The weights of the best matching unit and the unit within its neighborhood are adapted so that the new reference vectors lie henceforth closer to the input vector. The factor hci(t) 
controls the rate of change of the reference vectors and is called the learning rate.,
m t 1 m t h txt m t ...(4)
i   i  ci  i Where t denotes the index of the iteration step, x(t) is the vector-valued input sample of x in the iteration t. Here, the hci(t) is called the neighbourhood function around the winning node c. During training, hci(t) is a decreasing function of the distance between the i-th and c-th model of the map node. For convergence it is necessary that h (t)  0 ci when t   . 

## 4. Visual Decipherable Clustering Approach Using Self Organizing Map Method-An Example

A 1010 size matrix has been artificially generated by us (problem\#1 of table 1) for demonstrating the machine-part cell formation through visual decipherable clustering using our proposed SOM methodology. The SOM methodology was implemented using Matlab programming using somtoolbox and obtained the outputs of umatrix, component planes (figure 1), pc projection (figure 2) and histogram and scatterplots (figure 3). The outputs for the problem\#1 of table 1 are discussed below to generate the machine-part cell formation. The block diagonal form (table 2) of the cell formation for the problem\#1 was resulted from the output information of the SOM clustering. The details of clustering of machine-part cell formation for machine-part matrix of problem\#1 are discussed below.

## 4.1 Unified Distance Matrix (Umatrix)

The U-matrix makes the 2D visualization of multivariate data possible using codevectors of SOM as source of data. After the learning process is completed, it is derived by using property of topological relations among neurons. This algorithm generates a matrix where each component is a distance measure between two adjacent neurons, therefore we can visualize any multi-variated dataset in a two-dimensional display. Figure 1 shows a representation of a U-matrix calculation for a 1210 2D hexagonal SOM. By U-matrix we can detect topological relations among neurons and infer about the input data structure. 