
TopoMap: A 0dimensional Homology Preserving Projection of HighDimensional Data
Multidimensional Projection is a fundamental tool for highdimensional d...
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O(k)robust spanners in one dimension
A geometric tspanner on a set of points in Euclidean space is a graph c...
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Finding Inner Outliers in High Dimensional Space
Outlier detection in a largescale database is a significant and complex...
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Convex Optimization Learning of Faithful Euclidean Distance Representations in Nonlinear Dimensionality Reduction
Classical multidimensional scaling only works well when the noisy distan...
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Reconstruction of surfaces with ordinary singularities from their silhouettes
We present algorithms for reconstructing, up to unavoidable projective a...
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A Distancepreserving Matrix Sketch
Visualizing very large matrices involves many formidable problems. Vario...
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Understanding Sparse JL for Feature Hashing
Feature hashing and more general projection schemes are commonly used in...
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Optimal Bounds for JohnsonLindenstrauss Transformations
In 1984, Johnson and Lindenstrauss proved that any finite set of data in a highdimensional space can be projected to a lowerdimensional space while preserving the pairwise Euclidean distance between points up to a bounded relative error. If the desired dimension of the image is too small, however, Kane, Meka, and Nelson (2011) and Jayram and Woodruff (2013) independently proved that such a projection does not exist. In this paper, we provide a precise asymptotic threshold for the dimension of the image, above which, there exists a projection preserving the Euclidean distance, but, below which, there does not exist such a projection.
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