Optics
- 1. OPTICS: Ordering Points To Identify the Clustering Structure Presented By: Rohit Paul
- 2. Disadvantages of DBSCAN Requires two user inputs(Eps and MinPts) Unable to determine variable density cluster OPTICS: Able to get variable density cluster Mainly requires one inputs (i.e, MinPts) Eps can be considered as ‘infinite’
- 3. Idea Creates an augmented ordering of the database representing its density-based clustering structure Help us gain a high level understanding of the way data is structured
- 4. Observation For a constant MinPts value, density-based clusters with higher density are completely contained in density-connected sets with respect to a lower density. Extend the DBSCAN algorithm such that several distance parameters are processed at the same time
- 5. OPTICS An infinite number of distance parameters eps’ which are smaller than a “generating distance” eps (i.e. 0 <= eps’ <= eps). Order is stored in which the objects are processed and the information which would be used by an extended DBSCAN algorithm to assign cluster memberships This information consists of only two values for each object: the core-distance and a reachability- distance
- 6. Terminology Core distance of an object p: The core-distance of an object p is simply the smallest distance eps’ between p and an object in its e- neighborhood such that p would be a core object with respect to eps’ if this neighbor is contained in Ne(p). Reachability-distance object p w.r.t. object o: Reachability-distance of an object p with respect to another object o is the smallest distance such that p is directly density-reachable from o if o is a core object
- 7. Algorithm FOR i FROM 1 TO SetOfObjects.size DO IF NOT Object.Processed THEN 1. neighbors := SetOfObjects.neighbors(Object, e); 2. Object.Processed := TRUE; 3. Object.reachability_distance := UNDEFINED; 4. Object.setCoreDistance(neighbors, e, MinPts); 5. OrderedFile.write(Object); 6. IF Object.core_distance <> UNDEFINED THEN OrderSeeds.update(neighbors, Object); WHILE NOT orderSeeds.empty() DO Repeat Step 1, 2, 4, 5 and 6
- 8. If reachability-distance of the current object Object is larger than the clustering-distance eps’ Object is not density-reachable from any of the objects which are located before the current object in the cluster-ordering. We look at the core-distance of Object and start a new cluster if Object is a core object with respect to eps’ and MinPts; otherwise, Object is assigned to NOISE If reachability-distance of the current object is smaller than eps’ Can simply assign this object to the current cluster because then it is density-reachable from a preceding core object in the cluster-ordering.
- 9. Reachability plot insensitive to input parameter • The smaller the Eps value, the more objects have an UNDEFINED reachability-distance • Lower values MinPts reachability-plot looks more jagged and higher value smoothen the curve.
- 10. Thank You