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Register a new userUtility-efficient Differentially Private K-means Clustering based on Cluster Merging
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Added by
Zhili Chen Prof.
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Differential privacy is widely used in data analysis. State-of-the-art $k$-means clustering algorithms with differential privacy typically add an equal amount of noise to centroids for each iterative computation. In this paper, we propose a novel differentially private $k$-means clustering algorithm, DP-KCCM, that significantly improves the utility of clustering by adding adaptive noise and merging clusters. Specifically, to obtain $k$ clusters with differential privacy, the algorithm first generates $n times k$ initial centroids, adds adaptive noise for each iteration to get $n times k$ clusters, and finally merges these clusters into $k$ ones. We theoretically prove the differential privacy of the proposed algorithm. Surprisingly, extensive experimental results show that: 1) cluster merging with equal amounts of noise improves the utility somewhat; 2) although adding adaptive noise only does not improve the utility, combining both cluster merging and adaptive noise further improves the utility significantly.
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We introduce a new $(epsilon_p, delta_p)$-differentially private algorithm for the $k$-means clustering problem. Given a dataset in Euclidean space, the $k$-means clustering problem requires one to find $k$ points in that space such that the sum of squares of Euclidean distances between each data point and its closest respective point among the $k$ returned is minimised. Although there exist privacy-preserving methods with good theoretical guarantees to solve this problem [Balcan et al., 2017; Kaplan and Stemmer, 2018], in practice it is seen that it is the additive error which dictates the practical performance of these methods. By reducing the problem to a sequence of instances of maximum coverage on a grid, we are able to derive a new method that achieves lower additive error then previous works. For input datasets with cardinality $n$ and diameter $Delta$, our algorithm has an $O(Delta^2 (k log^2 n log(1/delta_p)/epsilon_p + ksqrt{d log(1/delta_p)}/epsilon_p))$ additive error whilst maintaining constant multiplicative error. We conclude with some experiments and find an improvement over previously implemented work for this problem.
Data collection under local differential privacy (LDP) has been mostly studied for homogeneous data. Real-world applications often involve a mixture of different data types such as key-value pairs, where the frequency of keys and mean of values under each key must be estimated simultaneously. For key-value data collection with LDP, it is challenging to achieve a good utility-privacy tradeoff since the data contains two dimensions and a user may possess multiple key-value pairs. There is also an inherent correlation between key and values which if not harnessed, will lead to poor utility. In this paper, we propose a locally differentially private key-value data collection framework that utilizes correlated perturbations to enhance utility. We instantiate our framework by two protocols PCKV-UE (based on Unary Encoding) and PCKV-GRR (based on Generalized Randomized Response), where we design an advanced Padding-and-Sampling mechanism and an improved mean estimator which is non-interactive. Due to our correlated key and value perturbation mechanisms, the composed privacy budget is shown to be less than that of independent perturbation of key and value, which enables us to further optimize the perturbation parameters via budget allocation. Experimental results on both synthetic and real-world datasets show that our proposed protocols achieve better utility for both frequency and mean estimations under the same LDP guarantees than state-of-the-art mechanisms.
Correlation clustering is a widely used technique in unsupervised machine learning. Motivated by applications where individual privacy is a concern, we initiate the study of differentially private correlation clustering. We propose an algorithm that achieves subquadratic additive error compared to the optimal cost. In contrast, straightforward adaptations of existing non-private algorithms all lead to a trivial quadratic error. Finally, we give a lower bound showing that any pure differentially private algorithm for correlation clustering requires additive error of $Omega(n)$.
We study the basic operation of set union in the global model of differential privacy. In this problem, we are given a universe $U$ of items, possibly of infinite size, and a database $D$ of users. Each user $i$ contributes a subset $W_i subseteq U$ of items. We want an ($epsilon$,$delta$)-differentially private algorithm which outputs a subset $S subset cup_i W_i$ such that the size of $S$ is as large as possible. The problem arises in countless real world applications; it is particularly ubiquitous in natural language processing (NLP) applications as vocabulary extraction. For example, discovering words, sentences, $n$-grams etc., from private text data belonging to users is an instance of the set union problem. Known algorithms for this problem proceed by collecting a subset of items from each user, taking the union of such subsets, and disclosing the items whose noisy counts fall above a certain threshold. Crucially, in the above process, the contribution of each individual user is always independent of the items held by other users, resulting in a wasteful aggregation process, where some item counts happen to be way above the threshold. We deviate from the above paradigm by allowing users to contribute their items in a $textit{dependent fashion}$, guided by a $textit{policy}$. In this new setting ensuring privacy is significantly delicate. We prove that any policy which has certain $textit{contractive}$ properties would result in a differentially private algorithm. We design two new algorithms, one using Laplace noise and other Gaussian noise, as specific instances of policies satisfying the contractive properties. Our experiments show that the new algorithms significantly outperform previously known mechanisms for the problem.
In differential privacy (DP), a challenging problem is to generate synthetic datasets that efficiently capture the useful information in the private data. The synthetic dataset enables any task to be done without privacy concern and modification to existing algorithms. In this paper, we present PrivSyn, the first automatic synthetic data generation method that can handle general tabular datasets (with 100 attributes and domain size $>2^{500}$). PrivSyn is composed of a new method to automatically and privately identify correlations in the data, and a novel method to generate sample data from a dense graphic model. We extensively evaluate different methods on multiple datasets to demonstrate the performance of our method.
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