density based method and expectation maximization
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This document discusses density-based clustering algorithms DBSCAN and OPTICS. DBSCAN clusters points based on density connectivity, defining clusters as areas of high density connected by chains of points with smaller neighborhoods. It directly assigns points to clusters or noise. OPTICS produces a special ordering of points based on density, representing the intrinsic clustering structure without predefined number of clusters. It extends DBSCAN to process points in a specific order based on lowest density reachability.
density based method and expectation maximization
- 1. k.Sivapriya Msc(IT) Nadar saraswathi college of arts and science
- 2. Density based methods Clusters – dense regions of objects Low density regions – Noise DBSCAN Density Based Spatial Clustering of Applications with Noise OPTICS Ordering Points To Identify the Clustering Structure DENCLUE DEN sity Based CLU stEring
- 3. DBSCAN Cluster – maximal set of density connected points Grows regions with sufficiently high density into clusters e-neighborhood MinPts and Core object Directly Density Reachable An object p is directly density reachable from object q if p is within the e-neighborhood of q and q is a core Object
- 4. DBSCAN Density Reachable An object p is density reachable from q, if there is a chain of objects p1, …pn, p1=q and pn=p such that pi+1 is directly density reachable from pi
- 5. Continue….. Density Connected: An object p is density connected to object q if there is an object o such that both p and q are density reachable from o.
- 6. Conti….. Arbitrarily select a point p Retrieve all points density-reachable from p If p is a core point, a cluster is formed. If p is a border point, no points are density-reachable from p, then DBSCAN visits the next point of the database. Continue the process until all of the points have been processed. Complexity : O(n log n) / O(n2)
- 7. OPTICS: A Cluster-OrderingMethod OPTICS: Ordering Points To Identify the Clustering Structure Produces a special order of the database with respect to its density-based clustering structure Good for both automatic and interactive cluster analysis, including finding intrinsic clustering structure Can be represented graphically or using visualization techniques
- 8. OPTICS In DBSCAN, for a constant MinPts value, density based clusters with respect to a higher density (lower value of e) are completely contained in lower density sets. DBSCAN is extended so that Objects are processed in a specific order. Selects an object that is density-reachable with respect to loweste value Core distance of an object p : smallest e’ value that makes {p} a core object Reachability distance of an object q with respect to p = max (core-distance of p, d(p,q))8