论文标题
关于Tanimoto-type内核对真实有价值功能的概括
On the generalization of Tanimoto-type kernels to real valued functions
论文作者
论文摘要
Tanimoto内核（Jaccard索引）是描述二进制属性集之间相似性的众所周知的工具。它已扩展到属性是非负实际值的情况。本文引入了更通用的Tanimoto内核公式，该公式允许测量任意实现功能的相似性。通过正确选择的集合统一属性的表示来构建此扩展。在得出内核的一般形式之后，从内核函数中提取了显式特征表示，并显示了一种简单的方式，将一般内核包含在Tanimoto内核中。最后，内核也表示为分段线性函数的商，并提供了平滑的近似值。
The Tanimoto kernel (Jaccard index) is a well known tool to describe the similarity between sets of binary attributes. It has been extended to the case when the attributes are nonnegative real values. This paper introduces a more general Tanimoto kernel formulation which allows to measure the similarity of arbitrary real-valued functions. This extension is constructed by unifying the representation of the attributes via properly chosen sets. After deriving the general form of the kernel, explicit feature representation is extracted from the kernel function, and a simply way of including general kernels into the Tanimoto kernel is shown. Finally, the kernel is also expressed as a quotient of piecewise linear functions, and a smooth approximation is provided.
