An Algebraic Topological Approach to Privacy: Numerical and Categorical Data

In this paper, we cast the classic problem of achieving k-anonymity for a given database as a problem in algebraic topology. Using techniques from this field of mathematics, we propose a framework for k-anonymity that brings new insights and algorithms to anonymize a database. We begin by addressing the simpler case when the data lies in a metric space. This case is instrumental to introduce the main ideas and notation. Specifically, by mapping a database to the Euclidean space and by considering the distance between datapoints, we introduce a simplicial representation of the data and show how concepts from algebraic topology, such as the nerve complex and persistent homology, can be applied to efficiently obtain the entire spectrum of k-anonymity of the database for various values of k and levels of generalization. For this representation, we provide an analytic characterization of conditions under which a given representation of the dataset is k-anonymous. We introduce a weighted barcode diagram which, in this context, becomes a computational tool to tradeoff data anonymity with data loss expressed as level of generalization. Some simulations results are used to illustrate the main idea of the paper. We conclude the paper with a discussion on how to extend this method to address the general case of a mix of categorical and metric data

On the Optimal Selection of k in the k-Anonymity Problem

Abstract — When disseminating data involving human subjects, researchers have to weigh in the requirements of privacy of the individuals involved in the data. A model widely used for enhancing individual privacy is k–anonymity, where an individual data record is rendered similar to k − 1 other records in the data set by using generalization and/or suppression operations on the data attributes. The drawback of this model is that such transformations result in considerable loss of information that is proportional to the choice of k. Studies in this context have so far focused on minimizing the information loss for some given value of k. However, owing to the presence of outliers, a specified k value may or may not be obtainable. Further, an exhaustive analysis is required to determine a k value that fits the loss constraint specified by a data publisher. In this paper, we formulate a multi-objective optimization problem to illustrate that the decision on k can be much more informed than being a choice solely based on the privacy requirement. The optimization problem is intended to resolve the issue of data privacy when data suppression is not allowed in order to obtain a particular value of k. An evolutionary algorithm is employed here to provide this insight. I