  An extreme learning machine (ELM) can be regarded as a two stage feed-forward
neural network (FNN) learning system which randomly assigns the connections
with and within hidden neurons in the first stage and tunes the connections
with output neurons in the second stage. Therefore, ELM training is essentially
a linear learning problem, which significantly reduces the computational
burden. Numerous applications show that such a computation burden reduction
does not degrade the generalization capability. It has, however, been open that
whether this is true in theory. The aim of our work is to study the theoretical
feasibility of ELM by analyzing the pros and cons of ELM. In the previous part
on this topic, we pointed out that via appropriate selection of the activation
function, ELM does not degrade the generalization capability in the expectation
sense. In this paper, we launch the study in a different direction and show
that the randomness of ELM also leads to certain negative consequences. On one
hand, we find that the randomness causes an additional uncertainty problem of
ELM, both in approximation and learning. On the other hand, we theoretically
justify that there also exists an activation function such that the
corresponding ELM degrades the generalization capability. In particular, we
prove that the generalization capability of ELM with Gaussian kernel is
essentially worse than that of FNN with Gaussian kernel. To facilitate the use
of ELM, we also provide a remedy to such a degradation. We find that the
well-developed coefficient regularization technique can essentially improve the
generalization capability. The obtained results reveal the essential
characteristic of ELM and give theoretical guidance concerning how to use ELM.
