Secure Two-Party k-Means Clustering
Abstract The k-Means Clustering problem is one of the most-explored prob-lems in data mining to date. With the advent of protocols that have proven to be successful in performing single database clustering, thefocus has changed in recent years to the question of how to extend the single database protocols to a multiple database setting. To datethere have been numerous attempts to create specific multiparty k-means clustering protocols that protect the privacy of each database, but according to the standard cryptographic definitions of "privacy-protection, " so far all such attempts have fallen short of providing adequate privacy.In this paper we describe a Two-Party k-Means Clustering Protocolthat guarantees privacy, and is more efficient than utilizing a general multiparty "compiler " to achieve the same task. In particular, a maincontribution of our result is a way to compute efficiently multiple iterations of k-means clustering without revealing the intermediate values.To achieve this, we use novel techniques to perform two-party division and sample uniformly at random from an unknown domain size.Our techniques are quite general and can be realized based on the existence of any semantically secure homomorphic encryption scheme.For concreteness, we describe our protocol based on Paillier Homomorphic Encryption scheme (see [23]). We will also demonstrate that ourprotocol is efficient in terms of communication, remaining competitive with existing protocols (such as [15]) that fail to protect privacy. Keywords: Multiparty Computation, k-means clustering