Lesson plan
Sammon mapping
Sammon mapping or Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling) by trying to preserve the structure of inter-point distances in high-dimensional space in the lower-dimension projection. It is particularly suited for use in exploratory data analysis. The method was proposed by John W. Sammon in 1969. It is considered a non-linear approach as the mapping cannot be represented as a linear combination of the original variables as possible in techniques such as principal component analysis, which also makes it more difficult to use for classification applications. 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 mapping aims to minimize the following error function, which is often referred to as Sammon's stress or Sammon's error: : E = \frac{1}{\sum\limits_{i The minimization can be performed either by gradient descent, as proposed initially, or by other means, usually involving iterative methods. The number of iterations needs to be experimentally determined and convergent solutions are not always guaranteed. Many implementations prefer to use the first Principal Components as a starting configuration.…
Article summary
Sammon mapping or Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling) by trying to preserve the structure of inter-point distances in high-dimensional space in the lower-dimension projection. It is particularly suited for use in exploratory data analysis. The method was proposed by John W. Sammon in 1969. It is considered a non-linear approach as the mapping cannot be represented as a linear combination of the original variables as possible in techniques such as principal component analysis, which also makes it more difficult to use for classification applications. 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 mapping aims to minimize the following error function, which is often referred to as Sammon's stress or Sammon's error: : E = \frac{1}{\sum\limits_{i The minimization can be performed either by gradient descent, as proposed initially, or by other means, usually involving iterative methods. The number of iterations needs to be experimentally determined and convergent solutions are not always guaranteed. Many implementations prefer to use the first Principal Components as a starting configuration.…
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.