A Multicategory Kernel Distance Weighted Discrimination Method for Multiclass Classification
A Multicategory Kernel Distance Weighted Discrimination Method for Multiclass Classification
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DOI：
10.1080/00401706.2018.1529629
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发表时间：
2019-07-03
期刊：
影响因子：
2.5
通讯作者：
Zou, Hui
中科院分区：
文献类型：
--
作者：
Wang, Boxiang;Zou, Hui
距离加权判别(DWD)是一种有趣的大间隔分类器，已被证明具有良好的性质和实验成功。原始的DWD只处理具有线性分类边界的二进制分类。多类分类问题自然而然地出现在各种领域，如语音识别、卫星图像分类、自动驾驶车辆等。对于这种复杂的分类问题，当最优决策边界是高度非线性时，需要对二进制离散余弦分布进行灵活的多类别核扩展。为此，我们提出了一种新的多类别核离散余弦分布，即定义为再生核Hilbert空间中的边际向量优化问题。结果表明，该公式具有Fisher一致性。我们开发了一种加速投影梯度下降算法来适应多类别核离散余弦分布。仿真和基准数据应用表明，与一些流行的多类分类器相比，我们的方法具有很强的竞争力。
Distance weighted discrimination (DWD) is an interesting large margin classifier that has been shown to enjoy nice properties and empirical successes. The original DWD only handles binary classification with a linear classification boundary. Multiclass classification problems naturally appear in various fields, such as speech recognition, satellite imagery classification, and self-driving vehicles, to name a few. For such complex classification problems, it is desirable to have a flexible multicategory kernel extension of the binary DWD when the optimal decision boundary is highly nonlinear. To this end, we propose a new multicategory kernel DWD, that is, defined as a margin-vector optimization problem in a reproducing kernel Hilbert space. This formulation is shown to enjoy Fisher consistency. We develop an accelerated projected gradient descent algorithm to fit the multicategory kernel DWD. Simulations and benchmark data applications are used to demonstrate the highly competitive performance of our method, as compared with some popular state-of-the-art multiclass classifiers.