On Using Linear Diophantine Equations for Efficient Hiding of Decision Tree Rules

Abstract

This paper focuses on preserving the privacy of sensitive patterns when inducing decision trees. We adopt a record augmentation approach for hiding sensitive classification rules in binary datasets. Such a hiding methodology is preferred over other heuristic solutions like output perturbation or cryptographic techniques -which restrict the usability of the datasince the raw data itself is readily available for public use. In this paper, we propose a look ahead approach using linear Diophantine equations in order to add the appropriate number of instances while minimally disturbing the initial entropy of the nodes.

Using Minimum Local Distortion to Hide Decision Tree Rules

“…The first one is that we do not need to add new instances to the original data set, and the second is that our new heuristic can be performed in only one step with much lower computational complexity compared to solving systems of Linear Diophantine Equations. However, our previous published techniques [ 20 , 21 ] guarantee the preservation of entropy values in every node of the tree before and after the modification.…”

“…This approach is critical because the sanitized data set may be subsequently published and even shared with the data set owner’s competitors, as can be the case with retail banking [ 19 ]. We extend this work in the papers [ 20 , 21 ] by formulating a generic look ahead technique that considers the structure of the decision tree from an affected leaf to the root. The main contribution of these publications was to improve the Swap-and-Add pass by following a look ahead approach instead of the greedy approach which was previously used.…”

Integer Solutions of the Diophantine Equation \(\left (1-\frac{1}{\mathit{x}}\right)\) \(\left (1-\frac{1}{\mathit{y}}\right)\) \(\left (1-\frac{1}{\mathit{z}}\right)\) = \(\frac{1}{\mathit{l}}\)

“…That is, we can obtain two integer solutions of the equation (1.1) , such as (x, y, z, l) = (9, 4, 4, 2), (6,5,4,2).…”

Inference Control in a Diabetes Data Set Using a Java-Based Prototype of LDH Algorithm

“…In articles [5][6][7][8], the authors proposed a series of strategies that would effectively protect against the disclosure of the sensitive classification rules. The LDH algorithm [9] was developed on the basis of the concept of preserving sensitive DT rules resulting from the use of data mining techniques.…”