论文标题
基于非线性相干状态的内核法
Kernel Method based on Non-Linear Coherent State
论文作者
论文摘要
在本文中，通过将数据集映射到一组非线性相干状态，重新解释了将输入作为非线性特征映射编码输入的过程。由于这一事实是，当数据映射到相干状态代表的复杂的希尔伯特状态时，径向基函数将被恢复，因此，非线性相干状态可以视为相关内核的自然概括。通过考虑具有可变质量的量子振荡器的非线性相干状态，我们提出了基于广义超几何函数的内核函数，即正交多项式函数。建议的内核在两个知名的数据集（制作圆圈，制作月亮）上使用支持向量机实现，即使在存在高噪声的情况下，也要优于基准。此外，我们通过使用考虑相关连贯状态的fubini-study指标来研究特征空间的几何特性（通过非线性相干状态获得）对SVM分类任务的影响。
In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered when data is mapped to a complex Hilbert state represented by coherent states, non-linear coherent states can be considered as natural generalisation of associated kernels. By considering the non-linear coherent states of a quantum oscillator with variable mass, we propose a kernel function based on generalized hypergeometric functions, as orthogonal polynomial functions. The suggested kernel is implemented with support vector machine on two well known datasets (make circles, and make moons) and outperforms the baselines, even in the presence of high noise. In addition, we study impact of geometrical properties of feature space, obtaining by non-linear coherent states, on the SVM classification task, by using considering the Fubini-Study metric of associated coherent states.
