Data clustering is the unsupervised classification of data records into groups. As one of the steps in data analysis, it has been widely\nresearched and applied in practical life, such as pattern recognition, image processing, information retrieval, geography, and\nmarketing. In addition, the rapid increase of data volume in recent years poses a huge challenge for resource-constrained data\nowners to perform computation on their data. This leads to a trend that users authorize the cloud to perform computation on\nstored data, such as keyword search, equality test, and outsourced data clustering. In outsourced data clustering, the cloud\nclassifies usersâ?? data into groups according to their similarities. Considering the sensitive information in outsourced data and\nmultiple data owners in practical application, it is necessary to develop a privacy-preserving outsourced clustering scheme under\nmultiple keys..................
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