
Faster Binary Embeddings for Preserving Euclidean Distances
We propose a fast, distancepreserving, binary embedding algorithm to tr...
read it

Fast binary embeddings, and quantized compressed sensing with structured matrices
This paper deals with two related problems, namely distancepreserving b...
read it

NearOptimal O(k)Robust Geometric Spanners
For any constants d> 1, ϵ >0, t>1, and any npoint set P⊂R^d, we show th...
read it

Distributed Learning and Democratic Embeddings: PolynomialTime Source Coding Schemes Can Achieve Minimax Lower Bounds for Distributed Gradient Descent under Communication Cons
In this work, we consider the distributed optimization setting where inf...
read it

Representation and Coding of Signal Geometry
Approaches to signal representation and coding theory have traditionally...
read it

A Unified and FineGrained Approach for Light Spanners
Seminal works on light spanners from recent years provide nearoptimal t...
read it

A Euclidean Algorithm for Binary Cycles with Minimal Variance
The problem is considered of arranging symbols around a cycle, in such a...
read it
Binarized JohnsonLindenstrauss embeddings
We consider the problem of encoding a set of vectors into a minimal number of bits while preserving information on their Euclidean geometry. We show that this task can be accomplished by applying a JohnsonLindenstrauss embedding and subsequently binarizing each vector by comparing each entry of the vector to a uniformly random threshold. Using this simple construction we produce two encodings of a dataset such that one can query Euclidean information for a pair of points using a small number of bit operations up to a desired additive error  Euclidean distances in the first case and inner products and squared Euclidean distances in the second. In the latter case, each point is encoded in nearlinear time. The number of bits required for these encodings is quantified in terms of two natural complexity parameters of the dataset  its covering numbers and localized Gaussian complexity  and shown to be nearoptimal.
READ FULL TEXT
Comments
There are no comments yet.