Related papers: Similarity Problems in High Dimensions
We study the problem of computing similarity joins under edit distance on a set of strings. Edit similarity joins is a fundamental problem in databases, data mining and bioinformatics. It finds important applications in data cleaning and…
We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…
Near neighbor problems are fundamental in algorithms for high-dimensional Euclidean spaces. While classical approaches suffer from the curse of dimensionality, locality sensitive hashing (LSH) can effectively solve a-approximate r-near…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by…
We study an indexing architecture to store and search in a database of high-dimensional vectors from the perspective of statistical signal processing and decision theory. This architecture is composed of several memory units, each of which…
Parallel corpora have driven great progress in the field of Text Simplification. However, most sentence alignment algorithms either offer a limited range of alignment types supported, or simply ignore valuable clues present in comparable…
Developing increasingly efficient and accurate algorithms for approximate nearest neighbor search is a paramount goal in modern information retrieval. A primary approach to addressing this question is clustering, which involves partitioning…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
We study the $r$-near neighbors reporting problem ($r$-NN), i.e., reporting \emph{all} points in a high-dimensional point set $S$ that lie within a radius $r$ of a given query point $q$. Our approach builds upon on the locality-sensitive…
The Nearest Neighbor Search (NNS) problem asks to design a data structure that preprocesses an $n$-point dataset $X$ lying in a metric space $\mathcal{M}$, so that given a query point $q \in \mathcal{M}$, one can quickly return a point of…
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…
We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric…
Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are,…
Similarity-preserving hashing is a widely-used method for nearest neighbour search in large-scale image retrieval tasks. There has been considerable research on generating efficient image representation via the deep-network-based hashing…
We propose a new clustering algorithm, Extended Affinity Propagation, based on pairwise similarities. Extended Affinity Propagation is developed by modifying Affinity Propagation such that the desirable features of Affinity Propagation,…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We…
We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…
This article introduces the novel notion of dimension preserving approximation for continuous functions defined on $[0,1]$ and initiates the study of it. Restrictions and extensions of continuous functions in regards to fractal dimensions…