As the analytic tools become more powerful, and more data are generated on a daily basis, the issue of data privacy arises. This leads to the study of the design of privacy-preserving machine learning algorithms. Given two objectives, namely, utility maximization and privacy-loss minimization, this work is based on two previously non-intersecting regimes - Compressive Privacy and multi-kernel method. Compressive Privacy is a privacy framework that employs utility-preserving lossy-encoding scheme to protect the privacy of the data, while multi-kernel method is a kernel-based machine learning regime that explores the idea of using multiple kernels for building better predictors. In relation to the neural-network architecture, multi-kernel method can be described as a two-hidden-layered network with its width proportional to the number of kernels. The compressive multi-kernel method proposed consists of two stages - the compression stage and the multi-kernel stage. The compression stage follows the Compressive Privacy paradigm to provide the desired privacy protection. Each kernel matrix is compressed with a lossy projection matrix derived from the Discriminant Component Analysis (DCA). The multikernel stage uses the signal-to-noise ratio (SNR) score of each kernel to non-uniformly combine multiple compressive kernels. The proposed method is evaluated on two mobile-sensing datasets - MHEALTH and HAR - where activity recognition is defined as utility and person identification is defined as privacy. The results show that the compression regime is successful in privacy preservation as the privacy classification accuracies are almost at the random-guess level in all experiments. On the other hand, the novel SNR-based multi-kernel shows utility classification accuracy improvement upon the state-of-the-art in both datasets. These results indicate a promising direction for research in privacy-preserving machine learning.