K-MEANS, C-MEANS OR ISODATA
K-means is a popular clustering algorithm which is defined as follows
![](img/onpages/kmeans.jpg)
Furthermore, the partition cost for N data vectors with k clusters is defined as
![](img/onpages/cost.jpg)
in which u_ji=1 if i^th data vector belongs to j^th cluster. Otherwise u_ji=0.
SELF-ORGANIZING MAP
Self-organizing map algorithm is an unsupervised learning algorithm which defines a mapping from a high-dimensional input data space into a lower-dimensional space. The basic algorithm is as follows,![](img/onpages/som3.jpg)
The best matching unit (BMU) for data vector x is defined as
![](img/onpages/som1.jpg)
and the weight vectors of the BMU and the units
that belong to the neighborhood of the BMU
are updated by using the below equation,
![](img/onpages/som2.jpg)
in which alpha is a decreasing learning rate.