OPTICS: Ordering Points To Identify Cluster Structure. A variable density clustering structure.

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