Output Layer Structure Optimization for Weighted Regularized Extreme Learning Machine Based on Binary Method

In this paper, we focus on the redesign of the output layer for the weighted regularized extreme learning machine (WRELM). For multi-classification problems, the conventional method of the output layer setting, named "one-hot method", is as follows: Let the class of samples be r; then, the output layer node number is r and the ideal output of s-th class is denoted by the s-th unit vector in R-r (1 <= s <= r). Here, in this article, we propose a "binary method" to optimize the output layer structure: Let 2(p-1) < r <= 2(p), where p >= 2, and p output nodes are utilized and, simultaneously, the ideal outputs are encoded in binary numbers. In this paper, the binary method is employed in WRELM. The weights are updated through iterative calculation, which is the most important process in general neural networks. While in the extreme learning machine, the weight matrix is calculated in least square method. That is, the coefficient matrix of the linear equations we solved is symmetric. For WRELM, we continue this idea. And the main part of the weight-solving process is a symmetry matrix. Compared with the one-hot method, the binary method requires fewer output layer nodes, especially when the number of sample categories is high. Thus, some memory space can be saved when storing data. In addition, the number of weights connecting the hidden and the output layer will also be greatly reduced, which will directly reduce the calculation time in the process of training the network. Numerical experiments are conducted to prove that compared with the one-hot method, the binary method can reduce the output nodes and hidden-output weights without damaging the learning precision.