en>Seaphoto: Reverted edits by 86.147.73.144 (talk) to last revision by Illia Connell (HG)

2014-02-16T18:25:04Z

Reverted edits by 86.147.73.144 (talk) to last revision by Illia Connell (HG)

en>Illia Connell: /* Single linkage */standardize journal name, replaced: Journal of the Royal Statistical Society. Series C (Applied Statistics) → Journal of the Royal Statistical Society, Series C using AWB

2013-04-21T06:10:30Z

Single linkage: standardize journal name, replaced: Journal of the Royal Statistical Society. Series C (Applied Statistics) → Journal of the Royal Statistical Society, Series C using AWB

← Older revision		Revision as of 08:10, 21 April 2013
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			In [[machine learning]], the '''hinge loss''' is a [[loss function]] used for training [[statistical classification\|classifiers]]. The hinge loss is used for "maximum-margin" classification, most notably for [[support vector machine]]s (SVMs).<ref>{{cite doi\|10.1162/089976604773135104}}</ref>
			For an intended output t = ±1 and a classifier score ''y'', the hinge loss of the prediction ''y'' is defined as

			:<math>\ell(y) = \max(0, 1-t \cdot y)</math>

	~~As software becomes more accessible and~~ the ~~borders between operating-system platforms blur it truly is good to hear connected with programs just like Dr~~. ~~Drum you~~ can ~~use on Macintosh or DESKTOP~~ and ~~work comfortably in Windows or maybe OSX. For~~ the ~~inspiring music producer~~, Dr. ~~Drum can be~~ a ~~blessing using a low price ticket~~, ~~at the moment that is usually.~~<br><br>~~This is~~ a ~~tool that should enable your pro or even amateur DJ~~ to ~~build great beats~~, ~~this bedrock on~~ the ~~dance~~-~~floor, coming from a [~~http://~~Www~~.~~Adobe~~.~~com~~/~~cfusion~~/~~search~~/~~index~~.~~cfm?term~~=~~&package&loc~~=~~en_us&siteSection~~=~~home package] with which has much to supply~~ and for ~~the price tag that is the envy of several of its long-established plus much more expensive opponents~~.<br><br>~~Supplied via a new download~~ for ~~the single monthly payment of all around $40 you become a pail load regarding tech that may allow even essentially the most [https~~://www.~~youtube~~.~~com~~/~~watch?v~~=~~Rztkiehibu4 beat maker] raw regarding amateurs to become putting out premium professional ‘beats’ inside hours~~. ~~In the box, you can expect your 12-pad drum ‘kit’, your 16-channel sequencer as well as a keyboard addressing four octaves~~.<br><br>~~Included with~~ the ~~instrumentation, Medical professional~~. ~~Drum requires a series regarding expertly produced instructional videos that will administer~~ the ~~user originating from a through Z from~~ the ~~processes to generate really hypnotic beats on~~ the ~~get go~~, ~~it doesn't matter what~~ the ~~type from ‘Dub Step’ to be able to disco.~~<br><br>~~At this time Dr. Drum is on offer for an occasional of $40 but will increase before too much time so it would be worth acquiring the dive now as opposed to waiting~~, ~~the advantage being that this is a one~~-~~off buy~~, ~~simply no annual permission~~, ~~not any update fees – when you are within~~, ~~that you're in.~~<br>~~<br>That makers use~~ a ~~bold lay claim~~, ~~your decide one that~~ many ~~people support by means~~ of ~~putting its money where their teeth~~ is~~; it~~ has ~~an 60-day no quibble make sure that when you aren’t content, they will give you~~ a ~~total refund.~~<br><br>~~Although being inventive isn’t practically affordable, it’s seriously about getting music~~ that ~~people want in order to hear, that will dance to and remember – Medical professional. Drum~~ is ~~a piece of digital overcom software that provide you with the self confidence to rise to the top within your genre.~~		Note that ''y'' should be the "raw" output of the SVM's decision function, not the predicted class label. E.g., in linear SVMs, <math>y = \mathbf{w} \cdot \mathbf{x} + b</math>.

			It can be seen that when <math>t</math> and <math>y</math> have the same sign (meaning <math>y</math> predicts the right class) and <math>y \ge 1</math>, <math>\ell(y) = 0</math>, but when they have opposite sign, <math>\ell(y)</math> increases linearly with <math>y</math> (one-sided error).

			==Extensions==
			While SVMs are commonly extended to [[multiclass classification]] in a one-vs.-all or one-vs.-one fashion,<ref name="duan2005">{{cite doi\|10.1007/11494683_28}}</ref>
			there exists a "true" multiclass version of the hinge loss due to Crammer and Singer,<ref>{{cite journal \|title=On the algorithmic implementation of multiclass kernel-based vector machines \|year=2001 \|url=http://jmlr.csail.mit.edu/papers/volume2/crammer01a/crammer01a.pdf \|journal=[[Journal of Machine Learning Research\|J. Machine Learning Research]] \|volume=2 \|pages=265–292 \|author=Crammer, Koby; and Singer, Yoram }}</ref>
			defined for a linear classifier as<ref>{{cite conference \|authors=Robert C. Moore and John DeNero \|title=L<sub>1</sub> and L<sub>2</sub> regularization for multiclass hinge loss models \|url=http://www.ttic.edu/sigml/symposium2011/papers/Moore+DeNero_Regularization.pdf\|booktitle=Proc. Symp. on Machine Learning in Speech and Language Processing \|year=2011}}</ref>

			:<math>\ell(y) = \max(0, 1 + \max_{y \ne t} \mathbf{w}_y \mathbf{x} - \mathbf{w}_t \mathbf{x})</math>

			In [[structured prediction]], the hinge loss can be further extended to structured output spaces. [[Structured support vector machine\|Structured SVMs]] use the following variant, where '''w''' denotes the SVM's parameters, ''φ'' the joint feature function, and Δ the [[Hamming loss]]:<ref>{{cite conference \|title=A comparison of discriminative classifiers for web news content extraction \|authors=Alex Spengler, Antoine Bordes and Patrick Gallinari \|year=2010 \|conference=RIAO}}</ref>

			:<math>\begin{align}
			\ell(\mathbf{y}) & = \Delta(\mathbf{y}, \mathbf{t}) + \langle \mathbf{w}, \phi(\mathbf{x}, \mathbf{y}) \rangle - \langle \mathbf{w}, \phi(\mathbf{x}, \mathbf{t}) \rangle \\
			& = \max_{y \in \mathcal{Y}} \left( \Delta(\mathbf{y}, \mathbf{t} + \langle \mathbf{w}, \phi(\mathbf{x}, \mathbf{y}) \rangle) \right) - \langle \mathbf{w}, \phi(\mathbf{x}, \mathbf{t}) \rangle
			\end{align}</math>

			==Optimization==
			The hinge loss is a [[convex function]], so many of the usual convex optimizers used in machine learning can work with it. It is not [[Differentiable function\|differentiable]], but has a [[Subderivative#The_subgradient\|subgradient]] with respect to model parameters <math>\mathbf{w}</math> of a linear SVM with score function <math>y = \mathbf{w} \cdot \mathbf{x}</math> that is given by

			:<math>\frac{\partial\ell}{\partial w_i} = \begin{cases} -t \cdot x_i & \text{if } t \cdot y < 1 \\ 0 & \text{otherwise} \end{cases}</math>

			== References ==
			{{Reflist}}

			[[Category:Loss functions]]
			[[Category:Support vector machines]]

en>Edward: link memoization using Find link

2012-06-27T17:21:09Z

link memoization using Find link

New page

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Nearest-neighbor chain algorithm - Revision history

en>Seaphoto: Reverted edits by 86.147.73.144 (talk) to last revision by Illia Connell (HG)

en>Illia Connell: /* Single linkage */standardize journal name, replaced: Journal of the Royal Statistical Society. Series C (Applied Statistics) → Journal of the Royal Statistical Society, Series C using AWB

en>Edward: link memoization using Find link