Robust Single Rotation Averaging

• URL: http://arxiv.org/abs/2004.00732v4
• Date: Thu, 5 Nov 2020 00:17:44 GMT
• Title: Robust Single Rotation Averaging
• Authors: Seong Hun Lee, Javier Civera
• Abstract summary: We propose a novel method for single rotation averaging using the Weiszfeld algorithm. We show that both our method and the state of the art perform equally well with the proposed outlier rejection scheme.
• Score: 20.02647320786556
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel method for single rotation averaging using the Weiszfeld algorithm. Our contribution is threefold: First, we propose a robust initialization based on the elementwise median of the input rotation matrices. Our initial solution is more accurate and robust than the commonly used chordal $L_2$-mean. Second, we propose an outlier rejection scheme that can be incorporated in the Weiszfeld algorithm to improve the robustness of $L_1$ rotation averaging. Third, we propose a method for approximating the chordal $L_1$-mean using the Weiszfeld algorithm. An extensive evaluation shows that both our method and the state of the art perform equally well with the proposed outlier rejection scheme, but ours is $2-4$ times faster.

Related papers

• Fast Nonlinear Two-Time-Scale Stochastic Approximation: Achieving $O(1/k)$ Finite-Sample Complexity [2.5382095320488665]
  This paper proposes to develop a new variant of the two-time-scale monotone approximation to find the roots of two coupled nonlinear operators. Our key idea is to leverage the classic Ruppert-Polyak averaging technique to dynamically estimate the operators through their samples. The estimated values of these averaging steps will then be used in the two-time-scale approximation updates to find the desired solution.
  arXiv  Detail & Related papers  (2024-01-23T13:44:15Z)
• Robust Single Rotation Averaging Revisited [14.533304890042361]
  We propose a novel method for robust single rotation averaging that can efficiently handle an extremely large fraction of outliers. Our method is robust against up to 99% outliers given a sufficient number of accurate inliers, outperforming the current state of the art.
  arXiv  Detail & Related papers  (2023-09-11T11:35:17Z)
• Strictly Low Rank Constraint Optimization -- An Asymptotically $\mathcal{O}(\frac{1}{t^2})$ Method [5.770309971945476]
  We propose a class of non-text and non-smooth problems with textitrank regularization to promote sparsity in optimal solution. We show that our algorithms are able to achieve a singular convergence of $Ofrac(t2)$, which is exactly same as Nesterov's optimal convergence for first-order methods on smooth convex problems.
  arXiv  Detail & Related papers  (2023-07-04T16:55:41Z)
• An Oblivious Stochastic Composite Optimization Algorithm for Eigenvalue Optimization Problems [76.2042837251496]
  We introduce two oblivious mirror descent algorithms based on a complementary composite setting. Remarkably, both algorithms work without prior knowledge of the Lipschitz constant or smoothness of the objective function. We show how to extend our framework to scale and demonstrate the efficiency and robustness of our methods on large scale semidefinite programs.
  arXiv  Detail & Related papers  (2023-06-30T08:34:29Z)
• A Cubic-regularized Policy Newton Algorithm for Reinforcement Learning [9.628032156001073]
  We propose two policy Newton algorithms that incorporate cubic regularization. Both algorithms employ the likelihood ratio method to form estimates of the gradient and Hessian of the value function. In particular, the sample complexity of our algorithms to find an $epsilon$-SOSP is $O(epsilon-3.5)$, which is an improvement over the state-of-the-art sample complexity of $O(epsilon-4.5)$.
  arXiv  Detail & Related papers  (2023-04-21T13:43:06Z)
• Revisiting Rotation Averaging: Uncertainties and Robust Losses [51.64986160468128]
  We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data via the estimated epipolar. We propose to better model the underlying noise distributions by directly propagating the uncertainty from the point correspondences into the rotation averaging.
  arXiv  Detail & Related papers  (2023-03-09T11:51:20Z)
• Stochastic Dimension-reduced Second-order Methods for Policy Optimization [11.19708535159457]
  We propose several new second-order algorithms for policy optimization that only require gradient and Hessian-vector product in each iteration. Specifically, we propose a dimension-reduced second-order method (DR-SOPO) which repeatedly solves a projected two-dimensional trust region subproblem. We show that DR-SOPO obtains an $mathcalO(epsilon-3.5)$ complexity for reaching approximate first-order stationary condition. In addition, we present an enhanced algorithm (DVR-SOPO) which further improves the complexity to $mathcalO
  arXiv  Detail & Related papers  (2023-01-28T12:09:58Z)
• Extra-Newton: A First Approach to Noise-Adaptive Accelerated Second-Order Methods [57.050204432302195]
  This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(sigma / sqrtT)$ convergence when the oracle feedback is with variance $sigma2$, and improves its convergence to $O( 1 / T3)$ with deterministic oracles.
  arXiv  Detail & Related papers  (2022-11-03T14:12:51Z)
• Explicit Second-Order Min-Max Optimization Methods with Optimal Convergence Guarantee [86.05440220344755]
  We propose and analyze inexact regularized Newton-type methods for finding a global saddle point of emphcon unconstrained min-max optimization problems. We show that the proposed methods generate iterates that remain within a bounded set and that the iterations converge to an $epsilon$-saddle point within $O(epsilon-2/3)$ in terms of a restricted function.
  arXiv  Detail & Related papers  (2022-10-23T21:24:37Z)
• Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation [58.24280149662003]
  We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. We develop new algorithms for list-decodable mean estimation, achieving nearly-optimal statistical guarantees.
  arXiv  Detail & Related papers  (2021-06-16T03:34:14Z)
• Correcting Momentum with Second-order Information [50.992629498861724]
  We develop a new algorithm for non-critical optimization that finds an $O(epsilon)$epsilon point in the optimal product. We validate our results on a variety of large-scale deep learning benchmarks and architectures.
  arXiv  Detail & Related papers  (2021-03-04T19:01:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.