Hashing based approximate nearest neighbor search has attracted considerable attention in various fields. Most of the existing hashing methods are centralized, which cannot be used for many large-scale applications with the data stored or collected in a distributed manner. In this article, we consider the distributed hashing problem. The main difficulty of hashing is brought by its inherent binary constraints, which makes the problem generally NP-hard. Most of the existing distributed hashing methods chose to relax the problem by dropping the binary constraints. However, such a manner will bring additional quantization error, which makes the binary codes less effective. In this paper, we propose a novel distributed discrete hashing method, which learns effective hash codes without using any relaxations. Specifically, we give a method to transform the discrete hashing problem into an equivalent distributed continuous optimization problem. After transformation, we devise a distributed discrete hashing (dDH) algorithm based on the idea of DC programming to solve the problem. To obtain more efficient hash codes, we further add bits balance and uncorrelation constraints to the hashing problem, and we also propose a distributed constrained discrete hashing algorithm (dCDH) to solve this problem. Extensive experiments are provided to show the superiority of the proposed methods.

中文翻译：

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通过等效连续公式进行分布式离散哈希

基于散列的近似最近邻居搜索已在各个领域引起了相当大的关注。现有的大多数散列方法都是集中式的，无法用于以分布式方式存储或收集数据的许多大型应用程序。在本文中，我们考虑分布式哈希问题。散列的主要困难是由其固有的二进制约束带来的，这使得该问题通常很难解决。大多数现有的分布式哈希方法选择通过消除二进制约束来缓解该问题。然而，这种方式将带来附加的量化误差，这使得二进制代码的有效性降低。在本文中，我们提出了一种新颖的分布式离散哈希算法，该方法无需使用任何松弛即可学习有效的哈希码。特别，我们给出了一种将离散哈希问题转化为等效的分布式连续优化问题的方法。转换后，我们基于DC编程的思想设计了一种分布式离散哈希（dDH）算法来解决该问题。为了获得更有效的哈希码，我们进一步将比特平衡和不相关约束添加到哈希问题中，并且我们还提出了一种分布式约束离散哈希算法（dCDH）来解决该问题。提供了广泛的实验来证明所提出方法的优越性。我们进一步将位平衡和不相关约束添加到哈希问题上，并且我们还提出了一种分布式约束离散哈希算法（dCDH）来解决此问题。提供了广泛的实验来证明所提出方法的优越性。我们进一步将位平衡和不相关约束添加到哈希问题上，并且我们还提出了一种分布式约束离散哈希算法（dCDH）来解决此问题。提供了广泛的实验来证明所提出方法的优越性。