Secure Sparse Modeling Through Linearized Kernel Dictionary Learning with Random Unitary Transformation

In this paper, we propose a linearized kernel dictionary learning based on random unitary transformation, which enables high-accuracy classification while protecting the privacy of data. The kernel-based K-SVD algorithm is known for improving classification performance compared to conventional linear K-SVD. It faces the challenge of dealing with very large kernel matrices, leading to significantly high computational costs. To address this issue, linearized kernel dictionary learning has been proposed, which reduces the computational load while maintaining estimation accuracy. Our proposed method introduces a secure linearized kernel dictionary learning using random unitary transformation. We theoretically prove that encrypting the observation signals using random unitary transformation preserves the same level of classification accuracy as when no encryption is performed. Additionally, through simulations on handwritten digit image data, we verify that there is no degradation in learning performance.