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Density based Clustering

Partitioning and hierarchical methods are designed to find spherical-shaped clusters. They often fail to find clusters of arbitrary shape.
The clusters can be found in arbitrary shape as dense region separated by sparse regions in the data space. The methods used in the density based are
  • DBSCAN (Density Based Spatial Clustering of Applications with Noise)
  • OPTICS (Ordering Points to Identify the Clustering Structure)
  • DENCLUE (Clustering Based on Density Distribution Functions)
DBSCAN method finds core objects that have dense neighborhoods. It connects core objects and their neighborhoods to form dense regions as clusters. A user-specified parameter ε > 0 is used to specify the radius of a neighborhood we consider for every object. The method uses a parameter, MinPts, which specifies the density threshold of dense regions. An object is a core object if the ε-neighborhood of the object contains at least MinPts objects.
All core objects can be identified with respect to the given parameters, ε and MinPts. The clustering task is therein reduced to using core objects and their neighborhoods to form clusters.
An object is density reachable from another object with respect to ε and MinPts in an object set if there is a chain of objects which are directly density reachable from the object with respect to ε and MinPts. The objects are density reachable to one another only if both are core objects. To connect core objects as well as their neighbors in a dense region, the method uses the notion of density-connectedness. The two objects are density connected with respect to ε and MinPts if there is an object in a set such that both objects are density reachable from the object with respect to ε and MinPts. 
The time complexity of DBSCAN is O(nlog n) if spatial index is used, otherwise O(n2).
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