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.

翻译：鉴于一个真正的内产物空间为V$和一组线性异美美元,我们用我们称之为最大过滤器的V美元建造了一个由G$和G$组成的家庭,用我们称之为最大过滤器的V美元建造了一个价值为G$的不变实际功能。在V ⁇ mathbb{R ⁇ d$和$G$是有限的情况下,一个合适的最大过滤器银行将轨道分离,甚至以商数衡量为双立式。在V=L2(\mathb{R ⁇ d)美元和$G$是翻译操作员的组合中,一个最大过滤器展示了像Mallat引进的分散变异的变异性的最大变异性。我们确定最大过滤器在理论和实践上都非常适合各种分类任务。