This document discusses DBSCAN (Density-Based Spatial Clustering of Applications with Noise), a density-based clustering algorithm. DBSCAN groups together closely packed points considered core points, and separates clusters based on density rather than assigning points to predefined clusters. It requires two parameters, epsilon which defines a neighborhood distance, and MinPts specifying the minimum number of points required to form a dense region. Points are classified as core, border or noise based on their epsilon-neighborhood. DBSCAN forms clusters by linking core points that are density-reachable from each other, and identifies outliers as noise points not belonging to any cluster.

1. Presented by –
Rohit Paul
Density-Based Clustering Algorithm

2. Disadvantages of Partitioning
Method
 Choosing k manually
 Clustering data of varying sizes and density
 Sensitive to outliers
Figure 2
Figure 1

3. Density-based Method
 Cluster in a data space is a contiguous region of
high point density
 Separated by lower density of points
 Density within the areas of noise is assumed to
be lower

4. DBSCAN
 Density Based Spatial Clustering of
Applications with Noise
 How is the density estimated?
 Estimates the density by counting the number
of points in a fixed-radius neighborhood
 KEY IDEA: For each point of a cluster the
neighborhood of a given radius has to contain
at least a minimum number of points
 Two input parameters required:
 Epsilon(ε)
 MinPts

5. ε-Neighborhood: Objects within a radius ε from
an object
Three types of points based on ε-Neighborhood:
 Core Point
 Border Point
 Noise Point

6. Terminology used:
 Directly density-reachable
o A point q is directly density-reachable from a
core point p if q is within the Eps-neighborhood
of p.
 Density-reachable
o A point q is density reachable
from p if there are a set of core
points leading from p to q.

7.  Density-connected
o Two points p and q are density connected if
there are a core point o, such that both p and q
are density reachable from o

8.  A cluster satisfy the following conditions:
 If p be a core point and the set of all point
which are density-reachable from p be O.
Then, this set O is a cluster with respect to
Eps and Minpts.
 For all p and q in cluster C, p is density-
connected to q with respect to Eps and
Minpts.
 Noise, a set of points which do not belongs to
any clusters

9.  Pseudo code of DBSCAN Algorithm

10. Scikit-learn implementation

11. Reference
 https://developers.google.com/machine-
learning/clustering/algorithm/advantages-
disadvantages
 https://towardsdatascience.com/dbscan-
clustering-explained-97556a2ad556
 https://scikit-
learn.org/stable/modules/generated/sklearn.clust
er.DBSCAN.html
 Martin Ester, Hans-Peter Kriegel, J¨org Sander,
and Xiaowei Xu. A density-based algorithm for
discovering clusters in large spatial databases
with noise.

12. Thank You