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In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It…

We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms). Goldschmidt and Hochbaum \cite{GH97} show that the mvms problem…

The reverse k-nearest neighbor (RkNN) query is an established query type with various applications reaching from identifying highly influential objects over incrementally updating kNN graphs to optimizing sensor communication and outlier…

We analyze greedy algorithms for the Hierarchical Aggregation (HAG) problem, a strategy introduced in [Jia et al., KDD 2020] for speeding up learning on Graph Neural Networks (GNNs). The idea of HAG is to identify and remove redundancies in…

Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…

The k-Nearest Neighbor (k-NN) classification algorithm is one of the most widely-used lazy classifiers because of its simplicity and ease of implementation. It is considered to be an effective classifier and has many applications. However,…

We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in $O(\log^2{n} / \epsilon)$ rounds on unweighted…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

The K-Nearest Neighbor (KNN) join is an expensive but important operation in many data mining algorithms. Several recent applications need to perform KNN join for high dimensional sparse data. Unfortunately, all existing KNN join algorithms…

We investigate the problem of finding reverse nearest neighbors efficiently. Although provably good solutions exist for this problem in low or fixed dimensions, to this date the methods proposed in high dimensions are mostly heuristic. We…

This paper proposes a soft range limited K nearest neighbours (SRL-KNN) localization fingerprinting algorithm. The conventional KNN determines the neighbours of a user by calculating and ranking the fingerprint distance measured at the…

In pattern recognition or machine learning, it is a very fundamental task to find nearest neighbors of a given point. All the methods for the task work basically by comparing the given point to all the points in the data set. That is why…

Nearest neighbor (NN) search is inherently computationally expensive in high-dimensional spaces due to the curse of dimensionality. As a well-known solution, locality-sensitive hashing (LSH) is able to answer c-approximate NN (c-ANN)…

Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the…

Robust obstacle avoidance is one of the critical steps for successful goal-driven indoor navigation tasks.Due to the obstacle missing in the visual image and the possible missed detection issue, visual image-based obstacle avoidance…

We consider the fundamental problem of decomposing a large-scale approximate nearest neighbor search (ANNS) problem into smaller sub-problems. The goal is to partition the input points into neighborhood-preserving shards, so that the…

Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…

Fast and reliable K-Nearest Neighbor Graph algorithms are more important than ever due to their widespread use in many data processing techniques. This paper presents a runtime optimized C implementation of the heuristic "NN-Descent"…

Shortest path search is a core operation in graph-based applications, yet existing methods face important limitations. Classical algorithms such as Dijkstra's and A* become inefficient as graphs grow more complex, while index-based…

With the continuous popularity of deep learning and representation learning, fast vector search becomes a vital task in various ranking/retrieval based applications, say recommendation, ads ranking and question answering. Neural network…