Related papers: Group-invariant max filtering

We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded…

If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f…

This paper focuses on improving the mathematical interpretability of convolutional neural networks (CNNs) in the context of image classification. Specifically, we tackle the instability issue arising in their first layer, which tends to…

The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…

Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X]^G in the case where G is reductive. Furthermore, we address the case where G is connected and…

Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…

Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $\alpha : \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant…

We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…

A quadrature mirror filter (QMF) function can be considered as the transition function for a Markov process on the unit interval. The QMF functions that generate scaling functions for multiresolution analyses are then distinguished by…

We introduce and study equivariant Hilbert series of ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid $Inc(\mathbb{N})$ of strictly increasing functions.…

We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical…

Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic…

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is…

In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…

For a second countable locally compact group $G$ and a closed abelian subgroup $H$, we give a range function classification of closed subspaces in $L^2(G)$ invariant under left translation by $H$. For a family $\mathscr{A} \subset L^2(G)$,…

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…

Landau-Ginzburg mirror symmetry studies isomorphisms between graded Frobenius algebras, known as A- and B-models. Fundamental to constructing these models is the computation of the finite, Abelian $\textit{maximal symmetry group}$…

We introduce a new class of functional correlated disordered materials, termed Gyromorphs, which uniquely combine liquid-like translational disorder with quasi-long-range rotational order, induced by a ring of $G$ delta peaks in their…

Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group $G$ acts…