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Advances in embedding models for text, image, audio, and video drive progress across multiple domains, including retrieval-augmented generation, recommendation systems, and others. Many of these applications require an efficient method to…
Approximate nearest neighbor (ANN) search is widely used in the retrieval stage of large-scale recommendation systems. In this stage, candidate items are indexed using their learned embedding vectors, and ANN search is executed for each…
The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X,D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).…
We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$…
The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…
In Near-Neighbor Search (NNS), a new client queries a database (held by a server) for the most similar data (near-neighbors) given a certain similarity metric. The Privacy-Preserving variant (PP-NNS) requires that neither server nor the…
We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false, for…
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…
In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data…
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…
Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…
The in-memory algorithms for approximate nearest neighbor search (ANNS) have achieved great success for fast high-recall search, but are extremely expensive when handling very large scale database. Thus, there is an increasing request for…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…
Locality-sensitive hashing (LSH) is an important tool for managing high-dimensional noisy or uncertain data, for example in connection with data cleaning (similarity join) and noise-robust search (similarity search). However, for a number…
Amidst an increasing number of infected cases during the Covid-19 pandemic, it is essential to trace, as early as possible, the susceptible people who might have been infected by the disease due to their close proximity with people who were…
We study the k nearest neighbors problem in the plane for general, convex, pairwise disjoint sites of constant description complexity such as line segments, disks, and quadrilaterals and with respect to a general family of distance…
Embedding-based retrieval aims to learn a shared semantic representation space for both queries and items, enabling efficient and effective item retrieval through approximate nearest neighbor (ANN) algorithms. In current industrial…
Contrastive learning is a representational learning paradigm in which a neural network maps data elements to feature vectors. It improves the feature space by forming lots with an anchor and examples that are either positive or negative…
We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest…