隐私的代数拓扑方法：数值和类别数据
An Algebraic Topological Approach to Privacy: Numerical and Categorical Data
摘要：
在本文中，我们投的经典问题，实现k-匿名给定的数据库作为一个问题的代数拓扑。使用这个数学领域的技术，我们提出了一个框架，为k-匿名，带来了新的见解和算法，匿名数据库。我们从处理数据位于度量空间的简单情况开始。这个案例有助于介绍主要思想和符号。具体来说，通过将数据库映射到欧几里得空间，并考虑数据点之间的距离，我们引入了一个简单的表示的数据，并显示如何从代数拓扑的概念，如神经复合体和持久的同源性，可以有效地获得整个频谱的k-匿名的数据库的各种值的k和水平的推广。对于这种表示，我们提供了一个分析表征的条件下，给定的数据集表示是k-匿名的。我们引入了一个加权的条形码图，在这种情况下，成为一个计算工具，以权衡数据匿名性与数据丢失表示为泛化水平。最后通过仿真结果说明了本文的主要思想。最后，我们讨论了如何扩展这种方法，以解决一般情况下的分类和度量数据的混合。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
