Grouping of Variables to Facilitate SDL Methods in Multivariate Data Sets
Data sets that are subject to Statistical Disclosure Limitation (SDL) often have many variables of different types that need to be altered for disclosure limitation. To produce a good quality public data set, the data protector needs to account for the relationships between the variables. Hence, ideally SDL methods should not be univariate, that is, treating each variable independently of others, but multivariate, handling many variables at the same time. However, if a data set has many variables, as most government survey data do, the task of developing and implementing a multivariate approach for SDL becomes difficult. In this paper we propose a pre-masking data processing procedure which consists of clustering the variables of high dimensional data sets, so that different groups of variables can be masked independently, thus reducing the complexity of SDL. We consider different hierarchical clustering methods, including our version of hierarchical clustering algorithm, that we call K-Link, and outline how the data protector can define an appropriate number of clusters for these methods. We implemented and applied these methods to two genuine multivariate data sets. The results of the experiments show that K-Link has a potential to solve this problem efficiently. The success of the method, however, depends on the correlation structure of the data. For the data sets where most of the variables are correlated, clustering of variables and subsequent independent application of SDL methods to different clusters may lead to attenuated correlation in the masked data, even for efficient clustering methods. Thereby, the proposed approach is a trade-off between the computational complexity of multivariate SDL methods and data utility loss due to independent treatment of different clusters by SDL methods.
KeywordsStatistical Disclosure Limitation (SDL) Hierarchical clustering Dimensionality reduction
The authors would like to thank Van Parsons from the National Center for Health Statistics (US) for providing cleansed version of NHIS public use sample file for our experiments and for his valuable suggestions. Also the authors would like to express their appreciation to Donald Malec also from the National Center for Health Statistics for his careful reading of the paper and many useful suggestions. The findings and conclusions in this paper are those of the authors and do not necessarily represent the official position of the Centers for Disease Control and Prevention.
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