Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran.
Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran.
Neural Netw. 2018 Feb;98:87-101. doi: 10.1016/j.neunet.2017.11.006. Epub 2017 Nov 16.
The Support Vector Machine (SVM) is a supervised learning algorithm to analyze data and recognize patterns. The standard SVM suffers from some limitations in nonlinear classification problems. To tackle these limitations, the nonlinear form of the SVM poses a modified machine based on the kernel functions or other nonlinear feature mappings obviating the mentioned imperfection. However, choosing an efficient kernel or feature mapping function is strongly dependent on data structure. Thus, a flexible feature mapping can be confidently applied in different types of data structures without challenging a kernel selection and its tuning. This paper introduces a new flexible feature mapping approach based on the Dirichlet distribution in order to develop an efficient SVM for nonlinear data structures. To determine the parameters of the Dirichlet mapping, a tuning technique is employed based on the maximum likelihood estimation and Newton's optimization method. The numerical results illustrate the superiority of the proposed machine in terms of the accuracy and relative error rate measures in comparison to the traditional ones.
支持向量机（SVM）是一种用于分析数据和识别模式的监督学习算法。标准 SVM 在非线性分类问题中存在一些局限性。为了克服这些局限性，SVM 的非线性形式提出了一种基于核函数或其他非线性特征映射的修改机器，从而避免了上述缺陷。然而，选择有效的核函数或特征映射函数强烈依赖于数据结构。因此，一种灵活的特征映射可以自信地应用于不同类型的数据结构，而无需对核选择及其调整提出挑战。本文提出了一种基于 Dirichlet 分布的新的灵活特征映射方法，以便为非线性数据结构开发有效的 SVM。为了确定 Dirichlet 映射的参数，我们采用了基于最大似然估计和牛顿优化方法的调整技术。数值结果表明，与传统方法相比，所提出的机器在准确性和相对误差率方面具有优越性。
