Neural network-based clustering techniques like self-organizing feature maps (SOM) and adaptive resonance theory (ART) are commonly used. SOM represents high-dimensional data in a low-dimensional form while preserving essence. ART consists of comparison and recognition layers and clusters input patterns in an unsupervised manner. Kernel-based clustering algorithms operate in a potentially infinite dimensional feature space and can form arbitrary cluster shapes, deal with noise/outliers, and estimate the number of clusters without prior topological knowledge.

1. B Y
S H U B H A M V I J A Y
R A H U L R A M A N
Neural & Kernel Based
Clustering

2. Neural Networks-Based Clustering
 A neural network is a collection of connected
artificial neurons.
 Neural networks-based clustering has been
dominated by SOFMs and adaptive resonance theory
(ART).
 Each artificial neuron is based on a simplified model
of the neurons found in the human brain.

3. Kohonen self-organizing map (SOM)
 represent high-dimensional data in a low-
dimensional form without loosing the ’essence’ of the
data
 Organize data on the basis of similarity by putting
entities geometrically close to each other.

4. Kohonen self-organizing map (SOM) Algoritham
 1) Define the topology of the SOFM; Initialize the prototype vectors randomly.
 2) Present an input pattern to the network; Choose the winning node that is closest to
 3) Update prototype vectors where is the neighborhood function that is often defined as where is the
monotonically decreasing learning rate, represents the position of corresponding neuron, and is the
monotonically decreasing kernel width function, or
if node belongs to the neighborhood of the winning node otherwise
 4) Repeat steps 2)–3) until no change of neuron positionthat is more than a small positive number is
observed.

5. SOM example

6. ART(adaptive resonance theory)
The ART architecture consists of two layers of
neurons, the comparison layer and the
recognition layer

7. ART Example
 We have binary Set of data
 0 0 1 0 0 1 1 0 0 DATA 1
 1 0 0 0 1 0 0 1 0 DATA 2
 0 1 0 1 0 0 0 0 1 DATA 3
 0 0 0 0 1 0 0 1 0 DATA 4
 0 0 1 0 0 1 1 0 0 DATA 5
 0 1 0 1 0 0 1 0 1 DATA 6
 0 1 0 1 0 0 0 0 0 DATA 7
 1 0 0 0 1 0 0 1 0 DATA 8
 0 0 0 0 0 0 1 0 0 DATA 9

8.  1 Part : 0 0 1 0 0 1 1 0 0 Cluster : 1
 2 Part : 1 0 0 0 1 0 0 1 0 Cluster : 2
 3 Part : 0 1 0 1 0 0 0 0 1 Cluster : 3
 4 Part : 0 0 0 0 1 0 0 1 0 Cluster : 2
 5 Part : 0 0 1 0 0 1 1 0 0 Cluster : 1
 6 Part : 0 1 0 1 0 0 1 0 1 Cluster : 3
 7 Part : 0 1 0 1 0 0 0 0 0 Cluster : 3
 8 Part : 1 0 0 0 1 0 0 1 0 Cluster : 4
 9 Part : 0 0 0 0 0 0 1 0 0 Cluster : 1

9. ART Advantage
 Its very high speed of computation.
 It can handle large input vectors, which are general
requirement of GT problems.
 It supports flexibility.

10. Kernel-Based Clustering
 Kernel-based learning algorithms are based on
Cover’s theorem.

11. Kernel-Based Clustering Algoritham
 1)Initialize the centers with the first , observation
patterns;
 2) Take a new pattern and calculate as shown in the
equation at the bottom of the page.
 3) Update the mean vector whose corresponding is 1
 4) Adapt the coefficients for each as
 5) Repeat steps 2)–4) until convergence is achieved

12. Kernel-Based Clustering Advantage
 1) It is more possible to obtain a linearly separable
hyperplane in the high-dimensional, or even infinite
feature space.
 2) They can form arbitrary clustering shapes other
than hyperellipsoid and hypersphere.
 3) Kernel-based clustering algorithms, like SVC, have
the capability of dealing with noise and outliers.
 4) For SVC, there is no requirement for prior
knowledge to determine the system topological
structure. In the kernel matrix can provide the
means to estimate the number of clusters.