  Single layer feedforward networks with random weights are known for their
non-iterative and fast training algorithms and are successful in a variety of
classification and regression problems. A major drawback of these networks is
that they require a large number of hidden units. In this paper, we propose a
technique to reduce the number of hidden units substantially without affecting
the accuracy of the networks significantly. We introduce the concept of primary
and secondary hidden units. The weights for the primary hidden units are chosen
randomly while the secondary hidden units are derived using pairwise
combinations of the primary hidden units. Using this technique, we show that
the number of hidden units can be reduced by at least one order of magnitude.
We experimentally show that this technique leads to significant drop in
computations at inference time and has only a minor impact on network accuracy.
A huge reduction in computations is possible if slightly lower accuracy is
acceptable.
