Comparison Based Nearest Neighbor Search

Haghiri, Siavash; Ghoshdastidar, Debarghya; Luxburg, Ulrike von

doi:10.48550/arxiv.1704.01460

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…Furthermore, the results depend strongly on the expansion rate, c. Some works such as Haghiri et al [2017], Dasgupta and Sinha [2013] trade accuracy for improved dependence on c or other measures of dimension. Instead, these algorithms guarantee that x q is correctly returned with probability at least 1 − δ c,n for any q.…”

Section: Discussionmentioning

confidence: 99%

“…In order to quantify the sample complexity of cover trees, we require a notion of the effective dimensionality of the points X . In this paper, we will make use of the expansion constant as in [Haghiri et al, 2017, Krauthgamer and Lee, 2004. Let B(x, r) denote the ball of radius r > 0 centered at x ∈ (M , d) according to the distance measure d. The expansion constant is sensitive to the geometry in X .…”

Section: Cover Trees For Nearest Neighbor Searchmentioning

confidence: 99%

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Nearest Neighbor Search Under Uncertainty

Mason,

Tripathy,

Nowak

2021

Preprint

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Nearest Neighbor Search (NNS) is a central task in knowledge representation, learning, and reasoning. There is vast literature on efficient algorithms for constructing data structures and performing exact and approximate NNS. This paper studies NNS under Uncertainty (NNSU). Specifically, consider the setting in which an NNS algorithm has access only to a stochastic distance oracle that provides a noisy, unbiased estimate of the distance between any pair of points, rather than the exact distance. This models many situations of practical importance, including NNS based on human similarity judgements, physical measurements, or fast, randomized approximations to exact distances. A naive approach to NNSU could employ any standard NNS algorithm and repeatedly query and average results from the stochastic oracle (to reduce noise) whenever it needs a pairwise distance. The problem is that a sufficient number of repeated queries is unknown in advance; e.g., a point may be distant from all but one other point (crude distance estimates suffice) or it may be close to a large number of other points (accurate estimates are necessary). This paper shows how ideas from cover trees and multi-armed bandits can be leveraged to develop an NNSU algorithm that has optimal dependence on the dataset size and the (unknown) geometry of the dataset. 1 We assume the oracle responses are independent and 1-subGaussian distributed throughout the paper.tance function is a known, componentwise function. Their algorithm subsamples to approximate distances. This improves dependence on dimension, though the dependence on n is linear.

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Section: Discussionmentioning

confidence: 99%

Section: Cover Trees For Nearest Neighbor Searchmentioning

confidence: 99%

Nearest Neighbor Search Under Uncertainty

Mason,

Tripathy,

Nowak

2021

Preprint

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“…It is most common to classify time series data using Nearest Neighbour classification based on a relative distance (such as those returned from the measures above) [15]. In fact, for more than a decade, the NN algorithm combined with the DTW measure was extremely difficult to beat [49].…”

Section: Nearest-neighbor Approachesmentioning

confidence: 99%

Proximity Forest: an effective and scalable distance-based classifier for time series

Lucas

Shifaz

Pelletier

et al. 2019

Data Min Knowl Disc

128

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Research into the classification of time series has made enormous progress in the last decade. The UCR time series archive has played a significant role in challenging and guiding the development of new learners for time series classification. The largest dataset in the UCR archive holds 10 thousand time series only; which may explain why the primary research focus has been on creating algorithms that have high accuracy on relatively small datasets.This paper introduces Proximity Forest, an algorithm that learns accurate models from datasets with millions of time series, and classifies a time series in milliseconds. The models are ensembles of highly randomized Proximity Trees. Whereas conventional decision trees branch on attribute values (and usually perform poorly on time series), Proximity Trees branch on the proximity of time series to one exemplar time series or another; allowing us to leverage the decades of work into developing relevant measures for time series. Proximity Forest gains both efficiency and accuracy by stochastic selection of both exemplars and similarity measures.Our work is motivated by recent time series applications that provide orders of magnitude more time series than the UCR benchmarks. Our experiments demonstrate that Proximity Forest is highly competitive on the UCR archive: it ranks among the most accurate classifiers while being significantly faster. We demonstrate on a 1M time series Earth observation dataset that Proximity Forest retains this accuracy on datasets that are many orders of magnitude greater than those in the UCR repository, while learning its models at least 100,000 times faster than current state of the art models Elastic Ensemble and COTE.

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Comparison Based Nearest Neighbor Search

Cited by 2 publications

References 14 publications

Nearest Neighbor Search Under Uncertainty

Nearest Neighbor Search Under Uncertainty

Proximity Forest: an effective and scalable distance-based classifier for time series

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