Related papers: Sketching and Embedding are Equivalent for Norms
In this paper we study {\em terminal embeddings}, in which one is given a finite metric $(X,d_X)$ (or a graph $G=(V,E)$) and a subset $K \subseteq X$ of its points are designated as {\em terminals}. The objective is to embed the metric into…
We consider the problem of embedding a finite set of points $\{x_1, \ldots, x_n\} \in \mathbb{R}^d$ that satisfy $\ell_2^2$ triangle inequalities into $\ell_1$, when the points are approximately low-dimensional. Goemans (unpublished,…
We propose a deep hashing framework for sketch retrieval that, for the first time, works on a multi-million scale human sketch dataset. Leveraging on this large dataset, we explore a few sketch-specific traits that were otherwise…
We give the first non-trivial decremental dynamic embedding of a weighted, undirected graph $G$ into $\ell_p$ space. Given a weighted graph $G$ undergoing a sequence of edge weight increases, the goal of this problem is to maintain a…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
We characterize the streaming space complexity of every symmetric norm $l$ (a norm on $\mathbb{R}^n$ invariant under sign-flips and coordinate-permutations), by relating this space complexity to the measure-concentration characteristics of…
Motivated by the problem of discrete-parameter simulation optimization (DPSO) of queueing systems, we consider the problem of embedding the discrete parameter space into a continuous one so that descent-based continuous-space methods could…
Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set…
Text indexing is a fundamental and well-studied problem. Classic solutions either replace the original text with a compressed representation, e.g., the FM-index and its variants, or keep it uncompressed but attach some redundancy - an index…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…
The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between…
Understanding geometric concepts, such as distance and shape, is essential for understanding the real world and also for many vision tasks. To incorporate such information into a visual representation of a scene, we propose learning to…
This paper presents our work on "SNaCK," a low-dimensional concept embedding algorithm that combines human expertise with automatic machine similarity kernels. Both parts are complimentary: human insight can capture relationships that are…
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…
The subspace approximation problem Subspace($k$,$p$) asks for a $k$-dimensional linear subspace that fits a given set of points optimally, where the error for fitting is a generalization of the least squares fit and uses the $\ell_{p}$ norm…
We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the…