By this update procedure described above, the net forms an elastic net that during learning folds onto the ``cloud'' formed by the input data. The codebook vectors tend to drift there where the data is dense, while there tends to be only a few codebook vectors where data is sparsely located. In this manner, the net tends to approximate the probability density function of the input data .
The Self-Organizing Map update rule for a unit is the following:
where t denotes time. This is, as mentioned above, a training process through time. The is the input vector drawn from the input data set at time t. is a non-increasing neighborhood function around the winner unit . More on the subject of the neighborhood function in the next section.