Locally Private k-Means in One Round

Chang, Alisa; Ghazi, Badih; Kumar, Ravi; Manurangsi, Pasin

doi:10.48550/arxiv.2104.09734

Cited by 3 publications

(3 citation statements)

References 27 publications

(41 reference statements)

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“…To enhance the privacy that hides the centroids in each iteration, they add noise to the reported centroid as well. Refererces [27] introduced a method for a one-round local differential privacy algorithm, which provides a similar additive error with the shuffled DP model applied to K-means clustering problem.…”

Section: K-means Clustering With Local Settingmentioning

confidence: 99%

K-Means Clustering with Local Distance Privacy

Yang,

Huang,

Tang

2023

Big Data Min. Anal.

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With the development of information technology, a mass of data are generated every day. Collecting and analysing these data help service providers improve their services and gain an advantage in the fierce market competition. K-means clustering has been widely used for cluster analysis in real life. However, these analyses are based on users' data, which disclose users' privacy. Local differential privacy has attracted lots of attention recently due to its strong privacy guarantee and has been applied for clustering analysis. However, existing K-means clustering methods with local differential privacy protection cannot get an ideal clustering result due to the large amount of noise introduced to the whole dataset to ensure the privacy guarantee. To solve this problem, we propose a novel method that provides local distance privacy for users who participate in the clustering analysis. Instead of making the users' records in-distinguish from each other in high-dimensional space, we map the user's record into a one-dimensional distance space and make the records in such a distance space not be distinguished from each other. To be specific, we generate a noisy distance first and then synthesize the high-dimensional data record.We propose a Bounded Laplace Method (BLM) and a Cluster Indistinguishable Method (CIM) to sample such a noisy distance, which satisfies the local differential privacy guarantee and local d E -privacy guarantee, respectively. Furthermore, we introduce a way to generate synthetic data records in high-dimensional space. Our experimental evaluation results show that our methods outperform the traditional methods significantly.

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Section: K-means Clustering With Local Settingmentioning

confidence: 99%

K-Means Clustering with Local Distance Privacy

Yang,

Huang,

Tang

2023

Big Data Min. Anal.

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“…To enhance the privacy and hide the cluster each user belongs to in the intermediate rounds, the reports regarding the users' closest center is perturbed by the LDP protocol as well. A very recent work [29] provides an approximation algorithm for K-means clustering problem in one-round local differential privacy. They show that the proposed method achieves a similar small additive error when applied in the shuffled DP model, where a shuffler sits between the encoder and decoder.…”

Section: Related Workmentioning

confidence: 99%

K-Means Clustering With Local dᵪ-Privacy for Privacy-Preserving Data Analysis

Yang

Tjuawinata

Lam

2022

IEEE Trans.Inform.Forensic Secur.

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Privacy-preserving data analysis is an emerging area that addresses the dilemma of performing data analysis on user data while protecting users' privacy. In this paper, we consider the problem of constructing privacy-preserving K-means clustering protocol for data analysis that provides local privacy to users' data. To enable a desirable degree of local privacy guarantee while maintaining high accuracy of the clustering, we adopt a generalized differential privacy definition, dχ-privacy, which quantifies the distinguishability level based on the distance between data records defined by the distance function dχ. In our work, we consider the space of data points as a metric space imbued with Euclidean distance and propose a bounded perturbation mechanism (BPM) with bounded sampling space of the perturbed data points, which is formally shown to achieve dχ-privacy. BPM perturbs the data as a whole instead of treating each dimension independently, which is desirable since the privacy budget is no longer required to be split among different dimensions. Bounded output space also means that we will not get into the case where the report or the statistical result is so far out of the data domain that it is hard to interpret. Furthermore, it can also help in limiting the amount of bandwidth needed to send such report to the server. The design of BPM is based on a probability density function which decreases exponentially as the Euclidean distance with respect to the true value grows. It is also designed with the aim of ensuring that BPM produces perturbed data that provides the claimed privacy guarantee while ensuring high utility response. To guarantee the efficiency of the perturbation method, we propose an efficient algorithm to sample from the proposed distribution and apply BPM to the design of dχ-private K-means clustering algorithms. Lastly, we analyse the privacy and utility guarantee provided by the proposed method and provide its experimental results.

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“…In Chang et al [2021] a one-round protocol for LDP k-means with similar cost guarantees as algorithm 1 is introduced, also surpassing the n 1/2+a barrier mentioned above. They operate in the ǫ-DP setting and get a multiplicative approximation of η(1 + α) where η is the multiplicative approximation guarantee of any given non-private k-means algorithm and an additive error term of k Oα(1) • √ nd ′ •poly log(n)/ǫ.…”

Section: Concurrent Workmentioning

confidence: 99%

Locally Private $k$-Means Clustering with Constant Multiplicative Approximation and Near-Optimal Additive Error

Chaturvedi¹,

Jones²,

Nguyêݱn³

2021

Preprint

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Given a data set of size n in d ′ -dimensional Euclidean space, the k-means problem asks for a set of k points (called centers) so that the sum of the ℓ 2 2 -distances between points of a given data set of size n and the set of k centers is minimized. Recent work on this problem in the locally private setting achieves constant multiplicative approximation with additive error Õ(n) and proves a lower bound of Ω( √ n) on the additive error for any solution with a constant number of rounds. In this work we bridge the gap between the exponents of n in the upper and lower bounds on the additive error with two new algorithms. Given any α > 0, our first algorithm achieves a multiplicative approximation guarantee which is at most a (1 + α) factor greater than that of any non-private k-means clustering algorithm with k Õ(1/α 2 ) √ d ′ n poly log n additive error. Given any c > √ 2, our second algorithm achieves O(k 1+ Õ(1/(2c 2 −1)) √ d ′ n poly log n) additive error with constant multiplicative approximation. Both algorithms go beyond the Ω(n 1/2+a ) factor that occurs in the additive error for arbitrarily small parameters a in previous work, and the second algorithm in particular shows for the first time that it is possible to solve the locally private k-means problem in a constant number of rounds with constant factor multiplicative approximation and polynomial dependence on k in the additive error arbitrarily close to linear.

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Locally Private k-Means in One Round

Cited by 3 publications

References 27 publications

K-Means Clustering with Local Distance Privacy

K-Means Clustering with Local Distance Privacy

K-Means Clustering With Local dᵪ-Privacy for Privacy-Preserving Data Analysis

Locally Private $k$-Means Clustering with Constant Multiplicative Approximation and Near-Optimal Additive Error

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