带理想的双核学习
Dual-to-kernel learning with ideals
摘要：
在本文中，我们提出了一个理论，它统一了核学习和符号代数方法。我们表明，这两个世界是天生的对偶彼此，我们使用这种对偶性相结合的结构意识的代数方法的效率和一般性的内核。其主要思想是将多项式环与特征空间、理想与流形联系起来，然后在核矩阵上利用这种生成-判别对偶。我们说明了这一点，提出了两个算法，IPCA和AVICA，同时流形和特征学习，并测试其准确性的合成和真实世界的数据。
英文摘要：
In this paper, we propose a theory which unifies kernel learning and symbolic algebraic methods. We show that both worlds are inherently dual to each other, and we use this duality to combine the structure-awareness of algebraic methods with the efficiency and generality of kernels. The main idea lies in relating polynomial rings to feature space, and ideals to manifolds, then exploiting this generative-discriminative duality on kernel matrices. We illustrate this by proposing two algorithms, IPCA and AVICA, for simultaneous manifold and feature learning, and test their accuracy on synthetic and real world data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
