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| {{distinguish|Nerve gas}}
| | [http://bigpolis.com/blogs/post/6503 phone psychic readings] Hello, my name is Andrew and my wife doesn't like it at all. Distributing production is where her main earnings arrives from. The favorite pastime for him and his kids is style and he'll be starting something else alongside with it. Mississippi is the only location I've been residing in but I will have to transfer in a yr or two.<br><br>Feel free to surf to my [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies good psychic] site; psychic phone readings - [http://www.chk.woobi.co.kr/xe/?document_srl=346069 woobi.co.kr] - |
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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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