Jameson Cahill, Joseph W. Iverson, Dustin G. Mixon, Daniel Packer
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引用次数: 0
Abstract
Given a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where \(V={\mathbb {R}}^d\) and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where \(V=L^2({\mathbb {R}}^d)\) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice.
给定一个实内积空间 V 和一个线性等距群 G，我们构建了一个 V 上的 G 不变实值函数族，我们称之为最大滤波器。在 \(V={\mathbb {R}}^d\) 和 G 有限的情况下，一个合适的最大滤波器库可以分离轨道，并且在商度量中甚至是双桥的。在\(V=L^2({\mathbb {R}}^d)\) 和 G 是平移算子群的情况下，最大滤波器对类似于马拉特引入的散射变换的衍射变形具有稳定性。我们从理论和实践上证明，最大滤波器非常适合各种分类任务。
期刊介绍：
Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer.
With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles.
The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.
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