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Found 41 papers, 11 papers with code
lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers
We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces.
A Novel M-Estimator for Robust PCA
That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed underlying subspace.
Robust computation of linear models by convex relaxation
Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers.
On the Sample Complexity of Robust PCA
This estimator is used in a convex algorithm for robust subspace recovery (i. e., robust PCA).
A New Approach To Two-View Motion Segmentation Using Global Dimension Minimization
We present a new approach to rigid-body motion segmentation from two views.
Better Feature Tracking Through Subspace Constraints
Our approach does not require direct modeling of the structure or the motion of the scene, and runs in real time on a single CPU core.
Fast, Robust and Non-convex Subspace Recovery
Further, under a special model of data, FMS converges to a point which is near to the global minimum with overwhelming probability.
Riemannian Multi-Manifold Modeling
This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$.
Fast Landmark Subspace Clustering
Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations.
Enhancing Feature Tracking With Gyro Regularization
We present a deeply integrated method of exploiting low-cost gyroscopes to improve general purpose feature tracking.
Distributed Robust Subspace Recovery
We propose distributed solutions to the problem of Robust Subspace Recovery (RSR).
A Well-Tempered Landscape for Non-convex Robust Subspace Recovery
The practicality of the deterministic condition is demonstrated on some statistical models of data, and the method achieves almost state-of-the-art recovery guarantees on the Haystack Model for different regimes of sample size and ambient dimension.
Exact Camera Location Recovery by Least Unsquared Deviations
We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of Ozyesil and Singer.
An Overview of Robust Subspace Recovery
This paper will serve as an introduction to the body of work on robust subspace recovery.
Graph Convolutional Neural Networks via Scattering
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs.
Ranked #58 on
Node Classification
on Cora
Estimation of Camera Locations in Highly Corrupted Scenarios: All About that Base, No Shape Trouble
We propose a strategy for improving camera location estimation in structure from motion.
Graph Generation via Scattering
These results are in contrast to experience with Euclidean data, where it is difficult to form a generative scattering network that performs as well as state-of-the-art methods.
Encoding Robust Representation for Graph Generation
The decoder is a simple fully connected network that is adapted to specific tasks, such as link prediction, signal generation on graphs and full graph and signal generation.
Ranked #2 on
Link Prediction
on Pubmed (biased evaluation)
Solving Jigsaw Puzzles By the Graph Connection Laplacian
The main contribution of this work is a method for recovering the rotations of the pieces when both shuffles and rotations are unknown.
Analysis and algorithms for $\ell_p$-based semi-supervised learning on graphs
In the first part of the paper we prove new discrete to continuum convergence results for $p$-Laplace problems on $k$-nearest neighbor ($k$-NN) graphs, which are more commonly used in practice than random geometric graphs.
Robust Subspace Recovery Layer for Unsupervised Anomaly Detection
The encoder maps the data into a latent space, from which the RSR layer extracts the subspace.
Unsupervised Anomaly Detection with Specified Settings -- 0.1% anomaly
Unsupervised Anomaly Detection with Specified Settings -- 10% anomaly
+3
Robust Subspace Recovery with Adversarial Outliers
The two estimators are fast to compute and achieve state-of-the-art theoretical performance in a noiseless RSR setting with adversarial outliers.
Robust Group Synchronization via Cycle-Edge Message Passing
We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption.
Depth Descent Synchronization in $\mathrm{SO}(D)$
We give robust recovery results for synchronization on the rotation group, $\mathrm{SO}(D)$.
Novelty Detection via Robust Variational Autoencoding
We establish both robustness to outliers and suitability to low-rank modeling of the Wasserstein metric as opposed to the KL divergence.
Robust Multi-object Matching via Iterative Reweighting of the Graph Connection Laplacian
We propose an efficient and robust iterative solution to the multi-object matching problem.
Message Passing Least Squares Framework and its Application to Rotation Synchronization
We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization.
Ensemble Riemannian Data Assimilation over the Wasserstein Space
Unlike the Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture translation and difference between the shapes of square-integrable probability distributions of the background state and observations -- enabling to formally penalize geophysical biases in state-space with non-Gaussian distributions.
Methodology
Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching
We develop new statistics for robustly filtering corrupted keypoint matches in the structure from motion pipeline.
Robust Vector Quantized-Variational Autoencoder
We experimentally demonstrate that RVQ-VAE is able to generate examples from inliers even if a large portion of the training data points are corrupted.
Stochastic and Private Nonconvex Outlier-Robust PCA
Our results emphasize the advantages of the nonconvex methods over another convex approach to solving this problem in the differentially private setting.
Fast, Accurate and Memory-Efficient Partial Permutation Synchronization
Previous partial permutation synchronization (PPS) algorithms, which are commonly used for multi-object matching, often involve computation-intensive and memory-demanding matrix operations.
An Unpooling Layer for Graph Generation
Since this unpooling layer is trainable, it can be applied to graph generation either in the decoder of a variational autoencoder or in the generator of a generative adversarial network (GAN).
Robust Group Synchronization via Quadratic Programming
We propose a novel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem.
Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method.
Monotone Generative Modeling via a Gromov-Monge Embedding
Generative Adversarial Networks (GANs) are powerful tools for creating new content, but they face challenges such as sensitivity to starting conditions and mode collapse.
Improved Convergence Rates of Windowed Anderson Acceleration for Symmetric Fixed-Point Iterations
This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, $x^{(k+1)}=q(x^{(k)})$.
The effect of Leaky ReLUs on the training and generalization of overparameterized networks
We investigate the training and generalization errors of overparameterized neural networks (NNs) with a wide class of leaky rectified linear unit (ReLU) functions.
Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator
It further shows that under the generalized haystack model, STE initialized by the Tyler's M-estimator (TME), can recover the subspace when the fraction of iniliers is too small for TME to handle.
A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion
We present the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers.
Message Passing Least Squares: A Unified Framework for Fast and Robust Group Synchronization
We propose an efficient algorithm for solving robust group synchronization given adversarially corrupted group ratios.
