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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 Large margin nearest neighbor ： ウィキペディア英語版 Large margin nearest neighbor Large margin nearest neighbor (LMNN) classification is a statistical machine learning algorithm. It learns a Pseudometric designed for k-nearest neighbor classification. The algorithm is based on semidefinite programming, a sub-class of convex optimization. The goal of supervised learning (more specifically classification) is to learn a decision rule that can categorize data instances into pre-defined classes. The k-nearest neighbor rule assumes a ''training'' data set of labeled instances (i.e. the classes are known). It classifies a new data instance with the class obtained from the majority vote of the k closest (labeled) training instances. Closeness is measured with a pre-defined metric. Large Margin Nearest Neighbors is an algorithm that learns this global (pseudo-)metric in a supervised fashion to improve the classification accuracy of the k-nearest neighbor rule. ==Setup== The main intuition behind LMNN is to learn a pseudometric under which all data instances in the training set are surrounded by at least k instances that share the same class label. If this is achieved, the leave-one-out error (a special case of cross validation) is minimized. Let the training data consist of a data set $D=\backslash \backslash subset\; R^d\backslash times\; C$, where the set of possible class categories is $C=\backslash$. The algorithm learns a pseudometric of the type :$d(\backslash vec\; x\_i,\backslash vec\; x\_j)=(\backslash vec\; x\_i-\backslash vec\; x\_j)^\backslash top\backslash mathbf(\backslash vec\; x\_i-\backslash vec\; x\_j)$. For $d(\backslash cdot,\backslash cdot)$ to be well defined, the matrix $\backslash mathbf$ needs to be positive semi-definite. The Euclidean metric is a special case, where $\backslash mathbf$ is the identity matrix. This generalization is often (falsely) referred to as Mahalanobis metric. Figure 1 illustrates the effect of the metric under varying $\backslash mathbf$. The two circles show the set of points with equal distance to the center $\backslash vec\; x\_i$. In the Euclidean case this set is a circle, whereas under the modified (Mahalanobis) metric it becomes an ellipsoid. The algorithm distinguishes between two types of special data points: ''target neighbors'' and ''impostors''. 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「Large margin nearest neighbor」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.