摘 要
基于广义特征值得最近支持向量机（Proximal Support Vector Machine via Generalized Eigenvalues GEPSVM）是一种新的、具有与SVM性能相当得两分类方法，通过求解广义特征值来获得两个彼此不平行的拟合两类样本的超平面。通过引入最近支持向量机使用的技术，可以避免(TWSVM)分类器。通过这种操作方式，我们制定了一个更简单的非平行平面近端分类器，通过减少TWSVM的显着计算负担来加速对它的训练。用于二进制数据分类的非平行平面近端分类器的公式相当于两个相同的均方误差优化问题，其导致在输入空间种求解两个小的线性方程组。经计算表明，非平行平面近端分类器的Matlab实现可以用300万个点的数据集训练，其中10个属性不到3秒。合成以及几个基准数集的计算结果表明了所提出的分类器在计算时间和测试精度方面的优势。本次设计的论文主要研究测试样本归为距其最近的超平面所在的类。然而，该规则再某些情形会导致较差的分类结果。对此，再GEPSVM基础上，通过怕再类似合超平面上寻找一个包含了所有训练样本投影的局部凸区域，来决定样本的类别。该局部方法不仅具有较GEPSVM更优的分类性能，同时，还衍生出了求解超平面上凸壳的简单且易于核化的新算法。最后再人工和UCI数据集上获得了验证。
关键词：最接近支持向量机；广义特征值问题；凸壳；局部化；分类
Design and implementation of a localized classification rule
Abstract
Recently, the Generalized eigenvector Machine via Generalized eigenvector Machine (SVM) is a new classification method with similar performance to SVM. By solving Generalized Eigenvalues, two hyperplanes fitting two classes of samples are obtained. The (TWSVM) classifier can be avoided by introducing techniques recently used by support vector machines. In this way, we develop a simpler non-parallel plane proximal classifier and accelerate its training by reducing the significant computational burden of TWSVM. The formula of the non-parallel plane proximal classifier for binary data classification is equivalent to two identical mean square error optimization problems which lead to the solution of two small linear equations in the input space. The calculation shows that the Matlab implementation of the non-parallel plane near-end classifier can be trained with data sets of 3 million points, 10 of which are less than 3 seconds. The synthesis and the calculation results of several reference sets show the advantages of the proposed classifier in computing time and test accuracy. In this paper, the test samples are classified into the nearest hyperplane class. However, this rule can lead to poor classification results in some cases. In this regard, based on GEPSVM, the category of samples is determined by looking for a local convex region containing the projection of all training samples on the hyperplane. This local method not only has better classification performance than GEPSVM, but also derives a new simple and easy nucleation algorithm for convex hull on hyperplane. Finally, the validation is obtained on the manual and UCI data sets.
Key words: Closest to support vector machine; Generalized eigenvalue problem; Convex hull. Localization; classification
目录
摘 要 II
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