@ARTICLE{Liu_06,
    AUTHOR      = {Kun Liu and Hillol Kargupta and Jessica Ryan},
    TITLE       = {{Random Projection-Based Multiplicative Data Perturbation for Privacy Preserving Distributed Data Mining}},
    JOURNAL     = {{IEEE Transactions on Knowledge and Data Engineering (TKDE)}},
    YEAR        = {2006},
    VOLUME      = {18},
    NUMBER      = {1},
    PAGES       = {92--106},
    MONTH       = {January},
    NOTE        = {},
    KEY         = {},
    KEYWORDS    = {},
    ISBN        = {1041-4347},
    URL         = {http://doi.ieeecomputersociety.org/10.1109/TKDE.2006.14},
    ABSTRACT    = {This paper explores the possibility of using multiplicative random projection matrices for privacy preserving
    distributed data mining. It specifically considers the problem of computing statistical aggregates like the inner product matrix,
    correlation coefficient matrix, and Euclidean distance matrix from distributed privacy sensitive data possibly owned by multiple
    parties. This class of problems is directly related to many other data-mining problems such as clustering, principal component
    analysis, and classification. This paper makes primary contributions on two different grounds. First, it explores Independent
    Component Analysis as a possible tool for breaching privacy in deterministic multiplicative perturbation-based models such as
    random orthogonal transformation and random rotation. Then, it proposes an approximate random projection-based technique to improve
    the level of privacy protection while still preserving certain statistical characteristics of the data. The paper presents extensive
    theoretical analysis and experimental results. Experiments demonstrate that the proposed technique is effective and can be successfully
    used for different types of privacy-preserving data mining applications. },
}