K-MEANS, C-MEANS OR ISODATA

K-means is a popular clustering algorithm which is defined as follows

Furthermore, the partition cost for N data vectors with k clusters is defined as

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,

The best matching unit (BMU) for data vector x is defined as

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,

in which alpha is a decreasing learning rate.