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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Privacy Integrated Queries (PINQ) is an extensible data analysis platform designed to provide unconditional privacy guarantees for the records of the underlying data sets. PINQ provides analysts with access to records through an SQL-like declarative language (LINQ) amidst otherwise arbitrary C# code. At the same time, the design of PINQ's analysis language and its careful implementation provide formal guarantees of differential privacy for any and all uses of the platform. PINQ's guarantees require no trust placed in the expertise or diligence of the analysts, broadening the scope for design and deployment of privacy-preserving data analyses, especially by privacy nonexperts. We demonstrate Damson, a novel and powerful tool for publishing the results of biomedical research with strong privacy guarantees. Damson is developed based on the theory of differential privacy, which ensures that the adversary cannot infer the presence or absence of any individual from the published results, even with substantial background knowledge. Damson supports a variety of analysis tasks that are common in biomedical studies, including histograms, marginals, data cubes, classification, regression, clustering, and ad-hoc selection-counts. Additionally, Damson contains an effective query optimization engine, which obtains high accuracy for analysis results, while minimizing the privacy costs of performing such analysis. We introduce a new, generic framework for private data analysis.The goal of private data analysis is to release aggregate information about a data set while protecting the privacy of the individuals whose information the data set contains.Our framework allows one to release functions f of the data withinstance-based additive noise. That is, the noise magnitude is determined not only by the function we want to release, but also bythe database itself. One of the challenges is to ensure that the noise magnitude does not leak information about the database. To address that, we calibrate the noise magnitude to the smoothsensitivity of f on the database x --- a measure of variabilityof f in the neighborhood of the instance x. The new frameworkgreatly expands the applicability of output perturbation, a technique for protecting individuals' privacy by adding a smallamount of random noise to the released statistics. To our knowledge, this is the first formal analysis of the effect of instance-basednoise in the context of data privacy. Our framework raises many interesting algorithmic questions. Namely,to apply the framework one must compute or approximate the smoothsensitivity of f on x. We show how to do this efficiently for several different functions, including the median and the cost ofthe minimum spanning tree. We also give a generic procedure based on sampling that allows one to release f(x) accurately on manydatabases x. This procedure is applicable even when no efficient algorithm for approximating smooth sensitivity of f is known orwhen f is given as a black box. We illustrate the procedure by applying it to k-SED (k-means) clustering and learning mixtures of Gaussians. epsilon-differential privacy is rapidly emerging as the state-of-the-art scheme for protecting individuals' privacy in published analysis results over sensitive data. The main idea is to perform random perturbations on the analysis results, such that any individual's presence in the data has negligible impact on the randomized results. This paper focuses on analysis tasks that involve model fitting, i.e., finding the parameters of a statistical model that best fit the dataset. For such tasks, the quality of the differentially private results depends upon both the effectiveness of the model fitting algorithm, and the amount of perturbations required to satisfy the privacy guarantees. Most previous studies start from a state-of-the-art, non-private model fitting algorithm, and develop a differentially private version. Unfortunately, many model fitting algorithms require intensive perturbations to satisfy -differential privacy, leading to poor overall result quality. Motivated by this, we propose PrivGene, a general-purpose differentially private model fitting solution based on genetic algorithms (GA). PrivGene needs significantly less perturbations than previous methods, and it achieves higher overall result quality, even for model fitting tasks where GA is not the first choice without privacy considerations. Further, PrivGene performs the random perturbations using a novel technique called the enhanced exponential mechanism, which improves over the exponential mechanism by exploiting the special properties of model fitting tasks. As case studies, we apply PrivGene to three common analysis tasks involving model fitting: logistic regression, SVM classification, and k-means clustering. Extensive experiments using real data confirm the high result quality of PrivGene, and its superiority over existing methods.