Related papers: Directional Statistics and Filtering Using libDire…
Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are…
Directional or Circular statistics are pertaining to the analysis and interpretation of directions or rotations. In this work, a novel probability distribution is proposed to model multidimensional sparse directional data. The Generalised…
The need for statistical models of orientations arises in many applications in engineering and computer science. Orientational data appear as sets of angles, unit vectors, rotation matrices or quaternions. In the field of directional…
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
Directional estimation is a common problem in many tracking applications. Traditional filters such as the Kalman filter perform poorly because they fail to take the periodic nature of the problem into account. We present a recursive filter…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
Directional data consists of unit vectors in q-dimensions that can be described in polar or Cartesian coordinates. Axial data can be viewed as a pair of directions pointed in opposite directions or as a projection matrix of rank 1.…
Angle halving, or alternatively the reverse operation of angle doubling, is a useful tool when studying directional distributions. It is especially useful on the circle where, in particular, it yields an identification between the wrapped…
We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…
The von Mises-Fisher (vMF) distribution has long been a mainstay for inference with data on the unit hypersphere in directional statistics. The performance of statistical inference based on the vMF distribution, however, may suffer when…
Many statistical problems and applications require repeated computation of order statistics, such as the median, but most statistical and programming environments do not offer in their main distribution linear selection algorithms. We…
Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward…
The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
In 2020, two novel distributions for the analysis of directional data were introduced: the spherical Cauchy distribution and the Poisson kernel-based distribution. This paper provides a detailed exploration of both distributions within…
We discuss generalized linear models for directional data where the conditional distribution of the response is a von Mises-Fisher distribution in arbitrary dimension or a Bingham distribution on the unit circle. To do this properly, we…
A comprehensive toolkit is developed for regression analysis of directional data based on a flexible class of angular Gaussian distributions. Informative testing procedures for isotropy and covariate effects on the directional response are…
Structural regularities in man-made environments reflect in the distribution of their surface normals. Describing these surface normal distributions is important in many computer vision applications, such as scene understanding, plane…
Uniform distribution of the points has been of interest to researchers for a long time and has applications in different areas of Mathematics and Computer Science. One of the well-known measures to evaluate the uniformity of a given…