Privacy-Preserving Multiparty Protocol for Feature Selection Problem

In this paper, we propose a secure multiparty protocol for the feature selection problem. Let $D$ be the set of data, $F$ the set of features, and $C$ the set of classes, where the feature value $x(F_i)$ and the class $x(C)$ are given for each $x\in D$ and $F_i \in F$. For a triple $(D,F,C)$, the feature selection problem is to find a consistent and minimal subset $F' \subseteq F$, where `consistent' means that, for any $x,y\in D$, $x(C)=y(C)$ if $x(F_i)=y(F_i)$ for $F_i\in F'$, and `minimal' means that any proper subset of $F'$ is no longer consistent. The feature selection problem corresponds to finding a succinct description of $D$, and has various applications in the field of artificial intelligence. In this study, we extend this problem to privacy-preserving computation model for multiple users. We propose the first algorithm for the privacy-preserving feature selection problem based on the fully homomorphic encryption. When parties $A$ and $B$ possess their own personal data $D_A$ and $D_B$, they jointly compute the feature selection problem for the entire data set $D_A\cup D_B$ without revealing their privacy under the \em{semi-honest} model.