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We consider the popular $k$-means problem in $d$-dimensional Euclidean space. Recently Friggstad, Rezapour, Salavatipour [FOCS'16] and Cohen-Addad, Klein, Mathieu [FOCS'16] showed that the standard local search algorithm yields a…
Fast Nearest Neighbor (NN) search is a fundamental challenge in large-scale data processing and analytics, particularly for analyzing multimedia contents which are often of high dimensionality. Instead of using exact NN search, extensive…
Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
Code embeddings are essential for semantic code search; however, current approaches often struggle to capture the precise syntactic and contextual nuances inherent in code. Open-source models such as CodeBERT and UniXcoder exhibit…
High-dimensional similarity search underpins modern retrieval systems, yet uniform search strategies fail to exploit the heterogeneous nature of real-world query distributions. We present an adaptive prefiltering framework that leverages…
We demonstrate three approaches for adapting the open-source Lucene search library to perform approximate nearest-neighbor search on arbitrary dense vectors, using similarity search on word embeddings as a case study. At its core, Lucene is…
Similarity search is a fundamental operation for analyzing data series (DS), which are ordered sequences of real values. To enhance efficiency, summarization techniques are employed that reduce the dimensionality of DS. SAX-based approaches…
For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…
Similar trajectory search is a fundamental problem and has been well studied over the past two decades. However, the similar subtrajectory search (SimSub) problem, aiming to return a portion of a trajectory (i.e., a subtrajectory) which is…
Similarity search in high-dimentional spaces is a pivotal operation found a variety of database applications. Recently, there has been an increase interest in similarity search for online content-based multimedia services. Those services,…
Density-based clustering is the most popular clustering algorithm since it can identify clusters of arbitrary shape as long as they are separated by low-density regions. However, a high-density region that is not separated by low-density…
Modern approaches for fast retrieval of similar vectors on billion-scaled datasets rely on compressed-domain approaches such as binary sketches or product quantization. These methods minimize a certain loss, typically the mean squared error…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
Traditional retrieval methods have been essential for assessing document similarity but struggle with capturing semantic nuances. Despite advancements in latent semantic analysis (LSA) and deep learning, achieving comprehensive semantic…
This paper considers the problem of approximate nearest neighbor search in the compressed domain. We introduce polysemous codes, which offer both the distance estimation quality of product quantization and the efficient comparison of binary…
Global optimization of crystal compositions is a significant yet computationally intensive method to identify stable structures within chemical space. The specific physical properties linked to a three-dimensional atomic arrangement make…
Dimensionality reduction techniques are essential for visualizing and analyzing high-dimensional biological sequencing data. t-distributed Stochastic Neighbor Embedding (t-SNE) is widely used for this purpose, traditionally employing the…
Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables…
We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…