DBSTREAM¶
DBSTREAM
DBSTREAM ^{1} is a clustering algorithm for evolving data streams. It is the first microclusterbased online clustering component that explicitely captures the density between microclusters via a shared density graph. The density information in the graph is then exploited for reclustering based on actual density between adjacent micro clusters.
The algorithm is divided into two parts:
Online microcluster maintenance (learning)
For a new point p
:

Find all micro clusters for which
p
falls within the fixed radius (clustering threshold). If no neighbor is found, a new micro cluster with a weight of 1 is created forp
. 
If no neighbor is found, a new micro cluster with a weight of 1 is created for
p
. If one or more neighbors ofp
are found, we update the micro clusters by applying the appropriate fading, increasing their weight and then we try to move them closer top
using the Gaussian neighborhood function. 
Next, the shared density graph is updated. To prevent collapsing micro clusters, we will restrict the movement for micro clusters in case they come closer than \(r\) (clustering threshold) to each other. Finishing this process, the time stamp is also increased by 1.

Finally, the cleanup will be processed. It is executed every
t_gap
time steps, removing weak micro clusters and weak entries in the shared density graph to recover memory and improve the clustering algorithm's processing speed.
Offline generation of macro clusters (clustering)
The offline generation of macro clusters is generated through the two following steps:

The connectivity graph
C
is constructed using shared density entries between strong micro clusters. The edges in this connectivity graph with a connectivity value greater than the intersection threshold (\(\alpha\)) are used to find connected components representing the final cluster. 
After the connectivity graph is generated, a variant of the DBSCAN algorithm proposed by Ester et al. is applied to form all macro clusters from \(\alpha\)connected micro clusters.
Parameters¶

clustering_threshold
Type → float
Default →
1.0
DBStream represents each micro cluster by a leader (a data point defining the micro cluster's center) and the density in an area of a userspecified radius \(r\) (
clustering_threshold
) around the center. 
fading_factor
Type → float
Default →
0.01
Parameter that controls the importance of historical data to current cluster. Note that
fading_factor
has to be different from0
. 
cleanup_interval
Type → float
Default →
2
The time interval between two consecutive time points when the cleanup process is conducted.

intersection_factor
Type → float
Default →
0.3
The intersection factor related to the area of the overlap of the micro clusters relative to the area cover by micro clusters. This parameter is used to determine whether a micro cluster or a shared density is weak.

minimum_weight
Type → float
Default →
1.0
The minimum weight for a cluster to be not "noisy".
Attributes¶

n_clusters
Number of clusters generated by the algorithm.

clusters
A set of final clusters of type
DBStreamMicroCluster
. However, these are either micro clusters, or macro clusters that are generated by merging all \(\alpha\)connected micro clusters. This set is generated through the offline phase of the algorithm. 
centers
Final clusters' centers.

micro_clusters
Micro clusters generated by the algorithm. Instead of updating directly the new instance points into a nearest micro cluster, through each iteration, the weight and center will be modified so that the clusters are closer to the new points, using the Gaussian neighborhood function.
Examples¶
from river import cluster
from river import stream
X = [
[1, 0.5], [1, 0.625], [1, 0.75], [1, 1.125], [1, 1.5], [1, 1.75],
[4, 1.5], [4, 2.25], [4, 2.5], [4, 3], [4, 3.25], [4, 3.5]
]
dbstream = cluster.DBSTREAM(
clustering_threshold=1.5,
fading_factor=0.05,
cleanup_interval=4,
intersection_factor=0.5,
minimum_weight=1
)
for x, _ in stream.iter_array(X):
dbstream.learn_one(x)
dbstream.predict_one({0: 1, 1: 2})
0
dbstream.predict_one({0: 5, 1: 2})
1
dbstream._n_clusters
2
Methods¶
learn_one
Update the model with a set of features x
.
Parameters
 x — 'dict'
 w — defaults to
None
predict_one
Predicts the cluster number for a set of features x
.
Parameters
 x — 'dict'
 w — defaults to
None
Returns
int: A cluster number.

Michael Hahsler and Matthew Bolanos (2016, pp 14491461). Clustering Data Streams Based on Shared Density between MicroClusters, IEEE Transactions on Knowledge and Data Engineering 28(6) . In Proceedings of the Sixth SIAM International Conference on Data Mining, April 20–22, 2006, Bethesda, MD, USA. ↩

Ester et al (1996). A DensityBased Algorithm for Discovering Clusters in Large Spatial Databases with Noise. In KDD96 Proceedings, AAAI. ↩