支援向量機

支援向量機(Support Vector Machine, SVM)是一種監督式學習的方法，一般是應用於分類(Classification/supervised learning)等相關議題上。SVM 基本運作模式如下：在給定一群訓練樣本之下，每個樣本會分別對應至兩個不同的類別(Category)，SVM 會嘗試從建構一個模型(Model)，並利用此模型將每一個樣本分配到一個類別上。

A support vector machine (SVM) is a concept in computer science for a set of related supervised learning methods that analyze data and recognize patterns, used for classification and regression analysis. The standard SVM takes a set of input data and predicts, for each given input, which of two possible classes the input is a member of, which makes the SVM a non-probabilistic binary linear classifier. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other. An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall on.

• Corinna Cortes and V. Vapnik, "Support-Vector Networks", Machine Learning, 20, 1995. http://www.springerlink.com/content/k238jx04hm87j80g/

典型的SVM是一種二元分類器(Two-class classifier)，因此，以下我們僅針對典型SVM來進行說明。

在二元分類中，SVM嘗試在訓練資料(x)所構成的空間中，尋找一個超平面(Hyperplane)能將不同類別的資料完美的分開，而且，希望此超平面與不同的類別的距離”愈大愈好”。如圖所示，藍色矩形為第一個類別(標記為+1)，紅色圓形為第二個類別(標記為-1)，而SVM則想要找出的超平面即是wx+b=0，此超平面可以使得兩個類別(邊界/Margin)的距離最大。

• David Meyer, Friedrich Leisch, and Kurt Hornik. The support vector machine under test. Neurocomputing 55(1–2): 169–186, 2003 http://dx.doi.org/10.1016/S0925-2312(03)00431-4

• Chih-Wei Hsu, Chih-Chung Chang, and Chih-Jen Lin (2003). A Practical Guide to Support Vector Classification. Technical Report Department of Computer Science and Information Engineering, National Taiwan University.

• Kai-Bo Duan and S. Sathiya Keerthi (2005). "Which Is the Best Multiclass SVM Method? An Empirical Study". Proceedings of the Sixth International Workshop on Multiple Classifier Systems.

• Chih-Wei Hsu and Chih-Jen Lin (2002). "A Comparison of Methods for Multiclass Support Vector Machines". IEEE Transactions on Neural Networks.