Question

In Sammon mapping, if the mapping is linear, namely, g(x|W) = W^Tx, how can W that minimizes the Sammon stress be calculated? Give the steps to a solution, i.e. how to optimize.

Answer 1

The error (stress) function E measures the difference between the present configuration of n points in the d - dimensional space and the configuration of n points in the original m - dimensional space. problem The problem of finding the right configuration in a low-dimensional space is an optimisation. In general this optimisation problem is difficult because of the very high dimensionality of the parameter space. The stress function is optimal when all the original distances ij are equal to the distances of the projected points dij. However this is not likely to happen exactly. Therefore the found distances will be distorted representations of the relations within the data. The larger the stress the greater the distance.