Algorithms often carry out equally many computations for “easy” and “hard” problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In this paper, we consider the approximate k-nearest-neighbor problem, which is the problem of finding a subset of O(k) points in a given set of points that contains the set of k nearest neighbors of a given query point. We pro- pose an algorithm based on adaptively estimating the distances, and show that it is essentially optimal out of algorithms that are only allowed to adaptively estimate distances. We then demonstrate both theoretically and experimentally that the algorithm can achieve significant speedups relative to the naive method.
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Random-Walk Based Approximate k-Nearest Neighbors Algorithm for Diffusion State Distance
Diffusion State Distance (DSD) is a data-dependent metric that compares data points using a data-driven diffusion process and provides a powerful tool for learning the underlying structure of high-dimensional data. While finding the exact nearest neighbors in the DSD metric is computationally expensive, in this paper, we propose a new random-walk based algorithm that empirically finds approximate k-nearest neighbors accurately in an efficient manner. Numerical results for real-world protein-protein interaction networks are presented to illustrate the efficiency and robustness of the proposed algorithm. The set of approximate k-nearest neighbors performs well when used to predict proteins’ functional labels.
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- NSF-PAR ID:
- 10346855
- Date Published:
- Journal Name:
- Large-Scale Scientific Computing. LSSC 2021, Springer Lecture Notes in Computer Science
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The K-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of n data points with labels and a query point q, we want to assign a label to q based on the labels of the K-nearest points to the query. We study this problem in the k-machine model, a model for distributed large-scale data. In this model, we assume that the n points are distributed (in a balanced fashion) among the k machines and the goal is to compute an answer given a query point to a machine using a small number of communication rounds. Our main result is a randomized algorithm in the k-machine model that runs in O(log K) communication rounds with high success probability (regardless of the number of machines k and the number of points n). The message complexity of the algorithm is small taking only O(k log K) messages. Our bounds are essentially the best possible for comparison-based algorithms. We also implemented our algorithm and show that it performs well in practice.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-97549-4_1
