Multiple kernel extreme learning machine
Extreme learning machine (ELM) has been an important research topic over the last decade due to its high efficiency, easy-implementation, unification of classification and regression, and unification of binary and multi-class learning tasks. Though integrating these advantages, existing ELM algorithms pay little attention to optimizing the choice of kernels, which is indeed crucial to the performance of ELM in applications. More importantly, there is the lack of a general framework for ELM to integrate multiple heterogeneous data sources for classification. In this paper, we propose a general learning framework, termed multiple kernel extreme learning machines (MK-ELM), to address the above two issues. In the proposed MK-ELM, the optimal kernel combination weights and the structural parameters of ELM are jointly optimized. Following recent research on support vector machine (SVM) based MKL algorithms, we first design a sparse MK-ELM algorithm by imposing an ℓ1-norm constraint on the kernel combination weights, and then extend it to a non-sparse scenario by substituting the ℓ1-norm constraint with an ℓp-norm (p>1) constraint. After that, a radius-incorporated MK-ELM algorithm which incorporates the radius of the minimum enclosing ball (MEB) is introduced. Three efficient optimization algorithms are proposed to solve the corresponding kernel learning problems. Comprehensive experiments have been conducted on Protein, Oxford Flower17, Caltech101 and Alzheimer's disease data sets to evaluate the performance of the proposed algorithms in terms of classification accuracy and computational efficiency. As the experimental results indicate, our proposed algorithms can achieve comparable or even better classification performance than state-of-the-art MKL algorithms, while incurring much less computational cost.