Clustering is an important tool for data exploration where the goal is to subdivide a data set into disjoint clusters that fit well into the underlying data structure. When dealing with sensitive data, privacy-preserving algorithms aim to approximate the non-private baseline while minimising the leakage of sensitive information. State-of-the-art privacy-preserving clustering algorithms tend to output clusters that are good in terms of the standard metrics, inertia, silhouette score, and clustering accuracy, however, the clustering result strongly deviates from the non-private KMeans baseline. In this work, we present a privacy-preserving clustering algorithm called DPM that recursively separates a data set into clusters based on a geometrical clustering approach. In addition, DPM estimates most of the data-dependent hyper-parameters in a privacy-preserving way. We prove that DPM preserves Differential Privacy and analyse the utility guarantees of DPM. Finally, we conduct an extensive empirical evaluation for synthetic and real-life data sets. We show that DPM achieves state-of-the-art utility on the standard clustering metrics and yields a clustering result much closer to that of the popular non-private KMeans algorithm without requiring the number of classes.

For research in medicine, economics and social sciences specific data of individuals is needed. Thus it should be publicly available, but this should not offend the privacy of each individual. Microaggregation applied to databases is a standard technique to protect privacy. It clusters similar people in larger groups to achieve so called k-anonymity – every individual is hidden in a cluster of size at least k. Then the data can be made public for all kinds of analysis, whereas other concepts like differential privacy keep the database secret and allow only specific questions about the data to be asked by outsiders. The modification of a database to achieve anonymity should be as small as possible to keep its utility – that means the loss of information should be minimized. In this respect microaggregation typically performs much better than other anonymization techniques like generalization or suppression. However, minimizing the information loss by k-anonymous microaggregation is an NP-hard optimization problem for k ≥ 3 . Not only computing optimal solutions efficiently is unlikely, nontrivial approximations are lacking, too. Therefore, a bunch of heuristics all with at least quadratic time complexity have been developed. This paper improves microaggregation significantly and provides a tradeoff between computational effort and utility. First, we make a detailed analysis and tuning of the maximum distance methodology – the common approach to generate a clustering that provides k-anonymity. We review the methods proposed so far and design a new algorithm ^*_γ that gives better utility on standard benchmarks. A different approach of quadratic time complexity based on Lloyd’s algorithm has been proposed and named ONA, but not completely analysed. This paper fills this gap and improves several steps resulting in a new algorithm ^* with better utility. Mondrian is a another approach for clustering data that can be adopted for microaggregation. It is quite fast, but typically achieves very pure utility. We improve on this and design an almost linear time algorithm that gives acceptable utility, however worse than the quadratic time algorithms. Finally, we combine both techniques, ONA and Mondrian, to construct a new class of parameterized algorithms called . They are quite fast with time complexity between almost linear and quadratic, and deliver competitive utility compared to the MDAV approach.

k-anonymous microaggregation of data in Rd with d≥2 is shown to be NP-hard for all k≥4, extending a previous result for the case k=3 only. The proof uses similarities between microaggregation and the k-means problem. A reduction of Planar 3-SAT to the k-means clustering problem is adapted to 4-anonymous clustering. Then this construction is extended to arbitrary k≥4.

k-anonymous microaggregation is a standard technique to improve privacy of individuals whose personal data is used in microdata databases. Unlike semantic privacy requirements like differential privacy, k-anonymity allows the unrestricted publication of data, suitable for all kinds of analysis since every individual is hidden in a cluster of size at least k. Microaggregation can preserve a high level of utility, that means small information loss caused by the aggregation procedure, compared to other anonymization techniques like generalization or suppression. Minimizing the information loss in k-anonymous microaggregation is an NP-hard clustering problem for k >= 3. Even more, no efficient approximation algorithms with a nontrivial approximation ratio are known. Therefore, a bunch of heuristics have been developed to restrain high utility - all with quadratic time complexity in the size of the database at least. We improve this situation in several respects providing a tradeoff between computational effort and utility. First, a quadratic time algorithm ONA* is presented that achieves significantly better utility for standard benchmarks. Next, an almost linear time algorithm is developed that gives worse, but still acceptable utility. This is achieved by a suitable adaption of the Mondrian clustering algorithm. Finally, combining both techniques a new class MONA of parameterized algorithms is designed that deliver competitive utility for user-specified time constraints between almost linear and quadratic.

Microaggregation is a technique to preserve privacy when confidential information about individuals shall be used by third parties. A basic property to be established is called k-anonymity. It requires that identifying information about individuals should not be unique, instead there has to be a group of size at least k that looks identical. This is achieved by clustering individuals into appropriate groups and then averaging the identifying information. The question arises how to select these groups such that the information loss by averaging is minimal. This problem has been shown to be NP-hard. Thus, several heuristics called MDAV ,V-MDAV , . . . have been proposed for finding at least a suboptimal clustering. This paper proposes a more sophisticated, but still efficient strategy called MDAV∗ to construct a good clustering. The question whether to extend a group locally by individuals close by or to start a new group with such individuals is investigated in more depth. This way, a noticeable lower information loss can be achieved which is shown by applying MDAV∗ to several established benchmarks of real data and also to specifically designed random data.