论文标题
在RKHM中学习：A $ C^*$ - 内核机器的代数扭曲
Learning in RKHM: a $C^*$-Algebraic Twist for Kernel Machines
论文作者
论文摘要
在繁殖内核希尔伯特太空（RKHS）和矢量值RKHS（VVRKHS）中进行了监督学习已有30多年的研究。在本文中，我们通过概括RKHS和VVRKHS的监督学习来重现核心Hilbert $ C^*$ - 模块（RKHM），并通过考虑$ C^*$ - Algebra的观点来构建有效的正定元素。与RKHS和VVRKHS的情况不同，我们可以使用$ C^*$ - 代数来扩大表示空间。这使我们能够构建RKHM的表示能力超出RKHSS，VVRKHSS和现有方法，例如卷积神经网络。我们的框架是合适的，例如，通过允许傅立叶组件的相互作用来有效地分析图像数据。
Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist to this rich literature by generalizing supervised learning in RKHS and vvRKHS to reproducing kernel Hilbert $C^*$-module (RKHM), and show how to construct effective positive-definite kernels by considering the perspective of $C^*$-algebra. Unlike the cases of RKHS and vvRKHS, we can use $C^*$-algebras to enlarge representation spaces. This enables us to construct RKHMs whose representation power goes beyond RKHSs, vvRKHSs, and existing methods such as convolutional neural networks. Our framework is suitable, for example, for effectively analyzing image data by allowing the interaction of Fourier components.
