论文标题
通过差异不变性测量差异
Measuring dissimilarity with diffeomorphism invariance
论文作者
论文摘要
相似性（或差异）的度量是许多机器学习算法的关键要素。我们介绍了DID，一种适用于广泛数据空间的成对差异度量，该度量利用数据的内部结构是不变的。我们证明，确实享有与理论研究和实际使用有关的属性。通过表示每个基准作为一个函数，将DID定义为在重现Hilbert空间中优化问题的解决方案，并且可以以封闭形式表示。实际上，它可以通过NyStröm采样有效地近似。经验实验支持DID的优点。
Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data's internal structure to be invariant to diffeomorphisms. We prove that DID enjoys properties which make it relevant for theoretical study and practical use. By representing each datum as a function, DID is defined as the solution to an optimization problem in a Reproducing Kernel Hilbert Space and can be expressed in closed-form. In practice, it can be efficiently approximated via Nyström sampling. Empirical experiments support the merits of DID.
