Discrete Signal Processing with Set Functions
نویسندگان
چکیده
Set functions are (or signals) indexed by the powerset (set of all subsets) a finite set N. They fundamental and ubiquitous in many application domains have been used, for example, to formally describe or quantify loss semantic image segmentation, informativeness sensors sensor networks utility sets items recommender systems, cooperative games game theory, bidders combinatorial auctions. In particular, subclass submodular occurs optimization machine learning problems. this paper, we derive discrete-set signal processing (SP), novel shift-invariant linear framework functions. Discrete-set SP considers different notions shift obtained from union difference operations. For each it provides associated filters, convolution, Fourier transform, frequency response. We provide intuition our using concept generalized coverage function that define, identify multivariate mutual information as special case spectrum, motivate ordering. Our work brings new tools analyzing functions, and, dealing with their exponential nature. show two prototypical applications experiments: compression sampling preference elicitation
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ژورنال
عنوان ژورنال: IEEE Transactions on Signal Processing
سال: 2021
ISSN: ['1053-587X', '1941-0476']
DOI: https://doi.org/10.1109/tsp.2020.3046972