Online social networks (OSNs) often refuse to publish their social network graphs due to privacy concerns. Recently, differential privacy has become the widely accepted criteria for privacy preserving data publishing. Although some work has been done on publishing matrices with differential privacy, they are computationally unpractical as they are not designed to handle large matrices such as adjacency matrices of OSN graphs. In this paper, we propose a random matrix approach to OSN data publishing, which achieves storage and computational efficiency by reducing dimensions of adjacency matrices and achieves differential privacy by adding a small amount of noise. Our key idea is to first project each row of an adjacency matrix into a low-dimensional space using random projection, and then perturb the projected matrix with random noise, and finally publish the perturbed and projected matrix. In this paper, we first prove that random projection plus random perturbation preserve differential privacy, and also that the random noise required to achieve differential privacy is small. We validate the proposed approach and evaluate the utility of the published data for three different applications, namely node clustering, node ranking, and node classification, using publicly available OSN graphs of Facebook, LiveJournal, and Pokec.

中文翻译：

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发布具有隐私保证的社交网络图特征谱

由于隐私问题，在线社交网络 (OSN) 通常拒绝发布其社交网络图。最近，差异隐私已成为广泛接受的隐私保护数据发布标准。尽管在发布具有差分隐私的矩阵方面已经做了一些工作，但它们在计算上是不切实际的，因为它们不是为处理大型矩阵而设计的，例如 OSN 图的邻接矩阵。在本文中，我们提出了一种用于 OSN 数据发布的随机矩阵方法，该方法通过降低邻接矩阵的维数来实现存储和计算效率，并通过添加少量噪声来实现差分隐私。我们的关键思想是首先使用随机投影将邻接矩阵的每一行投影到低维空间，然后用随机噪声扰乱投影矩阵，最后发布扰动和投影矩阵。在本文中，我们首先证明随机投影加随机扰动可以保护差分隐私，并且实现差分隐私所需的随机噪声很小。我们使用 Facebook、LiveJournal 和 Pokec 的公开可用 OSN 图验证了所提出的方法并评估了已发布数据在三个不同应用程序中的效用，即节点聚类、节点排名和节点分类。