Kernel-Based Multilayer Extreme Learning Machines for Representation Learning.

Recently, multilayer extreme learning machine (ML-ELM) was applied to stacked autoencoder (SAE) for representation learning. In contrast to traditional SAE, the training time of ML-ELM is significantly reduced from hours to seconds with high accuracy. However, ML-ELM suffers from several drawbacks: 1) manual tuning on the number of hidden nodes in every layer is an uncertain factor to training time and generalization; 2) random projection of input weights and bias in every layer of ML-ELM leads to suboptimal model generalization; 3) the pseudoinverse solution for output weights in every layer incurs relatively large reconstruction error; and 4) the storage and execution time for transformation matrices in representation learning are proportional to the number of hidden layers. Inspired by kernel learning, a kernel version of ML-ELM is developed, namely, multilayer kernel ELM (ML-KELM), whose contributions are: 1) elimination of manual tuning on the number of hidden nodes in every layer; 2) no random projection mechanism so as to obtain optimal model generalization; 3) exact inverse solution for output weights is guaranteed under invertible kernel matrix, resulting to smaller reconstruction error; and 4) all transformation matrices are unified into two matrices only, so that storage can be reduced and may shorten model execution time. Benchmark data sets of different sizes have been employed for the evaluation of ML-KELM. Experimental results have verified the contributions of the proposed ML-KELM. The improvement in accuracy over benchmark data sets is up to 7%.