论文标题
组不变的最大过滤
Group-invariant max filtering
论文作者
论文摘要
考虑到真正的内部产品空间$ v $和一个线性异构体的组$ g $，我们在$ g $ invariant实用值的函数上构建了我们称为Max Filters的$ V $。如果$ v = \ m athbb {r}^d $和$ g $是有限的，那么合适的最大过滤器库将轨道分开，甚至是商标中的bilipschitz。如果$ v = l^2（\ mathbb {r}^d）$和$ g $是一组翻译运算符，则最大过滤器表现出稳定性对差异变形的稳定性，例如Mallat引入的散射变换。我们确定Max过滤器在理论上和实践中都非常适合各种分类任务。
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.
