# Density-Based Spatial Clustering of Applications with Noise

## Details

`= {X`

`x`

_{1}= (

`x`

_{11}, ...,

`x`

_{1p}), ...,

`x`

_{n}= (

`x`

_{n1}, ...,

`x`

_{np})} of

`n`

`-dimensional feature vectors (further referred as observations), a positive floating-point number epsilon and a positive integerp`

`, the problem is to get clustering assignments for each input observation, based on the definitions below [Ester96]:minObservations`

- An observation
is called core observation if at leastxinput observations (includingminObservations) are within distancexfrom observationepsilon;x - An observation
is directly reachable fromyifxis within distanceyfrom core observationepsilon. Observations are only said to be directly reachable from core observations.x - An observation
is reachable from observationyif there is a pathxx_{1}, ...,x_{m}withx_{1}=andxx_{m}=, where eachyx_{i+1}is directly reachable fromx_{i}. This implies that all observations on the path must be core observations, with the possible exception of.y - All observations not reachable from any other observation are noise observations.
- Two observations
andxis considered to be in the same cluster if there is a core observationy, thatzandxare reachable fromy.z