ﻻ يوجد ملخص باللغة العربية
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.
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 $ell_2^2$-distances between points of a given data set of size $n$ and the set of $k$ centers
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
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 dif
Being able to efficiently and accurately select the top-$k$ elements with differential privacy is an integral component of various private data analysis tasks. In this paper, we present the oneshot Laplace mechanism, which generalizes the well-known
The correlations and network structure amongst individuals in datasets today---whether explicitly articulated, or deduced from biological or behavioral connections---pose new issues around privacy guarantees, because of inferences that can be made ab