arXiv research

Python tools for 3D shape analysis on Kendall's space.

A new algorithm for parallel transport on shape spaces is presented and compared to existing methods.

New method reconstructs 3D shapes from 2D images using Kendall's shape space.

Hierarchical geodesic model for analyzing shapes on manifolds.

Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty in dealing with non-Euclidean geometry. In this paper, motivated by the extrins…

In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Book…

Geomstats introduces shape module for analyzing shapes of objects.

Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.

A new privacy-preserving mechanism for shapes on manifolds.

New estimators reduce computation for Kendall's tau and conditional Kendall's tau matrices under structural assumptions.

ES-VAE models skeletal pose trajectories by removing nuisance factors.

Kendall transformation converts continuous data into categorical vectors for robust information theory.

Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has been relatively limited study of regression, classification, and testing problems …

We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to rela…

Improved portfolio optimization using Kendall-like correlation coefficients.

We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of $1$) or discordant (val…

Differentially private geodesic regression for non-Euclidean data.

This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spea…

New tests for conditional copulas based on decision trees.

We construct short retractions of a CAT(1) space to its small convex subsets. This construction provides an alternative geometric description of an analytic tool introduced by Wilfrid Kendall. Our construction uses a tractrix flow which can be defined as a gradient flow for a family of functions of certain type. In an …

Epilepsy is an important public health issue. An appropriate epileptiform discharge pattern detection of this neurological disease is a typical problem in biomedical engineering. In this paper, a new method is proposed for spike-and-wave discharge pattern detection based on Kendall's Tau-b coefficient. The proposed app…

Copula Discrepancy benchmarks sample dependence structure against known families.

Proposes Isometric Graph Neural Networks to preserve graph distances.

In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ({\em partial rankings}). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical frame…

High-dimensional data models, often with low sample size, abound in many interdisciplinary studies, genomics and large biological systems being most noteworthy. The conventional assumption of multinormality or linearity of regression may not be plausible for such models which are likely to be statistically complex due …

Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good prop…

We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space $\mathcal{X}$ and the goal is to order all possible observations x in $\mathcal{X}$ by means of a scoring function $s:\mathcal{X}…

A new shape space allows optimization of non-smooth shapes in fluid mechanics.

This paper studies the extreme dependencies between energy, agriculture and metal commodity markets, with a focus on local co-movements, allowing the identification of asymmetries and changing trend in the degree of co-movements. More precisely, starting from a non-parametric mixture copula, we use a novel copula-based…

In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every shape space studied so far in the literature, and offers a rigorou…

Classifies compact spaces by shape, finite spaces by weak homotopy.

We study the adaptive estimation of copula correlation matrix $Σ$ for the semi-parametric elliptical copula model. In this context, the correlations are connected to Kendall's tau through a sine function transformation. Hence, a natural estimate for $Σ$ is the plug-in estimator $\hatΣ$ with Kendall's tau statistic. We …

Hausdorff reflection keeps space shape intact.

Study measures uncertainty in MST identification across different correlation networks.

The paper explores three methods to assign a metric to shape spaces.

A novel method predicts shape development using Riemannian shape spaces.

We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on…

New method for summarizing ranking distributions using consensus ranking distributions.

Divides state space into regions with identical term structure shapes.

Coarse homotopy theory connects Euclidean cones to shape theory of compact spaces.

Framework clusters noisy MTS with robust fuzzy clustering, improving accuracy over existing methods.

Extended orbit model theory for shape analysis using graded group action framework.

Fine shape theory extends strong shape to noncompact metrizable spaces.

Fine shape of local compacta represented by ordinary maps.

In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A remarkable result of Younes, Michor, Shah and Mumford says that the space of closed p…

We introduce and develop fine shape, which has a very simple definition and aims to supersede all previously known shape theories for metrizable spaces. The problem with known shape theories of metrizable spaces is illustrated by the following bizarre situation. Čech cohomology is an invariant of shape, and a fortiori …

Universal spaces for finite topological spaces simplify shape descriptions.

Study eigenvalue estimates on Kähler and quaternion Kähler manifolds.