Semigroup Kernels on Measures
Semigroup Kernels on Measures
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发表时间：
2005-12
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通讯作者：
Marco Cuturi;K. Fukumizu;Jean-Philippe Vert
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作者：
Marco Cuturi;K. Fukumizu;Jean-Philippe Vert
我们提出了一系列关于度量的正定核，其特征在于两个度量之间的核值是它们之和的函数。这些内核可用于通过将结构化对象（例如图像和文本）表示为组件集（例如像素或单词）或更一般地表示为组件空间的度量来导出这些对象的内核。这项工作中研究的几个内核利用熵或广义方差等度量定义的常见量来检测相似性。给定组件本身空间上的先验内核，通过使用“内核技巧”在更高效和灵活的框架中重申先前的结果，可以进一步扩展该方法。最后，通过积分表示定理证明了这种正定核的建设性方法，然后给出了手写数字分类基准实验的实验结果以说明该方法的有效性。
We present a family of positive definite kernels on measures, characterized by the fact that the value of the kernel between two measures is a function of their sum. These kernels can be used to derive kernels on structured objects, such as images and texts, by representing these objects as sets of components, such as pixels or words, or more generally as measures on the space of components. Several kernels studied in this work make use of common quantities defined on measures such as entropy or generalized variance to detect similarities. Given an a priori kernel on the space of components itself, the approach is further extended by restating the previous results in a more efficient and flexible framework using the "kernel trick". Finally, a constructive approach to such positive definite kernels through an integral representation theorem is proved, before presenting experimental results on a benchmark experiment of handwritten digits classification to illustrate the validity of the approach.