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| {{Redirect|Elastic net|the statistical regularization technique|Elastic net regularization}}
| | How to decide on the best pocket knife will rely upon each people needs. So that you may need to do a little research into the person or individuals your buying for. Is that this particular person outside rather a lot? A pocket knife that has a knife and presumably different instruments is likely to be finest And remember the good friend who's a tail gaiter and at his favorite staff's parking zone for the big recreation. Some pocket knives have a helpful bottle opener and corkscrew which can not all the time be available in these situations. And what in regards to the avid golfer? There are those that enjoy camping, fishing and looking.<br><br>Ka-Bar Mule Field Folder Knife - Wow, we simply cannot imagine this knife is below $50.00. This undoubtedly deserves to be thought-about one of the best folding knives for the price. You possibly can put this knife up to any test, and it will cross your expectations by far. This knife weighs a little less than 1/2 of a pound – which is an efficient factor because this knife will last you awhile! The KA-BAR mule knife is ideal for any labor job, and great for being in the wilderness. The opening and closing method of this knife will be sure you don’t have any accidental closures on your finger.<br><br>Laguiole steak knives are the most effective steak knives you could find in the world right this moment when you think about their attributes together with however not limited to their value and the quality that they provide at the stated value. The rationale for these steak knives being known as one of the best in the world is twofold. One is the fact that these knives are manufactured to the most effective of their standards through the use of the best metal. This ensures knives of the very best quality and of the most sturdy kind, thereby cementing their place as a number of the finest steak knives out there in the market.<br><br>Before you make a large buy from an internet retailer reminiscent of World Jewels, what is the first thing that you do? You research the product and also you analysis the very best place to purchase the product. With the development of the web phrase of mouth opinions have been exchange by written ones. So individuals will learn World Jewels evaluations when attempting [http://www.thebestpocketknifereviews.com/aero-knife-reviews/ aero knife Infomercial] to decide of whether or to not buy from them. But when no one wrote World Jewels reviews than this follow would be not possible. So while it is very important do your homework and skim World Jewels opinions , additionally it is necessary to write them.<br><br>As we speak the corporate still lives on even stronger than it was 5 or ten years in the past in the same city where it was founded with a new location and an updated web site. The Christy Sliding Blade Pocket Knives are still made on the unique fifty three-operation production line and gear, which is now operated and produced by machinist Hal R. Christy, son of Earl Christy. There are very few fourth-era, family owned corporations on the earth, and this one continues to offer “the best pocket knife ever designed” out there within the Companion (nickel plated), Govt (polished black nickel plated), and the Traveler (matte finish Teflon nickel plated). Features & [http://wiki.crafta.com/wiki/index.php?title=Aero_Knife_Retailers operate]<br><br>The knife could be very gentle weight however you can tell that it is extremely sturdy and candle a beating. It feels very comfy in my hand with the finger grooves and it is extremely evident that the knife won't slip out of my hand because the grip is constructed of each exhausting and mushy polymers, therefore the double injection. It is a exhausting [http://Wiki.ippk.ru/index.php/Ming_Tsai_Aero_Knife durable deal] with however has the grip that you just need, I really feel like I have complete control of the knife whereas [http://Wiki.sibarcelona.es/index.php/Aero_Knife_Free_Shipping_Code holding] it. I even let my spouse hold the knife and asked her how it felt in her hand. |
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| [[File:Elmap breastcancer wiki.png|thumb|300px| Linear PCA versus nonlinear Principal Manifolds<ref name=Handbook>A. N. Gorban, A. Y. Zinovyev, [http://arxiv.org/abs/0809.0490 Principal Graphs and Manifolds], In: Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods and Techniques, Olivas E.S. et al Eds. Information Science Reference, IGI Global: Hershey, PA, USA, 2009. 28–59.</ref> for [[Scientific visualization|visualization]] of [[breast cancer]] [[microarray]] data: a) Configuration of nodes and 2D Principal Surface in the 3D PCA linear manifold. The dataset is curved and can not be mapped adequately on a 2D principal plane; b) The distribution in the internal 2D non-linear principal surface coordinates (ELMap2D) together with an estimation of the density of points; c) The same as b), but for the linear 2D PCA manifold (PCA2D). The “basal” breast cancer subtype is visualized more adequately with ELMap2D and some features of the distribution become better resolved in comparison to PCA2D. Principal manifolds are produced by the '''elastic map'''s algorithm. Data are available for public competition.<ref>Wang, Y., Klijn, J.G., Zhang, Y., Sieuwerts, A.M., Look, M.P., Yang, F., Talantov, D., Timmermans, M., Meijer-van Gelder, M.E., Yu, J. et al.: Gene expression profiles to predict distant metastasis of lymph-node-negative primary breast cancer. Lancet 365, 671–679 (2005); [http://www.ihes.fr/~zinovyev/princmanif2006/ Data online]</ref> Software is available for free non-commercial use.<ref>A. Zinovyev, [http://bioinfo-out.curie.fr/projects/vidaexpert/ ViDaExpert] - Multidimensional Data Visualization Tool (free for non-commercial use). [[Curie Institute (Paris)|Institut Curie]], Paris.</ref><ref>A. Zinovyev, [http://www.ihes.fr/~zinovyev/vida/ViDaExpert/ViDaOverView.pdf ViDaExpert overview], [http://www.ihes.fr IHES] ([[Institut des Hautes Études Scientifiques]]), Bures-Sur-Yvette, Île-de-France.</ref>]]
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| '''Elastic maps''' provide a tool for [[nonlinear dimensionality reduction]]. By their construction, they are system of elastic [[Spring (device)|springs]] embedded in the data
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| space.<ref name=Handbook/> This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured [[k-means]] [[Cluster analysis|clustering]] (zero elasticity) to the estimators located closely to linear [[Principal component analysis|PCA manifolds]] (for high bending and low stretching modules). With some intermediate values of the [[elasticity coefficient]]s, this system effectively approximates non-linear principal manifolds. This approach is based on a [[Mechanics|mechanical]] analogy between principal manifolds, that are passing through "the middle" of data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and A.A. Pitenko in 1996–1998.
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| == Energy of elastic map ==
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| Let data set be a set of vectors <math>S</math> in a finite-dimensional [[Euclidean space]]. The ''elastic map'' is represented by a set of nodes <math>W_j</math> in the same space. Each datapoint <math>s \in S</math> has a ''host node'', namely the closest node <math>W_j</math> (if there are several closest nodes then one takes the node with the smallest number). The data set <math>S</math> is divided on classes <math>K_j=\{s \ | \ W_j \mbox{ is a host of } s\}</math>.
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| The ''approximation energy'' D is the distortion
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| : <math>D=\frac{1}{2}\sum_{j=1}^k \sum_{s \in K_j}\|s-W_j\|^2</math>,
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| this is the energy of the springs with unit elasticity which connect each data point with its host node. It is possible to apply weighting factors to the terms of this sum, for example to reflect the [[standard deviation]] of the [[probability density function]] of any subset of data points <math>\{s_i\}</math>.
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| On the set of nodes an additional structure is defined. Some pairs of nodes, <math>(W_i,W_j)</math>, are connected by ''elastic edges''. Call this set of pairs <math>E</math>. Some triplets of nodes, <math>(W_i,W_j,W_k)</math>, form ''bending ribs''. Call this set of triplets <math>G</math>.
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| : The stretching energy is <math>U_{E}=\frac{1}{2}\lambda \sum_{(W_i,W_j) \in E} \|W_i -W_j\|^2 </math>,
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| : The bending energy is <math>U_G=\frac{1}{2}\mu \sum_{(W_i,W_j,W_l) \in G} \|W_i -2W_j+W_l\|^2 </math>,
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| where <math>\lambda</math> and <math>\mu</math> are the stretching and bending moduli respectively. The stretching energy is sometimes referred to as the "membrane" term, while the bending energy is referred to as the "thin plate" term.<ref>Michael Kass, Andrew Witkin, Demetri Terzopoulos, Snakes: Active contour models, Int.J. Computer Vision, 1988 vol 1-4 pp.321-331</ref>
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| For example, on the 2D rectangular grid the elastic edges are just vertical and horizontal edges (pairs of closest vertices) and the bending ribs are the vertical or horizontal triplets of consecutive (closest) vertices.
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| : The total energy of the elastic map is thus <math>U=D+U_E+U_G.</math> | |
| The position of the nodes <math>\{W_j\}</math> is determined by the mechanical equilibrium of the elastic map, i.e. its location is such that it minimizes the total energy <math>U</math>.
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| == Expectation-maximization algorithm ==
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| For a given splitting of the dataset <math>S</math> in classes <math>K_j</math> minimization of the quadratic functional <math>U</math> is a linear problem with the sparse matrix of coefficients. Therefore, similarly to PCA or ''k''-means, a splitting method is used:
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| * For given <math>\{W_j\}</math> find <math>\{K_j\}</math>;
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| * For given <math>\{K_j\}</math> minimize <math>U</math> and find <math>\{W_j\}</math>;
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| * If no change, terminate.
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| This [[expectation-maximization algorithm]] guarantees a local minimum of <math>U</math>. For improving the approximation various additional methods are proposed. For example, the ''softening'' strategy is used. This strategy
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| starts with a rigid grids (small length, small bending and large elasticity modules
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| <math>\lambda </math> and <math>\mu </math> coefficients) and finishes with soft grids (small <math>\lambda </math> and <math>\mu </math>). The training goes in several epochs, each epoch with its own grid rigidness. Another adaptive strategy is ''growing net'': one starts from small amount of nodes and gradually adds new nodes. Each epoch goes with its own number of nodes.
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| == Applications ==
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| [[File:SlideQualityLife.png|thumb|300px| Application of principal curves build by the elastic maps method: Nonlinear quality of life index.<ref>A. N. Gorban, A. Zinovyev, [http://arxiv.org/abs/1001.1122 Principal manifolds and graphs in practice: from molecular biology to dynamical systems], [[International Journal of Neural Systems]], Vol. 20, No. 3 (2010) 219–232.</ref> Points represent data of the [[United Nations|UN]] 171 countries in 4-dimensional space formed by the values of 4 indicators: [[Gross domestic product|gross product per capita]], [[life expectancy]], [[infant mortality]], [[tuberculosis]] incidence. Different forms and colors correspond to various geographical locations and years. Red bold line represents the '''principal curve''', approximating the dataset.]]
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| Most important applications are in bioinformatics<ref>A.N. Gorban, B. Kegl, D. Wunsch, A. Zinovyev (Eds.), [http://pca.narod.ru/contentsgkwz.htm Principal Manifolds for Data Visualisation and Dimension Reduction], LNCSE 58, Springer: Berlin – Heidelberg – New York, 2007. ISBN 978-3-540-73749-0</ref>
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| ,<ref>M. Chacón, M. Lévano, H. Allende, H. Nowak, [http://pca.narod.ru/ElNetChakon.pdf Detection of Gene Expressions in Microarrays by Applying Iteratively Elastic Neural Net], In: B. Beliczynski et al. (Eds.), Lecture Notes in Computer Sciences, Vol. 4432, Springer: Berlin – Heidelberg 2007, 355–363.</ref> for exploratory data analysis and visualisation of multidimensional data, for data visualisation in economics, social and political sciences,<ref>A. Zinovyev, [http://arxiv.org/abs/1008.1188 Data visualization in political and social sciences], In: SAGE "International Encyclopedia of Political Science", Badie, B., Berg-Schlosser, D., Morlino, L. A. (Eds.), 2011.</ref> as an auxiliary tool for data mapping in geographic informational systems and for visualisation of data of various nature.
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| Recently, the method is adapted as a support tool in the decision process underlying the selection, optimization, and management of [[financial portfolio]]s.<ref>M. Resta, [http://www.springerlink.com/content/6416210h727016t5/ Portfolio optimization through elastic maps: Some evidence from the Italian stock exchange], Knowledge-Based Intelligent Information and Engineering Systems, B. Apolloni, R.J. Howlett and L. Jain (eds.), Lecture Notes in Computer Science, Vol. 4693, Springer: Berlin – Heidelberg, 2010, 635-641.</ref>
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| ==References==
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| {{reflist}}
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| [[Category:Data mining]]
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| [[Category:Multivariate statistics]]
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| [[Category:Dimension reduction]]
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How to decide on the best pocket knife will rely upon each people needs. So that you may need to do a little research into the person or individuals your buying for. Is that this particular person outside rather a lot? A pocket knife that has a knife and presumably different instruments is likely to be finest And remember the good friend who's a tail gaiter and at his favorite staff's parking zone for the big recreation. Some pocket knives have a helpful bottle opener and corkscrew which can not all the time be available in these situations. And what in regards to the avid golfer? There are those that enjoy camping, fishing and looking.
Ka-Bar Mule Field Folder Knife - Wow, we simply cannot imagine this knife is below $50.00. This undoubtedly deserves to be thought-about one of the best folding knives for the price. You possibly can put this knife up to any test, and it will cross your expectations by far. This knife weighs a little less than 1/2 of a pound – which is an efficient factor because this knife will last you awhile! The KA-BAR mule knife is ideal for any labor job, and great for being in the wilderness. The opening and closing method of this knife will be sure you don’t have any accidental closures on your finger.
Laguiole steak knives are the most effective steak knives you could find in the world right this moment when you think about their attributes together with however not limited to their value and the quality that they provide at the stated value. The rationale for these steak knives being known as one of the best in the world is twofold. One is the fact that these knives are manufactured to the most effective of their standards through the use of the best metal. This ensures knives of the very best quality and of the most sturdy kind, thereby cementing their place as a number of the finest steak knives out there in the market.
Before you make a large buy from an internet retailer reminiscent of World Jewels, what is the first thing that you do? You research the product and also you analysis the very best place to purchase the product. With the development of the web phrase of mouth opinions have been exchange by written ones. So individuals will learn World Jewels evaluations when attempting aero knife Infomercial to decide of whether or to not buy from them. But when no one wrote World Jewels reviews than this follow would be not possible. So while it is very important do your homework and skim World Jewels opinions , additionally it is necessary to write them.
As we speak the corporate still lives on even stronger than it was 5 or ten years in the past in the same city where it was founded with a new location and an updated web site. The Christy Sliding Blade Pocket Knives are still made on the unique fifty three-operation production line and gear, which is now operated and produced by machinist Hal R. Christy, son of Earl Christy. There are very few fourth-era, family owned corporations on the earth, and this one continues to offer “the best pocket knife ever designed” out there within the Companion (nickel plated), Govt (polished black nickel plated), and the Traveler (matte finish Teflon nickel plated). Features & operate
The knife could be very gentle weight however you can tell that it is extremely sturdy and candle a beating. It feels very comfy in my hand with the finger grooves and it is extremely evident that the knife won't slip out of my hand because the grip is constructed of each exhausting and mushy polymers, therefore the double injection. It is a exhausting durable deal with however has the grip that you just need, I really feel like I have complete control of the knife whereas holding it. I even let my spouse hold the knife and asked her how it felt in her hand.