The Sparse Vector Technique (SVT) is a fundamental technique for satisfying differential privacy and has the unique quality that one can output some query answers without apparently paying any privacy cost. SVT has been used in both the interactive setting, where one tries to answer a sequence of queries that are not known ahead of the time, and in the non-interactive setting, where all queries are known. Because of the potential savings on privacy budget, many variants for SVT have been proposed and employed in privacypreserving data mining and publishing. However, most variants of SVT are actually not private. In this paper, we analyze these errors and identify the misunderstandings that likely contribute to them. We also propose a new version of SVT that provides better utility, and introduce an effective technique to improve the performance of SVT. These enhancements can be applied to improve utility in the interactive setting. Through both analytical and experimental comparisons, we show that, in the non-interactive setting (but not the interactive setting), the SVT technique is unnecessary, as it can be replaced by the Exponential Mechanism (EM) with better accuracy.

Graph data publishing under node-differential privacy (node-DP) is challenging due to the huge sensitivity of queries. However, since a node in graph data oftentimes represents a person, node-DP is necessary to achieve personal data protection. In this paper, we investigate the problem of publishing the degree distribution of a graph under node-DP by exploring the projection approach to reduce the sensitivity. We propose two approaches based on aggregation and cumulative histogram to publish the degree distribution. The experiments demonstrate that our approaches greatly reduce the error of approximating the true degree distribution and have significant improvement over existing works. We also present the introspective analysis for understanding the factors of publishing the degree distribution with node-DP.

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k -means clustering is a widely used clustering analysis technique in machine learning. In this article, we study the problem of differentially private k -means clustering. Several state-of-the-art methods follow the single-workload approach, which adapts an existing machine-learning algorithm by making each step private. However, most of them do not have satisfactory empirical performance. In this work, we develop techniques to analyze the empirical error behaviors of one of the state-of-the-art single-workload approaches, DPLloyd, which is a differentially private version of the Lloyd algorithm for k >-means clustering. Based on the analysis, we propose an improvement of DPLloyd. We also propose a new algorithm for k -means clustering from the perspective of the noninteractive approach, which publishes a synopsis of the input dataset and then runs k -means on synthetic data generated from the synopsis. We denote this approach by EUGkM. After analyzing the empirical error behaviors of EUGkM, we further propose a hybrid approach that combines our DPLloyd improvement and EUGkM. Results from extensive and systematic experiments support our analysis and demonstrate the effectiveness of the DPLloyd improvement, EUGkM, and the hybrid approach.

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