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- 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 , and the distance between their projections by . Sammon's mapping aims to minimize the following error function, which is often referred to as Sammon's stress or Sammon's error: 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. The Sammon mapping has been one of the most successful nonlinear metric multidimensional scaling methods since its advent in 1969, but effort has been focused on algorithm improvement rather than on the form of the stress function. The performance of the Sammon mapping has been improved by extending its stress function using left Bregman divergence and right Bregman divergence. (en)
- 새몬 매핑(Sammon's mapping)은 고차원 자료를 저차원으로 사상하는 알고리즘이다. 새몬 사상 또는 새몬 사영(Sammon's projection)이라고 할 수도 있으나 보통 영어를 그대로 쓴다. 이 알고리즘은 그래프 그리기에도 응용된다. 새몬 매핑은 새몬 압력이라고 하는 아래 오차 함수의 값을 최소화하는 것을 목표로 한다. 여기서 는 원래 공간에서 i번째와 j번째 개체 사이의 거리이고, 는 사영된 뒤의 거리이다. 실제 계산을 할 때는 새몬이 원래 논문에서 제안한 대로 (gradient descent)법을 주로 쓰지만, 다른 방법을 쓸 수도 있다. (ko)
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- 새몬 매핑(Sammon's mapping)은 고차원 자료를 저차원으로 사상하는 알고리즘이다. 새몬 사상 또는 새몬 사영(Sammon's projection)이라고 할 수도 있으나 보통 영어를 그대로 쓴다. 이 알고리즘은 그래프 그리기에도 응용된다. 새몬 매핑은 새몬 압력이라고 하는 아래 오차 함수의 값을 최소화하는 것을 목표로 한다. 여기서 는 원래 공간에서 i번째와 j번째 개체 사이의 거리이고, 는 사영된 뒤의 거리이다. 실제 계산을 할 때는 새몬이 원래 논문에서 제안한 대로 (gradient descent)법을 주로 쓰지만, 다른 방법을 쓸 수도 있다. (ko)
- 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. Denote the distance between ith and jth objects in the original space by , and the distance between their projections by . (en)
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- 새몬 매핑 (ko)
- Sammon mapping (en)
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