε-neighborhood of p.
Density-reachable
Transitive relation where a point is reachable from a core point through a chain of density-directly reachable points.
Density-connected
Symmetric relation where two points are connected if there exists a common core point from which they are both density-reachable.
OPTICS
Algorithm extending DBSCAN that produces a density-based clustering order, allowing extraction of clusters with varying densities.
HDBSCAN
Hierarchical variant of DBSCAN that builds a hierarchy of clusters with varying densities and automatically selects stable clusters.
R-tree index
Spatial indexing data structure optimizing neighbor search within ε radius, significantly accelerating DBSCAN on large datasets.
Curse of Dimensionality
Phenomenon where distance measure loses its meaning in high-dimensional spaces, affecting the performance of density-based algorithms.
Silhouette Score
Evaluation metric measuring intra-cluster cohesion and inter-cluster separation, used to optimize ε and MinPts parameters.
Arbitrary-shaped clusters
Major advantage of DBSCAN allowing detection of non-convex and complex-shaped clusters, unlike algorithms like K-means.
Anomaly Detection
Natural application of DBSCAN where points identified as noise correspond to anomalies or outliers in the data.
Spatial Partitioning
Process of dividing the data space into regions based on density, the foundation of how DBSCAN and similar algorithms work.
Neighborhood Graph
Graphical representation where nodes are points and edges connect points in the ε-neighborhood, used to visualize density structure.
Reachability Distance
Modified distance used in OPTICS and HDBSCAN that takes into account local density to order points based on their accessibility.
Core Distance
Minimum distance required for a point to become a core point, calculated as the distance to the MinPts-th nearest neighbor.