en>David Eppstein: /* External links */ rm broken link that probably should better have been formatted as a reference to an actual journal paper. That way it might not have been so irretrievably broken.

2013-10-23T06:01:48Z

External links: rm broken link that probably should better have been formatted as a reference to an actual journal paper. That way it might not have been so irretrievably broken.

← Older revision		Revision as of 08:01, 23 October 2013
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	~~The author~~'~~s name~~ is ~~Christy Brookins. Distributing manufacturing is how he tends~~ to ~~make~~ a ~~living~~. ~~Ohio~~ is ~~where his house~~ is and ~~his family members enjoys it~~. It's not a ~~typical thing but what~~ I ~~like doing is to climb~~ but ~~I don't have~~ the ~~time lately~~.<br><br>~~Here is my web-site~~ ... ~~are psychics real (~~[http://www.~~familysurvivalgroup~~.com/~~easy-methods-planting-looking-backyard~~/ ~~relevant web page~~])		'''Sammon mapping''' or '''Sammon projection''' is an algorithm that [[Map (mathematics)\|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.<ref>{{cite journal\|author=Sammon JW\|title=A nonlinear mapping for data structure analysis\|journal=IEEE Transactions on Computers\| volume=18\|year=1969\|pages=401–409\|url=http://theoval.cmp.uea.ac.uk/~gcc/matlab/sammon/sammon.pdf}}</ref> 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.<ref>{{cite journal\|author=Lerner, B; Hugo Guterman, Mayer Aladjem, Itshak Dinsteint, Yitzhak Romem\|title= On pattern classification with Sammon's nonlinear mapping an experimental study\|journal= Pattern Recognition\|volume=31\|issue=4\|year=1998\|pages=371–381\| doi=10.1016/S0031-3203(97)00064-2}}</ref>

			Denote the distance between '''i'''th and '''j'''th objects in the original space by <math>\scriptstyle d^{*}_{ij}</math>, and the distance between their projections by <math>\scriptstyle d^{}_{ij}</math>. Sammon's mapping aims to minimize the following error function, which is often referred to as '''Sammon's stress''' or '''Sammon's error''':

			:<math>E = \frac{1}{\sum\limits_{i<j}d^{}_{ij}}\sum_{i<j}\frac{(d^{}_{ij}-d_{ij})^2}{d^{*}_{ij}}.</math>

			The minimization can be performed either by [[gradient descent]], as proposed initially, or by other means, usually involving iterative methods. The number of iterations need to be experimentally determined and convergent solutions are not always guaranteed. Many implementations prefer to use the first Principal Components as a starting configuration.<ref>{{cite journal\|journal=Pattern Analysis & Applications\|volume=3\|issue=2\|pages=61–68\|doi=10.1007/s100440050006\|title= On the Initialisation of Sammon's Nonlinear Mapping\|author=Lerner, B; H. Guterman, M. Aladjem and I. Dinstein}}</ref>

			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]]
			<ref>{{cite journal\|journal=Pattern Recognition\|volume=44\|issue=5\|pages=1137–1154\|title= Extending metric multidimensional scaling with Bregman divergences\|author=J. Sun, M. Crowe, C. Fyfe\|year=May 2011\|doi=10.1016/j.patcog.2010.11.013}}</ref> and right Bregman divergence.<ref>{{cite journal\|journal=Information Sciences\|title= Extending Sammon mapping with Bregman divergences\|author=J. Sun, C. Fyfe, M. Crowe\|year=2011\|doi= 10.1016/j.ins.2011.10.013}}</ref>

			== References ==
			{{reflist\|2}}

			==External links==
			* [http://hisee.sourceforge.net/ HiSee – an open-source visualizer for high dimensional data]
			* [http://www.codeproject.com/KB/recipes/SammonProjection.aspx A C# based program with code on CodeProject].
			* [http://theoval.cmp.uea.ac.uk/~gcc/matlab/default.html#sammon Matlab code and method introduction]

			[[Category:Functions and mappings]]
			[[Category:Dimension reduction]]


			{{Statistics-stub}}

en>Mayooranathan at 14:31, 24 June 2011

2011-06-24T14:31:45Z

New page

The author's name is Christy Brookins. Distributing manufacturing is how he tends to make a living. Ohio is where his house is and his family members enjoys it. It's not a typical thing but what I like doing is to climb but I don't have the time lately.<br><br>Here is my web-site ... are psychics real ([http://www.familysurvivalgroup.com/easy-methods-planting-looking-backyard/ relevant web page])

Swastika curve - Revision history

en>David Eppstein: /* External links */ rm broken link that probably should better have been formatted as a reference to an actual journal paper. That way it might not have been so irretrievably broken.

en>Mayooranathan at 14:31, 24 June 2011