基于非线性相干态的核方法
Kernel Method based on Non-Linear Coherent State
摘要：
本文通过将数据集映射到一组非线性相干态，将输入在量子态中编码为非线性特征映射的过程重新解释。由于当数据被映射到由相干态表示的复希尔伯特态时径向基函数被恢复的事实，非线性相干态可以被认为是相关联的核的自然概括。考虑变质量量子振子的非线性相干态，提出了一种基于广义超几何函数的核函数，作为正交多项式函数。建议的内核在两个众所周知的数据集（make circles和make moons）上使用支持向量机实现，即使在存在高噪声的情况下也优于基线。此外，我们研究的特征空间的几何性质的影响，获得非线性相干态，对SVM分类任务，通过考虑相关相干态的Fubini-Study度量。
英文摘要：
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.
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