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| {{distinguish|Nerve gas}}
| | Hi there. Let me start by introducing the author, her name is Sophia Boon but she by no means really liked that title. Mississippi is exactly where his home is. As a woman what she truly likes is style and she's been doing it for fairly a while. Credit authorising is how she makes a living.<br><br>Also visit my blog post: [https://www-ocl.gist.ac.kr/work/xe/?document_srl=605236 online psychics] |
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| '''Neural gas''' is an [[artificial neural network]], inspired by the [[self-organizing map]] and introduced in 1991 by [[Thomas Martinetz]] and [[Klaus Schulten]].<ref>{{cite conference
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| |title=A "neural gas" network learns topologies
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| |booktitle=Artificial Neural Networks
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| |author=Thomas Martinetz and Klaus Schulten
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| |publisher=[[Elsevier]]
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| |year=1991
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| |pages=397–402
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| |url=http://www.ks.uiuc.edu/Publications/Papers/PDF/MART91B/MART91B.pdf
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| }}</ref> The neural gas is a simple algorithm for finding optimal data representations based on [[feature vector]]s. The algorithm was coined "neural gas" because of the dynamics of the feature vectors during the adaptation process, which distribute themselves like a gas within the data space. It is applied where [[data compression]] or [[vector quantization]] is an issue, for example [[speech recognition]],<ref>{{cite conference
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| |url=http://books.google.com/books?id=nJKLv5eheZoC&pg=PA109&dq=%22neural+gas%22+speech+recognition&hl=en&ei=ER4RTJqsF57hnQfuzbDrBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q=%22neural%20gas%22%20speech%20recognition&f=false
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| |title=Competitive learning methods for efficient Vector Quantizations in a speech recognition environment
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| |authors=F. Curatelli and O. Mayora-Iberra
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| |booktitle=MICAI 2000: Advances in artificial intelligence : Mexican International Conference on Artificial Intelligence, Acapulco, Mexico, April 2000 : proceedings
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| |page=109
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| |ISBN=978-3-540-67354-5
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| |editors=Osvaldo Cairó, L. Enrique Sucar, Francisco J. Cantú-Ortiz
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| |publisher=Springer
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| |year=2000}}</ref> [[image processing]]<ref>{{Cite conference
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| |url=http://books.google.com/books?id=xI0g7vqVkdoC&pg=PA210&dq=%22neural+gas%22+image+processing&hl=en&ei=pR8RTLynLOLpnQeOxsHpBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q=%22neural%20gas%22%20image%20processing&f=false
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| |title=Automatic landmarking of 2D medical shapes using the growing neural gas network
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| |authors=Angelopoulou, Anastassia and Psarrou, Alexandra and Garcia Rodriguez, Jose and Revett, Kenneth
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| |booktitle=Computer vision for biomedical image applications: first international workshop, CVBIA 2005, Beijing, China, October 21, 2005 : proceedings
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| |publisher=Springer
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| |year=2005
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| |editors=Yanxi Liu, Tianzi Jiang, Changshui Zhang
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| |doi=10.1007/11569541_22
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| |ISBN=978-3-540-29411-5
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| |page=210}}</ref> or [[pattern recognition]]. As a robustly converging alternative to the [[k-means clustering]] it is also used for [[cluster analysis]].<ref>{{cite conference
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| |url=http://books.google.com/books?id=JMQk1HJmhv0C&pg=PA684&dq=%22neural+gas%22+cluster+analysis&cd=1#v=onepage&q=%22neural%20gas%22%20cluster%20analysis&f=false
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| |title=Modification of the growing neural gas algorithm for cluster analysis
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| |authors=Fernando Canales and Max Chacon
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| |booktitle=Progress in pattern recognition, image analysis and applications: 12th Iberoamerican Congress on Pattern Recognition, CIARP 2007, Viña del Mar-Valparaiso, Chile, November 13–16, 2007 ; proceedings
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| |year=2007|
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| publisher=Springer
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| |editors=Luis Rueda, Domingo Mery, Josef Kittler, International Association for Pattern Recognition
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| |pages=684–693
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| |doi=10.1007/978-3-540-76725-1_71
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| |ISBN=978-3-540-76724-4}}</ref>
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| ==Algorithm==
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| Given a [[probability distribution]] ''P(x)'' of data vectors ''x'' and a finite number of [[feature vector]]s ''w<sub>i</sub>, i=1,...,N''.
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| With each time step ''t'' a data vector randomly chosen from ''P'' is presented. Subsequently, the distance order of the feature vectors to the given data vector ''x'' is determined. ''i<sub>0</sub>'' denotes the index of the closest feature vector, ''i<sub>1</sub>'' the index of the second closest feature vector etc. and ''i<sub>N-1</sub>'' the index of the feature vector most distant to ''x''. Then each feature vector (''k=0,...,N-1'') is adapted according to
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| <center><math> w_{i_k}^{t+1} = w_{i_k}^{t} + \epsilon\cdot e^{-k/\lambda}\cdot (x-w_{i_k}^{t}) </math></center>
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| with ε as the adaptation step size and λ as the so-called neighborhood range. ε and λ are reduced with increasing ''t''. After sufficiently many adaptation steps the feature vectors cover the data space with minimum representation error.<ref>http://wwwold.ini.rub.de/VDM/research/gsn/JavaPaper/img187.gif</ref>
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| The adaptation step of the neural gas can be interpreted as [[gradient descent]] on a [[Loss function|cost function]]. By adapting not only the closest feature vector but all of them with a step size decreasing with increasing distance order, compared to (online) [[k-means clustering]] a much more robust convergence of the algorithm can be achieved. The neural gas model does not delete a node and also does not create new nodes.
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| ==Further reading==
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| * T. Martinetz, S. Berkovich, and K. Schulten. "Neural-gas" Network for Vector Quantization and its Application to Time-Series Prediction. IEEE-Transactions on Neural Networks, 4(4):558-569, 1993.
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| * T. Martinetz and K. Schulten. Topology representing networks. Neural Networks, 7(3):507-522, 1994.
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://www.demogng.de DemoGNG] Java applet which demonstrates neural gas, growing neural gas, self-organizing maps and other methods related to competitive learning.
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| * [http://homepages.feis.herts.ac.uk/~nngroup/software.php Java Competitive Learning Applications] Unsupervised Neural Networks (including Self-organizing map) in Java with source codes.
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| * [http://wwwold.ini.rub.de/VDM/research/gsn/JavaPaper/node16.html Neural gas algorithm]
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| {{DEFAULTSORT:Neural Gas}}
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| [[Category:Neural networks]]
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Hi there. Let me start by introducing the author, her name is Sophia Boon but she by no means really liked that title. Mississippi is exactly where his home is. As a woman what she truly likes is style and she's been doing it for fairly a while. Credit authorising is how she makes a living.
Also visit my blog post: online psychics