Privacy preserving mining of distributed data is an important direction for data mining, and privacy preserving clustering is one of the main researches. Privacy-preserving data mining techniques enable knowledge discovery without requiring disclosure of private data. The existing privacy preserving algorithms mainly concentrated on association rules and classification, only few algorithms on privacy preserving clustering, and these algorithms mainly concentrated on centralized and vertically partitioned data. So we proposed privacy preserving hierarchical k-means clustering algorithm on horizontally partitioned data, denoted as HPPHKC.

The complexity on k-means clustering algorithm is only O(n), so most existing privacy preserving clustering algorithms are concentrated on k-means and based on two parties and the trusted third party, these algorithms have the drawbacks of inaccurate results because of choosing initial clustering centers randomly and applying to multi-party difficult and revealing privacy because of depending on the third party excessively. By introduction of three protocols for secure multi-party computation: distance computation, cluster center computation, and standardization and combination of the merits of hierarchical and k-means clustering, we presented a privacy-preserving hierarchical-k-means clustering algorithm on horizontally partitioned data for semi-honest parties using some secure multi-party computation protocols. The algorithm uses the security protocol mentioned above to achieve the protection of the privacy data, and uses the hierarchical clustering algorithm to obtain k cluster centers, then uses the k-means clustering algorithm to obtain the final k clusters. We introduce the clustering feature and the clustering feature tree, which are used to summarize the cluster representations. A clustering feature (CF) is a three-dimensional vector summarizing information about clusters of objects. The i^th clustering feature is CF_i = (cn_i,cc_i,cp_i), where cn_i is the number of ^th clusters, denoted as the size of ^th cluster, cc_i is the center of the cni objects, and cp_i is the pointer of the list of cni objects. The algorithm has two phases: the first phase, every object can be as a cluster, a secure computation protocol is used to compute the dissimilarity matrix and the most similar clusters will be merged. This process is repeated until we get the assigned clusters number k and get k clustering centers. In the second phase, the semi-honest third party and all data involved parties use the k-means algorithm refine the results of the first phase and get the final clustering results. Finally, we give the proof of security of the algorithm and analysis of communication costs, and we show that our scheme is secure and complete with good efficiency.