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.
Differentially private cluster analysis has also be studied in prior work. @cite_2 proposed differentially private model fitting based on genetic algorithms, with applications to -means clustering. McSherry @cite_34 introduced the PINQ framework, which has been applied to achieve differential privacy for -means clustering using an iterative algorithm @cite_1 . @cite_25 proposed the sample-aggregate framework that calibrates the noise magnitude according to the smooth sensitivity of a function. They showed that their framework can be applied to -means clustering under the assumption that the dataset is well-separated. These research efforts primarily focus on centroid-based clustering, such as -means, that is most suited for separating convex clusters and presents insufficient spatial information to detect clusters with complex shapes, e.g. concave shapes. In contrast to these research efforts, we propose techniques that enforce differential privacy on WaveCluster, which is not restricted to well-separated datasets, and can detect clusters with arbitrary shapes.
@cite_34 @cite_1 @cite_25 @cite_2
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We present an approach to differentially private computation in which one does not scale up the magnitude of noise for challenging queries, but rather scales down the contributions of challenging records. While scaling down all records uniformly is equivalent to scaling up the noise magnitude, we show that scaling records non-uniformly can result in substantially higher accuracy by bypassing the worst-case requirements of differential privacy for the noise magnitudes. This paper details the data analysis platform wPINQ, which generalizes the Privacy Integrated Query (PINQ) to weighted datasets. Using a few simple operators (including a non-uniformly scaling Join operator) wPINQ can reproduce (and improve) several recent results on graph analysis and introduce new generalizations (e.g., counting triangles with given degrees). We also show how to integrate probabilistic inference techniques to synthesize datasets respecting more complicated (and less easily interpreted) measurements. We present an approach to differentially private computation in which one does not scale up the magnitude of noise for challenging queries, but rather scales down the contributions of challenging records. While scaling down all records uniformly is equivalent to scaling up the noise magnitude, we show that scaling records non-uniformly can result in substantially higher accuracy by bypassing the worst-case requirements of differential privacy for the noise magnitudes. This paper details the data analysis platform wPINQ, which generalizes the Privacy Integrated Query (PINQ) to weighted datasets. Using a few simple operators (including a non-uniformly scaling Join operator) wPINQ can reproduce (and improve) several recent results on graph analysis and introduce new generalizations (e.g., counting triangles with given degrees). We also show how to integrate probabilistic inference techniques to synthesize datasets respecting more complicated (and less easily interpreted) measurements. Differential privacy has recently emerged as the de facto standard for private data release. This makes it possible to provide strong theoretical guarantees on the privacy and utility of released data. While it is well-understood how to release data based on counts and simple functions under this guarantee, it remains to provide general purpose techniques to release data that is useful for a variety of queries. In this paper, we focus on spatial data such as locations and more generally any multi-dimensional data that can be indexed by a tree structure. Directly applying existing differential privacy methods to this type of data simply generates noise. We propose instead the class of private spatial decompositions'': these adapt standard spatial indexing methods such as quad trees and kd-trees to provide a private description of the data distribution. Equipping such structures with differential privacy requires several steps to ensure that they provide meaningful privacy guarantees. Various basic steps, such as choosing splitting points and describing the distribution of points within a region, must be done privately, and the guarantees of the different building blocks composed to provide an overall guarantee. Consequently, we expose the design space for private spatial decompositions, and analyze some key examples. A major contribution of our work is to provide new techniques for parameter setting and post-processing the output to improve the accuracy of query answers. Our experimental study demonstrates that it is possible to build such decompositions efficiently, and use them to answer a variety of queries privately with high accuracy. Various paradigms, based on differential privacy, have been proposed to release a privacy-preserving dataset with statistical approximation. Nonetheless, most existing schemes are limited when facing highly correlated attributes, and cannot prevent privacy threats from untrusted servers. In this paper, we propose a novel Copula- based scheme to efficiently synthesize and release multi-dimensional crowdsourced data with local differential privacy. In our scheme, each participant's (or user's) data is locally transformed into bit strings based on a randomized response technique, which guarantees a participant's privacy on the participant (user) side. Then, Copula theory is leveraged to synthesize multi-dimensional crowdsourced data based on univariate marginal distribution and attribute dependence. Univariate marginal distribution is estimated by the Lasso-based regression algorithm from the aggregated privacy- preserving bit strings. Dependencies among attributes are modeled as multivariate Gaussian Copula, of which parameter is estimated by Pearson correlation coefficients. We conduct experiments to validate the effectiveness of our scheme. Our experimental results demonstrate that our scheme is effective for the release of multi-dimensional data with local differential privacy guaranteed to distributed participants.