Related papers: Constructing packings in Grassmannian manifolds vi…

We present an algorithm to generate diverse foreground objects and composite them into background images using a GAN architecture. Given an object class, a user-provided bounding box, and a background image, we first use a mask generator to…

Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as…

We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…

Given a set $P$ of $n$ planar points, two axes and a real-valued score function $f()$ on subsets of $P$, the Optimal Planar Box problem consists in finding a box (i.e. axis-aligned rectangle) $H$ maximizing $f(H\cap P)$. We consider the…

This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the…

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of…

We present a novel approach to Riemannian interpolation on the Grassmann manifold. Instead of relying on the Riemannian normal coordinates, i.e. the Riemannian exponential and logarithm maps, we approach the interpolation problem with an…

Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference…

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…

Machine learning enables unbinned, highly-differential cross section measurements. A recent idea uses generative models to morph a starting simulation into the unfolded data. We show how to extend two morphing techniques, Schr\"odinger…

Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption. These models map between two domains by fooling a probabilistic discriminator, thereby…

We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality…

In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…

We develop projection pursuit for data that admit a natural representation in matrix form. For projection indices, we propose extensions of the classical kurtosis and Mardia's multivariate kurtosis. The first index estimates projections for…

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…

This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…

Geometrical objects describing the material geometry of continuously defective graphene sheets are introduced and their compatibility conditions are formulated. Effective edge dislocations embedded in the Riemann-Cartan material space and…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…