Closure phase: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Seriouslyandy
No edit summary
en>Kogge
 
Line 1: Line 1:
A '''growing self-organizing map (GSOM)''' is a growing variant of the popular [[self-organizing map]] (SOM). The GSOM was developed to address the issue of identifying a suitable map size in the [[Self Organizing Map|SOM]]. It starts with a minimal number of nodes (usually 4) and grows new nodes on the boundary based on a heuristic. By using the value called Spread Factor (SF), the data analyst has the ability to control the growth of the GSOM.
For some explanation he often [http://Www.Palpakchurch.org/?document_srl=2231 appeared] to be even worse on Fridays. One particular Friday a quantity of the boys bought some glass tubing from the regional pharmacy and have been using it as pea-shooters. This truly incensed him, and soon after the lunch crack he lined up all the offenders in entrance of the course at the massive flat oak desk in the center of the room, and set all the glass tubing on the table and proceeded to smash it into slivers utilizing one of the sticks. And he then proceeded to give each of the pupils "six cuts" with that stick. <br>What can we find out from this? What fundamentally matters is that what is composed is inventive. Then see if it meets the standards of what we phone "correct" or "wrong" or fact or fiction. My evocation of that place scene was inventive. No matter whether I could listen to the bees was not the level. If there is correct creativeness, unstressed twin-hemisphere action, then the author and perhaps the reader will gain by it. Collections of facts are of system critical, but we have to also nurture that creative leap past the "norm"—and as a result possibly inspire a main breakthrough in the knowing of the human condition and its treatment method.<br>Of program, all is going as well well catastrophe strikes. You step out of that taxi and slam the doorway behind you. The taxi rolls forward a bit hunting for a spot to drift into visitors. You really feel a tough pull at your throat and realize that the scarf is clamped into the doorway that you just exited. Oh my! The crook drops his knife to the sidewalk, spins on his feet and is long gone into the darkness not to be observed or listened to from once more. Camping. How else will you sharpen the level of a stick in preparation for stabbing your prey? And by prey I mean hot puppy.<br>If you can’t get a hand on an old pocket knife, or the one your father or grandpa gave you is no lengthier usable, choose yourself up a new 1. You can uncover pocket knives at any out of doors keep. Much better however, uncover a knife keep in town so you have a broader variety to pick from. Nothing else issues if the knife is poorly created and receiving the appropriate ergonomics is a essential portion of the layout approach. In basic conditions, ergonomics refers to how comfortable the knife feels in your hand. A quality knife designer can develop some thing that feels like an extension of your hand. Worth for money<br>Thing to consider #five - How a lot need to you pay out for a pocket knife ? Even though there are actually no tough policies or suggestions to follow listed here, keep in mind that you will get what you pay out for. That being stated, you can normally decide up a respectable pocket knife for $thirty to $60. There are also less expensive blades but the quality is most likely to fall with the price as nicely, and there are more high-priced blades which often arrive with a far better high quality knife , occasionally not. To locate out far more about best pocket knife you should truly feel totally free to examine out the web site. You can make contact with us additionally by means of e-mail.<br>Why be in line when you can be on the internet. This statement is very real in the current context. Nowadays everything is available at just a click of the mouse. This is the simplicity with which things are accessible to us now. Purchasing practices have also undergone a huge adjust. Just think, would you have ever considered of buying a pocket knife on the [http://Thebestpocketknifereviews.com/best-pocket-knife-brand-good-knives-in-the-world/ best pocket knife in The world] web at any time. But this has turn into a truth. Your buddies will be ready for any tiny emergencies with this flexible pocket knife , built of sturdy stainless metal and straightforward-to-grip rubber. Every customized tool features a Philip screw driver, flat-head screwdriver, knife and file - all constructed to previous.<br>The very good news is that even though you can not carry your pocket knife on an airplane, you are permitted to examine it in your luggage. Of course, if you might be in the practice of putting your pocket knife in your pocket, there is certainly a very good [http://doc.Froza.ru/index.php/Best_German_Knife_Brand chance you'll] overlook and stop up walking by means of stability. Effectively, then you evidently do not have much inclination to flavor or handiness. Thankfully, you can find a huge variety of pocket knives at web sites all over the web. And if you are not persuaded you want a pocket knife, you might want to have your head examined.<br>There are a number of various brands of pen knives that you can purchase, with the popular ones coming from Switzerland due to the fact that is truly the birthplace of the present day pocket knife But there are some that are manufactured in other nations like the US and Israel that are of similar quality. You must not really get pocket knives solely based on their manufacturer names, store around until finally uncover the one that you come to feel comfortable utilizing. All round, I am truly content with this obtain. I acquired the Smith & Wesson CKTACBSD Tactical knife for about $ten from Amazon, but it typically goes for about $sixteen.ninety five.<br>A starting woodcarver can get started really inexpensively. For considerably carving, a great deal can be carried out with just a knife. Aid carving will necessarily require a lot more tools but for the beginning woodcarver intrigued in carving tiny figures a knife or two will fit the novice nicely. A lot of carvers in no way use yet another instrument. Despite the fact that there is a vast assortment of shapes and dimensions and, of course, expenses, the novice does not have to look for much or commit a whole lot for a really serviceable knife. As an alternative of searching for 1, you can use this knife and get the task carried out. There are also do-it-by yourself initiatives which might demand this multi instrument.<br>The CKTACBSD Knife has serrated edges on the base part of the knife to lower via rope and twine, and I need to say that the factors on people have been truly pretty sharp. I nonetheless sharpen them up a bit but to be sincere they didn't genuinely need it. I analyzed the building of the pocket knife and identified that there was no perform or motion when wiggling the blade all around so it always stays in place while it is open up. I do not truly feel like the knife will crack or go traveling out when I flick it open or near it.
 
All the starting nodes of the GSOM are boundary nodes, i.e. each node has the freedom to grow in its own direction at the beginning. (Fig. 1) New Nodes are grown from the boundary nodes. Once a node is selected for growing all its free neighboring positions will be grown new nodes. The figure shows the three possible node growth options for a rectangular GSOM.
 
[[Image:GSOM-new-node-growth.gif|thumb|Node growth options in GSOM: (a) one new node, (b) two new nodes and (c) three new nodes.]]
 
==The algorithm==
The GSOM process is as follows:
#Initialization phase:
##Initialize the weight vectors of the starting nodes (usually four) with random numbers between 0 and 1.
##Calculate the growth threshold (<math>GT</math>) for the given data set of dimension <math>D</math> according to the spread factor (<math>SF</math>) using the formula <math>GT = - D \times \ln ( SF )</math>
#Growing Phase:
##Present input to the network.
##Determine the weight vector that is closest to the input vector mapped to the current feature map (winner), using Euclidean distance (similar to the [[Self Organizing Map|SOM]]). This step can be summarized as: find <math>q'</math> such that <math>\left | v - w_{q'} \right \vert \le \left | v - w_q \right \vert \forall q \in \mathbb{N}</math> where <math>v</math>, <math>w</math> are the input and weight vectors respectively, <math>q</math> is the position vector for nodes and <math>\mathbb{N}</math> is the set of natural numbers.
##The weight vector adaptation is applied only to the neighborhood of the winner and the winner itself. The neighborhood is a set of neurons around the winner, but in the GSOM the starting neighborhood selected for weight adaptation is smaller compared to the SOM (localized weight adaptation). The amount of adaptation (learning rate) is also reduced exponentially over the iterations. Even within the neighborhood, weights that are closer to the winner are adapted more than those further away. The weight adaptation can be described by <math>w_j ( k + 1 ) = \begin{cases} w_j ( k ) & \mbox{if}j \notin \Nu_{k+1} \\ w_j ( k ) + LR ( k ) \times (x_k - w_j ( k ) ) & \mbox{if}j \in \Nu_{k+1} \end{cases}</math> where the Learning Rate <math>LR ( k )</math>, <math>k \in \mathbb{N}</math> is a sequence of positive parameters converging to zero as <math>k \to \infty</math>. <math>w_j ( k )</math>, <math>w_j ( k + 1 )</math> are the weight vectors of the node <math>j</math> before and after the adaptation and <math>\Nu_{k+1}</math> is the neighbourhood of the winning neuron at the <math>( k + 1 )</math>th iteration. The decreasing value of <math>LR ( k )</math> in the GSOM depends on the number of nodes existing in the map at time <math>k</math>.
##Increase the error value of the winner (error value is the difference between the input vector and the weight vectors).
##When <math>TE_i > GT</math>(where <math>TE_i</math>  is the total error of node <math>i</math> and <math>GT</math> is the growth threshold). Grow nodes if i is a boundary node. Distribute weights to neighbors if <math>i</math> is a non-boundary node.
##Initialize the new node weight vectors to match the neighboring node weights.
##Initialize the learning rate (<math>LR</math>) to its starting value.
##Repeat steps 2 – 7 until all inputs have been presented and node growth is reduced to a minimum level.
#Smoothing phase.
##Reduce learning rate and fix a small starting neighborhood.
##Find winner and adapt the weights of the winner and neighbors in the same way as in growing phase.
 
[[File:SOM versus GSOM.png|thumb|300px|left|Approximation of a spiral with noise by 1D SOM (the upper row) and GSOM (the lower row) with 50 (the first column) and 100 (the second column) nodes.  The [[Fraction of variance unexplained]] is: a) 4.68% (SOM, 50 nodes); b) 1.69% (SOM, 100 nodes); c) 4.20% (GSOM, 50 nodes); d) 2.32% (GSOM, 100 nodes). The initial approximation for SOM was equidistribution of nodes in a segment on the first principal component with the same variance as for the data set. The initial approximation for GSOM was the mean point. <ref>The illustration is prepared using free software: E.M. Mirkes, [http://www.math.le.ac.uk/people/ag153/homepage/PCA_SOM/PCA_SOM.html Principal Component Analysis and Self-Organizing Maps: applet]. University of Leicester, 2011.</ref>]]
 
== Applications ==
 
The GSOM can be used for many preprocessing tasks in [[Data mining]], for [[Nonlinear dimensionality reduction]], for approximation of principal curves and manifolds, for [[cluster analysis|clustering]] and [[classification in machine learning|classification]]. It gives often the better representation of the data geometry than the SOM (see the classical benchmark for principal curves on the left).
 
== References ==
{{Reflist}}
 
== Bibliography ==
# Hsu, A., Tang, S. and Halgamuge, S. K. (2003) An unsupervised hierarchical dynamic self-organizing approach to cancer class discovery and marker gene identification in microarray data. Bioinformatics 19(16): pp 2131-2140
# Alahakoon, D., Halgamuge, S. K. and Sirinivasan, B. (2000) Dynamic Self Organizing Maps With Controlled Growth for Knowledge Discovery, IEEE Transactions on Neural Networks, Special Issue on Knowledge Discovery and Data Mining, 11, pp 601-614.
# Alahakoon, D., Halgamuge, S. K. and Sirinivasan, B. (1998) A Structure Adapting Feature Map for Optimal Cluster Representation  in Proceedings of The 5th International Conference on Neural Information Processing (ICONIP 98), Kitakyushu, Japan, pp 809-812
# Alahakoon, D., Halgamuge, S. K. and Sirinivasan, B. (1998) A Self Growing Cluster Development Approach to Data Mining  in Proceedings of IEEE International Conference on Systems, Man and Cybernetics, San Diego, USA, pp 2901-2906
# Alahakoon, D. and Halgamuge, S. K. (1998) Knowledge Discovery with Supervised and Unsupervised Self Evolving Neural Networks  in Proceedings of 5th International Conference on Soft Computing and Information/Intelligent Systems, Fukuoka, Japan, pp 907-910
 
==See also==
* [[Self-organizing map]]
*[[Time Adaptive Self-Organizing Map]]
* [[Elastic map]]
* [[Artificial intelligence]]
* [[Machine learning]]
* [[Data mining]]
* [[Nonlinear dimensionality reduction]]
 
[[Category:Machine learning algorithms]]
[[Category:Neural networks]]

Latest revision as of 21:54, 29 March 2014

For some explanation he often appeared to be even worse on Fridays. One particular Friday a quantity of the boys bought some glass tubing from the regional pharmacy and have been using it as pea-shooters. This truly incensed him, and soon after the lunch crack he lined up all the offenders in entrance of the course at the massive flat oak desk in the center of the room, and set all the glass tubing on the table and proceeded to smash it into slivers utilizing one of the sticks. And he then proceeded to give each of the pupils "six cuts" with that stick.
What can we find out from this? What fundamentally matters is that what is composed is inventive. Then see if it meets the standards of what we phone "correct" or "wrong" or fact or fiction. My evocation of that place scene was inventive. No matter whether I could listen to the bees was not the level. If there is correct creativeness, unstressed twin-hemisphere action, then the author and perhaps the reader will gain by it. Collections of facts are of system critical, but we have to also nurture that creative leap past the "norm"—and as a result possibly inspire a main breakthrough in the knowing of the human condition and its treatment method.
Of program, all is going as well well catastrophe strikes. You step out of that taxi and slam the doorway behind you. The taxi rolls forward a bit hunting for a spot to drift into visitors. You really feel a tough pull at your throat and realize that the scarf is clamped into the doorway that you just exited. Oh my! The crook drops his knife to the sidewalk, spins on his feet and is long gone into the darkness not to be observed or listened to from once more. Camping. How else will you sharpen the level of a stick in preparation for stabbing your prey? And by prey I mean hot puppy.
If you can’t get a hand on an old pocket knife, or the one your father or grandpa gave you is no lengthier usable, choose yourself up a new 1. You can uncover pocket knives at any out of doors keep. Much better however, uncover a knife keep in town so you have a broader variety to pick from. Nothing else issues if the knife is poorly created and receiving the appropriate ergonomics is a essential portion of the layout approach. In basic conditions, ergonomics refers to how comfortable the knife feels in your hand. A quality knife designer can develop some thing that feels like an extension of your hand. Worth for money
Thing to consider #five - How a lot need to you pay out for a pocket knife ? Even though there are actually no tough policies or suggestions to follow listed here, keep in mind that you will get what you pay out for. That being stated, you can normally decide up a respectable pocket knife for $thirty to $60. There are also less expensive blades but the quality is most likely to fall with the price as nicely, and there are more high-priced blades which often arrive with a far better high quality knife , occasionally not. To locate out far more about best pocket knife you should truly feel totally free to examine out the web site. You can make contact with us additionally by means of e-mail.
Why be in line when you can be on the internet. This statement is very real in the current context. Nowadays everything is available at just a click of the mouse. This is the simplicity with which things are accessible to us now. Purchasing practices have also undergone a huge adjust. Just think, would you have ever considered of buying a pocket knife on the best pocket knife in The world web at any time. But this has turn into a truth. Your buddies will be ready for any tiny emergencies with this flexible pocket knife , built of sturdy stainless metal and straightforward-to-grip rubber. Every customized tool features a Philip screw driver, flat-head screwdriver, knife and file - all constructed to previous.
The very good news is that even though you can not carry your pocket knife on an airplane, you are permitted to examine it in your luggage. Of course, if you might be in the practice of putting your pocket knife in your pocket, there is certainly a very good chance you'll overlook and stop up walking by means of stability. Effectively, then you evidently do not have much inclination to flavor or handiness. Thankfully, you can find a huge variety of pocket knives at web sites all over the web. And if you are not persuaded you want a pocket knife, you might want to have your head examined.
There are a number of various brands of pen knives that you can purchase, with the popular ones coming from Switzerland due to the fact that is truly the birthplace of the present day pocket knife But there are some that are manufactured in other nations like the US and Israel that are of similar quality. You must not really get pocket knives solely based on their manufacturer names, store around until finally uncover the one that you come to feel comfortable utilizing. All round, I am truly content with this obtain. I acquired the Smith & Wesson CKTACBSD Tactical knife for about $ten from Amazon, but it typically goes for about $sixteen.ninety five.
A starting woodcarver can get started really inexpensively. For considerably carving, a great deal can be carried out with just a knife. Aid carving will necessarily require a lot more tools but for the beginning woodcarver intrigued in carving tiny figures a knife or two will fit the novice nicely. A lot of carvers in no way use yet another instrument. Despite the fact that there is a vast assortment of shapes and dimensions and, of course, expenses, the novice does not have to look for much or commit a whole lot for a really serviceable knife. As an alternative of searching for 1, you can use this knife and get the task carried out. There are also do-it-by yourself initiatives which might demand this multi instrument.
The CKTACBSD Knife has serrated edges on the base part of the knife to lower via rope and twine, and I need to say that the factors on people have been truly pretty sharp. I nonetheless sharpen them up a bit but to be sincere they didn't genuinely need it. I analyzed the building of the pocket knife and identified that there was no perform or motion when wiggling the blade all around so it always stays in place while it is open up. I do not truly feel like the knife will crack or go traveling out when I flick it open or near it.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Closure_phase&oldid=268014"