WaveCluster is an important family of grid-based clustering algorithms that are capable of finding clusters of arbitrary shapes. In this paper, we investigate techniques to perform WaveCluster while ensuring differential privacy. Our goal is to develop a general technique for achieving differential privacy on WaveCluster that accommodates different wavelet transforms. We show that straightforward techniques based on synthetic data generation and introduction of random noise when quantizing the data, though generally preserving the distribution of data, often introduce too much noise to preserve useful clusters. We then propose two optimized techniques, PrivTHR and PrivTHREM, which can significantly reduce data distortion during two key steps of WaveCluster: the quantization step and the significant grid identification step. We conduct extensive experiments based on four datasets that are particularly interesting in the context of clustering, and show that PrivTHR and PrivTHREM achieve high utility when privacy budgets are properly allocated.
More recent work has focused on practical applications of differential privacy for privacy-preserving data publishing. An approach proposed by @cite_11 encoded marginals with Fourier coefficients and then added noise to the released coefficients. @cite_14 exploited consistency constraints to reduce noise for histogram counts. @cite_28 proposed , which uses wavelet transforms to reduce noise for histogram counts. @cite_22 indexed data by -trees and -trees, developing effective budget allocation strategies for building the noisy trees and obtaining noisy counts for the tree nodes. @cite_8 proposed uniform-grid and adaptive-grid methods to derive appropriate partition granularity in differentially private synopsis publishing. @cite_16 proposed the and techniques for constructing optimal noisy histograms, using dynamic programming and Exponential mechanism. These data publishing techniques are specifically crafted for answering range queries. Unfortunately, synthesizing the dataset and applying WaveCluster on top of it often render WaveCluster results useless, since these differentially private data publishing techniques do not capture the essence of WaveCluster and introduce too much unnecessary noise for WaveCluster.
@cite_14 @cite_22 @cite_8 @cite_28 @cite_16 @cite_11
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Differential privacy has emerged as one of the most promising privacy models for private data release. It can be used to release different types of data, and, in particular, histograms, which provide useful summaries of a dataset. Several differentially private histogram releasing schemes have been proposed recently. However, most of them directly add noise to the histogram counts, resulting in undesirable accuracy. In this paper, we propose two sanitization techniques that exploit the inherent redundancy of real-life datasets in order to boost the accuracy of histograms. They lossily compress the data and sanitize the compressed data. Our first scheme is an optimization of the Fourier Perturbation Algorithm (FPA) presented in RN10 . It improves the accuracy of the initial FPA by a factor of 10. The other scheme relies on clustering and exploits the redundancy between bins. Our extensive experimental evaluation over various real-life and synthetic datasets demonstrates that our techniques preserve very accurate distributions and considerably improve the accuracy of range queries over attributed histograms. Privacy-preserving data publishing has attracted considerable research interest in recent years. Among the existing solutions, ∈-differential privacy provides the strongest privacy guarantee. Existing data publishing methods that achieve ∈-differential privacy, however, offer little data utility. In particular, if the output data set is used to answer count queries, the noise in the query answers can be proportional to the number of tuples in the data, which renders the results useless. In this paper, we develop a data publishing technique that ensures ∈-differential privacy while providing accurate answers for range-count queries, i.e., count queries where the predicate on each attribute is a range. The core of our solution is a framework that applies wavelet transforms on the data before adding noise to it. We present instantiations of the proposed framework for both ordinal and nominal data, and we provide a theoretical analysis on their privacy and utility guarantees. In an extensive experimental study on both real and synthetic data, we show the effectiveness and efficiency of our solution. Privacy-preserving data publishing is an important problem that has been the focus of extensive study. The state-of-the-art solution for this problem is differential privacy, which offers a strong degree of privacy protection without making restrictive assumptions about the adversary. Existing techniques using differential privacy, however, cannot effectively handle the publication of high-dimensional data. In particular, when the input dataset contains a large number of attributes, existing methods require injecting a prohibitive amount of noise compared to the signal in the data, which renders the published data next to useless. To address the deficiency of the existing methods, this paper presents P riv B ayes , a differentially private method for releasing high-dimensional data. Given a dataset D, P riv B ayes first constructs a Bayesian network N, which (i) provides a succinct model of the correlations among the attributes in D and (ii) allows us to approximate the distribution of data in D using a set P of low-dimensional marginals of D. After that, P riv B ayes injects noise into each marginal in P to ensure differential privacy and then uses the noisy marginals and the Bayesian network to construct an approximation of the data distribution in D. Finally, P riv B ayes samples tuples from the approximate distribution to construct a synthetic dataset, and then releases the synthetic data. Intuitively, P riv B ayes circumvents the curse of dimensionality, as it injects noise into the low-dimensional marginals in P instead of the high-dimensional dataset D. Private construction of Bayesian networks turns out to be significantly challenging, and we introduce a novel approach that uses a surrogate function for mutual information to build the model more accurately. We experimentally evaluate P riv B ayes on real data and demonstrate that it significantly outperforms existing solutions in terms of accuracy. A mechanism for releasing information about a statistical database with sensitive data must resolve a trade-off between utility and privacy. Publishing fully accurate information maximizes utility while minimizing privacy, while publishing random noise accomplishes the opposite. Privacy can be rigorously quantified using the framework of differential privacy, which requires that a mechanism's output distribution is nearly the same whether a given database row is included. The goal of this paper is to formulate and provide strong and general utility guarantees, subject to differential privacy. We pursue mechanisms that guarantee near-optimal utility to every potential user, independent of its side information (modeled as a prior distribution over query results) and preferences (modeled via a symmetric and monotone loss function). Our main result is the following: for each fixed count query and differential privacy level, there is a geometric mechanism @math ---a discrete variant of the simple and well-studi...