Related papers: Provable Non-Convex Euclidean Distance Matrix Comp…
We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the…
Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a…
Many important geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given a set of relative measurements between them. This problem is typically formulated as…
Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified…
The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
Consider the sum of the first $N$ eigenspaces for the Laplacian on a Riemannian manifold. A basis for this space determines a map to Euclidean space and for $N$ sufficiently large the map is an embedding. In analogy with a fruitful idea of…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in…
We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…
The Euclidean Median (EM) of a set of points $\Omega$ in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in $\Omega$. While there exits no closed-form expression for the EM, it…
We consider the problem of recovering the topology and the edge conductance value, as well as characterizing a set of electrical networks that satisfy the limitedly available Thevenin impedance measurements. The measurements are obtained…
Deciding whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable. This paper takes a step towards understanding a broad class of nonconvex-nonconcave minimax problems that do remain…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…