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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Structured support vector machine ： ウィキペディア英語版 Structured support vector machine The structured support vector machine is a machine learning algorithm that generalizes the Support Vector Machine (SVM) classifier. Whereas the SVM classifier supports binary classification, multiclass classification and regression, the structured SVM allows training of a classifier for general structured output labels. As an example, a sample instance might be a natural language sentence, and the output label is an annotated parse tree. Training a classifier consists of showing pairs of correct sample and output label pairs. After training, the structured SVM model allows one to predict for new sample instances the corresponding output label; that is, given a natural language sentence, the classifier can produce the most likely parse tree. ==Training== For a set of $\backslash ell$ training instances $(\backslash boldsymbol\_n,y\_n)\; \backslash in\; \backslash mathcal\backslash times\backslash mathcal$, $n=1,\backslash dots,\backslash ell$ from a sample space $\backslash mathcal$ and label space $\backslash mathcal$, the structured SVM minimizes the following regularized risk function. :$\backslash underset\; \backslash quad\; \backslash |\backslash boldsymbol\backslash |^2\; +\; C\; \backslash sum\_^$ \underset \left(\Delta(y_n,y) + \boldsymbol'\Psi(\boldsymbol_n,y) - \boldsymbol'\Psi(\boldsymbol_n,y_n)\right) The function is convex in $\backslash boldsymbol$ because the maximum of a set of affine functions is convex. The function $\backslash Delta:\; \backslash mathcal\; \backslash times\; \backslash mathcal\; \backslash to\; \backslash mathbb\_+$ measures a distance in label space and is an arbitrary function (not necessarily a metric) satisfying $\backslash Delta(y,z)\; \backslash geq\; 0$ and $\backslash Delta(y,y)=0\; \backslash ;\backslash ;\; \backslash forall\; y,z\; \backslash in\; \backslash mathcal$. The function $\backslash Psi:\; \backslash mathcal\; \backslash times\; \backslash mathcal\; \backslash to\; \backslash mathbb^d$ is a feature function, extracting some feature vector from a given sample and label. The design of this function depends very much on the application. Because the regularized risk function above is non-differentiable, it is often reformulated in terms of a quadratic program by introducing one slack variable $\backslash xi\_n$ for each sample, each representing the value of the maximum. The standard structured SVM primal formulation is given as follows. :$\backslash begin$ \underset} & \|\boldsymbol\|^2 + C \sum_^ \xi_n\\ \textrm & \boldsymbol' \Psi(\boldsymbol_n,y_n) - \boldsymbol' \Psi(\boldsymbol_n,y) + \xi_n \geq \Delta(y_n,y),\qquad n=1,\dots,\ell,\quad \forall y \in \mathcal \end 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Structured support vector machine」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.