Optimal Load Factor for Approximate Nearest Neighbor Search under Exact Euclidean Locality Sensitive Hashing

Buaba, Ruben; Homaifar, Abdollah; Kihn, E. A.

doi:10.5120/12096-8258

Cited by 2 publications

(2 citation statements)

References 45 publications

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“…amplification gap), which is obtained by selecting α that minimizes this ratio at a specific c. An approximate solution is given as ρ(c) ≈ 1/c by [20] α = 4. However, we show that α = 5 gives a better optimal value for ρ than that of α = 4 [37].…”

Section: S-stable Distributionmentioning

confidence: 63%

Randomized Algorithm for Approximate Nearest Neighbor Search in High Dimensions

Buaba¹,

Homaifar²,

Hendrix

et al. 2014

JPRR

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A randomized algorithm employs a degree of randomness as part of its logic with uniform random bits as an auxiliary input to guide its behavior, in the hope of achieving good average runtime performance over all possible choices of the random bits. In this paper, we formulate a randomized algorithm capable of finding approximate nearest neighbors, specifically in high dimensional datasets. The random bits of this algorithm are sets of kernels chosen from the Gaussian normal distribution, which are used to create a data structure that guarantees sublinear runtime complexity and retrieval accuracy. The algorithm focuses on selecting the optimal cardinalities of the kernels and their members. These cardinalities influence computational, memory and runtime complexities of the algorithm. We demonstrate that using the cardinality of the kernels to determine the kernel size guarantees the highest provable lower bound of the probability of collision of related items; thus accurate retrieval of nearest neighbors. When implemented on Cray XE6 machine using 76 processes, our algorithm achieves speedup of 69 and approximately 48x performance gain in average query runtime with the retrieval accuracy of 90.5%.

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Section: S-stable Distributionmentioning

confidence: 63%

Randomized Algorithm for Approximate Nearest Neighbor Search in High Dimensions

Buaba¹,

Homaifar²,

Hendrix

et al. 2014

JPRR

Self Cite

View full text Add to dashboard Cite

show abstract

“…On one hand, the ENN is generally determined by a predefined constant or a spherical space with a specific radius. The reasonable neighborhood range is crucial for accurate and reliable normal vector estimation, especially when dealing with LSSPC [11]. On the other hand, these ENN-based algorithms are perhaps reasonable in the distance but are not reasonable in spatial distribution [12].…”

Section: Introductionmentioning

confidence: 99%

An Investigation of the High Efficiency Estimation Approach of the Large-Scale Scattered Point Cloud Normal Vector

Meng

Liu

2018

Applied Sciences

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Abstract:The normal vector estimation of the large-scale scattered point cloud (LSSPC) plays an important role in point-based shape editing. However, the normal vector estimation for LSSPC cannot meet the great challenge of the sharp increase of the point cloud that is mainly attributed to its low computational efficiency. In this paper, a novel, fast method-based on bi-linear interpolation is reported on the normal vector estimation for LSSPC. We divide the point sets into many small cubes to speed up the local point search and construct interpolation nodes on the isosurface expressed by the point cloud. On the premise of calculating the normal vectors of these interpolated nodes, a normal vector bi-linear interpolation of the points in the cube is realized. The proposed approach has the merits of accurate, simple, and high efficiency, because the algorithm only needs to search neighbor and calculates normal vectors for interpolation nodes that are usually far less than the point cloud. The experimental results of several real and simulated point sets show that our method is over three times faster than the Elliptic Gabriel Graph-based method, and the average deviation is less than 0.01 mm.

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Optimal Load Factor for Approximate Nearest Neighbor Search under Exact Euclidean Locality Sensitive Hashing

Cited by 2 publications

References 45 publications

Randomized Algorithm for Approximate Nearest Neighbor Search in High Dimensions

Randomized Algorithm for Approximate Nearest Neighbor Search in High Dimensions

An Investigation of the High Efficiency Estimation Approach of the Large-Scale Scattered Point Cloud Normal Vector

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