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  • A Singer
  • 2011
The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles θ(1), …, θ(n) from m noisy measurements of their offsets θ(i) - θ(j) mod 2π. Of particular interest is angle recovery in the presence of many outlier measurements that are uniformly distributed in [0, 2π) and carry no(More)
We introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing massive high-dimensional data sets, images, and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and other nonlinear dimensionality reduction methods, such as LLE, ISOMAP, and Laplacian eigenmaps. While existing methods are(More)
Variation in the genes of the major histocompatibility complex (MHC) contributes to unique individual odors (odortypes) in mice, as demonstrated by the ability of trained mice in a Y-maze olfactometer to discriminate nearly identical inbred mice that differ genetically only at the MHC (MHC congenic mice), while they cannot distinguish genetically identical(More)
  • Amit Singer
  • 2008
Finding the global positioning of points in Euclidean space from a local or partial set of pairwise distances is a problem in geometry that emerges naturally in sensor networks and NMR spectroscopy of proteins. We observe that the eigenvectors of a certain sparse matrix exactly match the sought coordinates. This translates to a simple and efficient(More)
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision, and control. Most recent work has been focused on constructing efficient algorithms for exact or approximate recovery of the(More)
The synchronization problem over the special orthogonal group SO(d) consists of estimating a set of unknown rotations R 1 , R 2 ,. .. , R n from noisy measurements of a subset of their pairwise ratios R −1 i R j. The problem has found applications in computer vision, computer graphics, and sensor network local-ization, among others. Its least squares(More)
We consider the problem of clustering a graph G into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables Y = B<sub>G</sub>x &#x2295; Z, where B<sub>G</sub> is the incidence matrix of a graph G, x is the vector of unknown vertex variables (with a uniform prior), and Z is a(More)
We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding, and aligning uniquely realizable subsets of neighboring sensors called patches. In the noise-free case, each patch agrees with its global positioning up to an unknown rigid motion of translation,(More)
In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we(More)