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Found 10 papers, 3 papers with code
Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment
Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly translated and corrupted by additive noise.
Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms
In particular, we show the discrete eigenvalues and eigenvectors converge to their continuum analogues at a dimension-dependent rate, which allows us to interpret the efficacy of discrete spectral clustering using Fermat distances in terms of the resulting continuum limit.
Linear Distance Metric Learning with Noisy Labels
In linear distance metric learning, we are given data in one Euclidean metric space and the goal is to find an appropriate linear map to another Euclidean metric space which respects certain distance conditions as much as possible.
Taxonomy of Benchmarks in Graph Representation Learning
Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry.
Towards a Taxonomy of Graph Learning Datasets
Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data.
Unbiasing Procedures for Scale-invariant Multi-reference Alignment
We propose a method that recovers the power spectrum of the hidden signal by applying a data-driven, nonlinear unbiasing procedure, and thus the hidden signal is obtained up to an unknown phase.
Balancing Geometry and Density: Path Distances on High-Dimensional Data
New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented.
Wavelet invariants for statistically robust multi-reference alignment
After unbiasing the representation to remove the effects of the additive noise and random dilations, we recover an approximation of the power spectrum by solving a convex optimization problem, and thus reduce to a phase retrieval problem.
Exact Cluster Recovery via Classical Multidimensional Scaling
Classical multidimensional scaling is an important dimension reduction technique.
Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms
We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters.
