Sammon's Projection
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High Quality Content by WIKIPEDIA articles! Sammon's projection, or Sammon's mapping is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling). Denote the distance between ith and jth objects in the original space by scriptstyle d^{ }_{ij}, and the distance between their projections by scriptstyle d^{}_{ij}. Sammon's projection aims to minimize the following error function, which is often referred to as Sammon's stress: E = frac{1}{sum_{ij}d^{ }_{ij}}sumsum_{ij}frac{(d^{ }_{ij}-d_{ij})^2}{d^{ }_{ij}}. The minimization can be performed ...
High Quality Content by WIKIPEDIA articles! Sammon's projection, or Sammon's mapping is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling). Denote the distance between ith and jth objects in the original space by scriptstyle d^{ }_{ij}, and the distance between their projections by scriptstyle d^{}_{ij}. Sammon's projection aims to minimize the following error function, which is often referred to as Sammon's stress: E = frac{1}{sum_{ij}d^{ }_{ij}}sumsum_{ij}frac{(d^{ }_{ij}-d_{ij})^2}{d^{ }_{ij}}. The minimization can be performed either by gradient descent, as proposed initially, or by other means.
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