HDKV: High-Dimensional Similarity Query in Key-Value Stores-白红宇

HDKV: High-Dimensional Similarity Query in Key-Value Stores

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发布时间：2019-06-13

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Locality-sensitive hashing (LSH) is a method of performing probabilistic of high-dimensional data. The basic idea is to the input items so that similar items are mapped to the same buckets with high probability (the number of buckets being much smaller than the universe of possible input items).

Stable distributions

The hash function $h_{\mathbf{a},b} (\boldsymbol{\upsilon}) : \mathcal{R}^d \to \mathcal{N}$ maps a d dimensional vector $\boldsymbol{\upsilon}$ onto a set of integers. Each hash function in the family is indexed by a choice of random $\mathbf{a}$ and $b$ where $\mathbf{a}$ is a d dimensional vector with entries chosen independently from a and $b$ is a real number chosen uniformly from the range [0,r]. For a fixed $\mathbf{a},b$ the hash function $h_{\mathbf{a},b}$ is given by $h_{\mathbf{a},b} (\boldsymbol{\upsilon}) = \left \lfloor \frac{\mathbf{a}\cdot \boldsymbol{\upsilon}+b}{r} \right \rfloor$ .

Other construction methods for hash functions have been proposed to better fit the data. In particular k-means hash functions are better in practice than projection-based hash functions, but without any theoretical guarantee.

The key idea of locality-sensitive hash (LSH) is to hash the points using several hash functions so as to ensure that, for each function, the probability of

collision is much higher for objects which are close to each other than for those which are far apart. Then, one can determine near neighbors by hashing the

query point and retrieving elements stored in buckets containing that point.

转载于:https://www.cnblogs.com/zhangzhang/archive/2012/02/17/2355143.html

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