Related papers: Estimating axial symmetry using random projections
We consider the problem of testing whether a multivariate distribution is axially symmetric about some unknown direction. Under a simple-spectrum assumption on the covariance matrix, any symmetry axis must coincide with an eigenvector of…
Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
Most of the work on checking spherical symmetry assumptions on the distribution of the $p$-dimensional random vector $Y$ has its focus on statistical tests for the null hypothesis of exact spherical symmetry. In this paper, we take a…
Motivated by the central role played by rotationally symmetric distributions in directional statistics, we consider the problem of testing rotational symmetry on the hypersphere. We adopt a semiparametric approach and tackle problems where…
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
Symmetry is a fundamental concept that has been extensively studied, yet detecting it in complex scenes remains a significant challenge in computer vision. Recent heatmap-based approaches can localize potential regions of symmetry axes but…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
In this technical report, we will make two observations concerning symmetries of the probability distribution resulting from projection of a piece of p-dimensional data onto a random m-dimensional subspace of $\mathbb{R}^p$, where m < p. In…
Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object…
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…
Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point…
The angular correlation is a method for measuring the distribution of structure in the Universe, through the statistical properties of the angular distribution of galaxies on the sky. We measure the angular correlation of galaxies from the…
We briefly present a new coordinate-invariant statistical test dedicated to the study of the orientations of transverse quantities of non-uniformly distributed sources on the celestial sphere. These quantities can be projected spin-axes or…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…