Privacy-Preserving Feature Selection with Fully Homomorphic Encryption

For the feature selection problem, we propose an efficient privacy-preserving algorithm. Let D, F, and C be data, feature, and class sets, respectively, where the feature value x(Fi) and the class label x(C) are given for each x∈ D and Fi ∈ 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∈ D, x(C)=y(C) if x(Fi)=y(Fi) for Fi∈ F', and `minimal' means that any proper subset of F' is no longer consistent. On distributed datasets, we consider feature selection as a privacy-preserving problem: Assume that semi-honest parties textsf A and textsf B have their own personal Dtextsf A and Dtextsf B. The goal is to solve the feature selection problem for Dtextsf Acup Dtextsf B without revealing their privacy. In this paper, we propose a secure and efficient algorithm based on fully homomorphic encryption, and we implement our algorithm to show its effectiveness for various practical data. The proposed algorithm is the first one that can directly simulate the CWC (Combination of Weakest Components) algorithm on ciphertext, which is one of the best performers for the feature selection problem on the plaintext.