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A Sub-linear Time Framework for Geometric Optimization with Outliers in High Dimensions
[article]
2020
arXiv
pre-print
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d, for MEB with outliers in high dimensions. ...
Furthermore, we observe that these two techniques can be generalized to deal with a broader range of geometric optimization problems with outliers in high dimensions, including flat fitting, k-center clustering ...
for MEB with outliers and other related high dimensional geometric optimization problems. ...
arXiv:2004.10090v2
fatcat:aomkj6r7angwbnqz2xvc5xlm5q
Distributed Robust Learning
[article]
2015
arXiv
pre-print
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We propose a framework for distributed robust statistical learning on big contaminated data. ...
This is in stark contrast with naive division-and-averaging implementation, which may reduce the breakdown point by a factor of k when k computing nodes are used. ...
For example, in RPCA [18] , the computational time is O((n + n 1 )p 2 r) where r is the intrinsic dimension of the subspace and p is the ambient dimension. ...
arXiv:1409.5937v2
fatcat:sy52ja4uuvgdhhz5gpv2lc5mxu
Locality preserving embedding for face and handwriting digital recognition
2011
Neural computing & applications (Print)
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The criterion, similar to the classical Fisher criterion, is a Rayleigh quotient in form, and the optimal linear projections are obtained by solving a generalized Eigen equation. ...
LPE can give a low-dimensional embedding for discriminative multi-class sub-manifolds and preserves principal structure information of the local sub-manifolds. ...
In practice, the feature dimension m is often very high. ...
doi:10.1007/s00521-011-0577-7
fatcat:yv6r5uepgnh3zenjwiiirzanra
Robust Shape Reconstruction and Optimal Transportation
2013
Actes des rencontres du CIRM
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cedram Texte mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques Abstract We describe a framework for robust shape reconstruction from raw point sets, based on optimal ...
In addition to robustness to defect-laden point sets, hampered with noise and outliers, our approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries. ...
To obtain high robustness to noise and outliers we formulate the problem with a general transport plan where each input sample point can be split into sub-masses, each transported to different locations ...
doi:10.5802/acirm.57
fatcat:6mfjsh5ydzg7haltejd2bauyx4
Surface fitting and registration of point clouds using approximations of the unsigned distance function
2010
Computer Aided Geometric Design
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Many problems in computer aided geometric design and geometry processing are stated as leastsquares optimizations. ...
Least-squares problems are well studied and widely used but exhibit immanent drawbacks such as high sensitivity to outliers. ...
For point clouds with n elements, an optimization problem of dimension dim was solved in it iterations, taking T seconds. ...
doi:10.1016/j.cagd.2009.09.001
fatcat:xfq73lv77vgnvhxrmjw362muce
AN INNOVATIVE IDEA TO DISCOVER THE TREND ON MULTI-DIMENSIONAL SPATIO-TEMPORAL DATASETS
2014
International Journal of Research in Engineering and Technology
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Spatio-temporal data is any information regarding space and time. It is frequently updated data with 1TB/hr, are greatly challenging our ability to digest the data. ...
From the literature survey it has listed a number of issues. And also it contributes several phases, in which each and every phase output must be very helpful to go for the next phase input. ...
The proposed algorithms evaluation process of this research will be learned in our next research paper. ...
doi:10.15623/ijret.2014.0303046
fatcat:qoyuzflmbvfozgle4nmwkvl23q
Pushing the Envelope of Rotation Averaging for Visual SLAM
[article]
2020
arXiv
pre-print
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We apply the scale parameter with l_1-norm in the pose-graph optimization to address the rotation averaging robustness against outliers. ...
In this paper, we lift these limitations and propose a novel optimization backbone for visual SLAM systems, where we leverage rotation averaging to improve the accuracy, efficiency and robustness of conventional ...
Conclusion In this paper, we propose a rotation averaging optimization framework for backend of visual SLAM systems. ...
arXiv:2011.01163v1
fatcat:wjre7zskhvffnpdqvahivrimoq
Robust feature extraction via information theoretic learning
2009
Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09
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In this paper, we present a robust feature extraction framework based on informationtheoretic learning. ...
In addition, the popular algorithms LPP, SRDA and LapRLS for feature extraction are all justified to be the special cases within this framework. ...
Shuicheng Yan for reading an earlier version of this manuscript and his valuable feedbacks for refinement. ...
doi:10.1145/1553374.1553526
dblp:conf/icml/YuanH09
fatcat:q6l6rfccvratxdpasr2cvqzrui
Novel Co-variant Feature Point Matching Based on Gaussian Mixture Model
[article]
2019
arXiv
pre-print
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We proposed three sub-versions in our method for solving the matching problem in different conditions: rigid, affine and non-rigid, respectively, which all optimized by expectation maximization algorithm ...
In this paper, we develop a novel method considering all the feature center position coordinates, the local feature shape and orientation information based on Gaussian Mixture Model for co-variant feature ...
It includes an additional uniform distribution in the mixture model to account for outliers and noise and is optimized by expectation maximization. ...
arXiv:1910.11981v1
fatcat:t2gaxbkolfdclhedw2wyldbi3q
The Effectiveness of Johnson-Lindenstrauss Transform for High Dimensional Optimization With Adversarial Outliers, and the Recovery
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2002.11923v4 fatcat:lhwe7accxrhwrechbqokatjm4mOther Versions
In this paper, we consider robust optimization problems in high dimensions. ...
We focus on two fundamental optimization problems: SVM with outliers and k-center clustering with outliers. ...
Our Contributions In this paper, we study the effectiveness of JL transform in particular for the optimization problems with outliers in high dimensions. ...
arXiv:2002.11923v5
fatcat:5zsz2knm4baqvac6vx45rflgfy
Efficient Large Scale Inlier Voting for Geometric Vision Problems
[article]
2021
arXiv
pre-print
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We provide a recipe for casting a variety of geometric problems as finding a point in R^d which maximizes the number of nearby surfaces (and thus inliers). ...
Outlier rejection and equivalently inlier set optimization is a key ingredient in numerous applications in computer vision such as filtering point-matches in camera pose estimation or plane and normal ...
Acknowledgements The authors would like to thank Micha Sharir for helpful discussions concerning the general surface-box intersection. ...
arXiv:2107.11810v2
fatcat:5youfprpljarpecpjsjakvypty
Estimation in high dimensions: a geometric perspective
[article]
2014
arXiv
pre-print
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This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. ...
The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation ...
Estimation with constraints. This chapter provides an exposition of an emerging mathematical framework for high-dimensional estimation problems with constraints. ...
arXiv:1405.5103v2
fatcat:6q434wf6tnaz5nrxmp2fypgica
Estimation in High Dimensions: A Geometric Perspective
[chapter]
2015
Sampling Theory, a Renaissance
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This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. ...
The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation ...
Estimation with constraints. This chapter provides an exposition of an emerging mathematical framework for high-dimensional estimation problems with constraints. ...
doi:10.1007/978-3-319-19749-4_1
fatcat:cnnlmjl5ifdujha4ajpyctrhtq
Global Point-to-hyperplane ICP: Local and global pose estimation by fusing color and depth
2017
2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)
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In this paper, a local hybrid approach named Point-to-hyperplane ICP has been combined with a global Branch and Bound strategy in order to estimate the 6DOF (degrees of freedom) pose parameters. ...
However, the optimization is performed locally and by consequence it can get trapped in local minima. ...
Therefore, the geometric and photometric measurements can be normalized to maintain a unitary half-sphere in n-dimensions (b). ...
doi:10.1109/mfi.2017.8170402
dblp:conf/mfi/MunozC17
fatcat:4wbmw3j55zgefbqssly2b3e4iu
Adaptive Rendering Based on Weighted Local Regression
2014
ACM Transactions on Graphics
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Given the local regression on estimated local space, we provide a novel two-step optimization process for selecting bandwidths of features locally in a data-driven way. ...
A novel local space estimation process is proposed for employing the local regression, by robustly addressing noisy high dimensional features. ...
In rendering, outliers are often defined as spike noise with extremely high energy. ...
doi:10.1145/2641762
fatcat:i6ji5eywc5hazoa3zqzwfnqpbi
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