Sparse Modeling On Distributed Encryption Data

Big-data analysis by edge/cloud systems is becoming more important. However, when information may lead to personal identification, such information tends to be encrypted and restricted to its owners to ensure privacy protection. The resulting data is often insufficiently detailed to permit useful analysis. As a result, the desired analysis accuracy may not be achieved. To deal with this issue, several studies have examined encryptions based on the random unitary transform. This is because the random unitary transform has lower computational complexity than other encryption schemes, and its encryption domain supports several signal processing algorithms. However, analysis models on distributed encrypted data, have not been studied deeply enough. In this paper, we construct an analysis model for data encrypted with the random unitary transform by deriving a LASSO solution for encrypted data. The analytical model can derive the same LASSO solution as that yielded by processing the original data (i.e. without encryption). The analytical model supports distributed encryption, where a data set consists of different components that are encrypted at different sites independently. The collaboration enables us to improve the accuracy of analysis for distributed privacy-sensitive information.