A Discrete Signal Processing Framework for Set Functions
A Discrete Signal Processing Framework for Set Functions
复制标题
集合函数的离散信号处理框架
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Markus Püschel
中科院分区：
文献类型：
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作者：
Markus Püschel
集合函数将一个真实的（或复）值与给定有限集合S的每个子集相关联。在本文中，我们推导出一种新的离散信号处理（DSP）框架，这样的功能。这意味着我们定义并推导出基本DSP概念的适当概念，包括移位、滤波、频率响应、傅立叶变换和卷积定理。核心是子集上的移位的定义，我们考虑了两个最自然的选择，即，这些最类似于标准DSP中的时移。集合函数自然地出现在与概率分布、图切割、传感器放置、互信息、随机变量集合的熵等相关联的许多上下文中。我们的工作为它们的处理提供了一套新的工具。
A set function associates a real (or complex) value with every subset of a given finite set $S$. In this paper, we derive a novel discrete signal processing (DSP) framework for such functions. This means we define and derive suitable notions of basic DSP concepts including shift, filtering, frequency response, Fourier transform, and convolution theorems. At the heart is the definition of the shift on subsets for which we consider the two most natural choices, i.e., those most analogous to the time shift in standard DSP. Set functions naturally occur in many contexts associated with probability distributions, graph cuts, sensor placements, mutual information, entropy of sets of random variables, and others. Our work offers a new set of tools for their processing.