This code implements a matrix-regularized multiple kernel learning (MKL) technique based on a notion of (r, p) norms. This extends vector ℓ p-norm regularization and helps explore the dependences and interactions among kernels leading to better performance. We gave a simple alternating optimization with closed-form solution for the kernel weights and shown the global convergence of the proposed problem that can always be guaranteed. We analyzed such a regularizer using a Rademacher complexity bound, and we also proved that (r, p)-norm MKL yields strictly better generalization bounds than ℓ p-norm MKL. Finally, we reported the results of (r, p)-MKL on several publicly available data sets. (r, p)-MKL was shown to achieve consistently superior performances to canonical ℓ p-MKL, demonstrating the benefits of revealing the higher order kernel-pair relationships. Nevertheless, this project constitutes only a preliminary study and that a deeper analysis with more expressive formulation and efficient solving strategy should be further investigated.

Please cite the following papers if you find this work is useful:

Yina Han, Yixin Yang, Xuelong Li, Qingyu Liu, Yuanliang Ma, Matrix-Regularized Multiple Kernel Learning via (r,p) Norms[J]. IEEE Transactions on Neural Networks and Learning Systems. Volume: 29, Issue: 10, pp.4997 - 5007. 2018.

See MatrixMKL_main.m for more details.