Related papers: Locality Sensitive Hashing in Hyperbolic Space
Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects -- either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity…
Spatiotemporal Local Binary Pattern (STLBP) is a widely used dynamic texture descriptor, but it suffers from extremely high dimensionality. To tackle this, STLBP features are often extracted on three orthogonal planes, which sacrifice…
DNA barcoding has emerged as a cost-effective approach for species identification. However, the scarcity of tools used for searching the booming reference database becomes an obstacle, currently with BLAST as the only practical choice.…
We have developed a new halo finding method, Physically Self-Bound (PSB) group finding algorithm, which can efficiently identify halos located even at crowded regions. This method combines two physical criteria such as the tidal radius of a…
Recently, inspired by Transformer, self-attention-based scene text recognition approaches have achieved outstanding performance. However, we find that the size of model expands rapidly with the lexicon increasing. Specifically, the number…
We consider the problem of approximating an unknown function $u\in L^2(D,\rho)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $\rho$ is a probability measure. The…
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…
Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used,…
We use a special tiling for the hyperbolic $d$-space $\mathbb{H}^d$ for $d=2,3,4$ to construct an (almost) explicit isomorphism between the Lipschitz-free space $\mathcal{F}(\mathbb{H}^d)$ and $\mathcal{F}(P)\oplus\mathcal{F}(\mathcal{N})$…
An $(n,r,h,a,q)$-Local Reconstruction Code (LRC) is a linear code over $\mathbb{F}_q$ of length $n$, whose codeword symbols are partitioned into $n/r$ local groups each of size $r$. Each local group satisfies `$a$' local parity checks to…
Entity resolution seeks to merge databases as to remove duplicate entries where unique identifiers are typically unknown. We review modern blocking approaches for entity resolution, focusing on those based upon locality sensitive hashing…
In recent years, binary code learning, a.k.a hashing, has received extensive attention in large-scale multimedia retrieval. It aims to encode high-dimensional data points to binary codes, hence the original high-dimensional metric space can…
We consider static, external memory indexes for exact and approximate versions of the $k$-nearest neighbor ($k$-NN) problem, and show new lower bounds under a standard indivisibility assumption: - Polynomial space indexing schemes for…
Fast approximate nearest neighbor (NN) search in large databases is becoming popular. Several powerful learning-based formulations have been proposed recently. However, not much attention has been paid to a more fundamental question: how…
A linear block code with dimension $k$, length $n$, and minimum distance $d$ is called a locally repairable code (LRC) with locality $r$ if it can retrieve any coded symbol by at most $r$ other coded symbols. LRCs have been recently…
The sensitivity of long-time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction, the uniformly-bounded-in-time solution of the sensitivity equations. Although its existence is…
Nearest Neighbor Search (NNS) over generalized weighted distances is fundamental to a wide range of applications. The problem of NNS over the generalized weighted square Euclidean distance has been studied in previous work. However,…
Compositional zero-shot learning (CZSL) aims to recognize unseen state-object compositions by generalizing from a training set of their primitives (state and object). Current methods often overlook the rich hierarchical structures, such as…
Many graph neural networks have been developed to learn graph representations in either Euclidean or hyperbolic space, with all nodes' representations embedded in a single space. However, a graph can have hyperbolic and Euclidean geometries…
We present SLASH (Sketched LocAlity Sensitive Hashing), an MPI (Message Passing Interface) based distributed system for approximate similarity search over terabyte scale datasets. SLASH provides a multi-node implementation of the popular…