PWARX Model Identification Based on Clustering Approach - Complex System Modelling and Control Through Intelligent Soft Computations - page 171

reachable from q. The objects p and q are said to be density-connected if there exist
an object g that both p and q are density-reachable from.
The DBSCAN algorithm de

ne then a cluster as the set of objects in a data set
that are density-connected to a particular core object. Any object that is not part of a
cluster is categorized as noise. For a given data set S

N
k¼1 ,

¼ hfg e and MinPts as

inputs, the e -neighborhood of a point h i is de ned as:

e

N e ðh i Þ ¼ h j 2 S ; h i h j ð 17 Þ

The DBSCAN constructs clusters by checking the e -neighborhood of each object

in the data set. If the cardinal of the -neighborhood (denoted by cN e ) of an object

h k contains more than MinPts, a new cluster is created having

e

h k as core. The
DBSCAN then iteratively collects directly density-reachable objects from these
core objects. The process terminates when no new objects can be added to any
cluster. The main steps of this algorithm can be summarized as follows:

Algorithm 2: DBSCAN algorithm
Data : Define the input parameters:

N
k =1

S = {ʸ k } , MinPts and

Main steps :
for k=1:N do
if

ʸ k is not in a cluster then
Compute N

( ʸ k )

if <MinPts then

Mark ʸ k as noise
else cluster-label=cluster-label+1
for j=1:cN ( ʸ k ) do
Mark all point in

cN ( ʸ k )

N ( ʸ k ) with the current cluster label

end
Lend N ( ʸ k ) to the Seed list L S =[ L S N ( ʸ k )]

while L S is not empty do
ʸ r = L S (1)

Compute N ( ʸ r )
if cN ≥ MinPts then

for o=1:cN

( ʸ r )

( ʸ r ) do

if ʸ o is not in a cluster nor marked as noise then

Mark ʸ o with the current cluster-label
Lend

N ( ʸ r ) to the Seed list L S =[ L S N ( ʸ r )]

L S (1) = [ ]

end
end
else
L S (1) = [ ]

end
end
end
end
end
Result : Determination of the number of clusters

s

s and the parameters {ʸ i }