论文标题
通过变形的Weyl-Heisenberg代数构建“支撑矢量”机器特征空间
Construction of 'Support Vector' Machine Feature Spaces via Deformed Weyl-Heisenberg Algebra
论文作者
论文摘要
本文基于变形的WEYL-HEISENBERG代数，该状态通过公共参数统一了众所周知的SU（2），Weyl-Heisenberg和SU（1,1）基团的变形Weyl-Heisenberg代数。我们表明，变形的相干状态为元内核函数提供了理论基础，即元素又定义了内核函数。内核功能推动了机器学习领域的发展和本文介绍的元内核功能，为内核功能的定义和探索开辟了新的理论途径。元内核函数将相关的革命表面应用于具有非线性相干状态的特征空间。一项实证研究比较了从元内核中得出的变形的SU（2）和SU（1,1）内核，该元素显示出与径向基核类似的性能，并提供了新的见解（基于变形的Weyl-Heisenberg代数）。
This paper uses deformed coherent states, based on a deformed Weyl-Heisenberg algebra that unifies the well-known SU(2), Weyl-Heisenberg, and SU(1,1) groups, through a common parameter. We show that deformed coherent states provide the theoretical foundation of a meta-kernel function, that is a kernel which in turn defines kernel functions. Kernel functions drive developments in the field of machine learning and the meta-kernel function presented in this paper opens new theoretical avenues for the definition and exploration of kernel functions. The meta-kernel function applies associated revolution surfaces as feature spaces identified with non-linear coherent states. An empirical investigation compares the deformed SU(2) and SU(1,1) kernels derived from the meta-kernel which shows performance similar to the Radial Basis kernel, and offers new insights (based on the deformed Weyl-Heisenberg algebra).
