  We present a closed form expression for initializing the input weights in a
multi-layer perceptron, which can be used as the first step in synthesis of an
Extreme Learning Ma-chine. The expression is based on the standard function for
a separating hyperplane as computed in multilayer perceptrons and linear
Support Vector Machines; that is, as a linear combination of input data
samples. In the absence of supervised training for the input weights, random
linear combinations of training data samples are used to project the input data
to a higher dimensional hidden layer. The hidden layer weights are solved in
the standard ELM fashion by computing the pseudoinverse of the hidden layer
outputs and multiplying by the desired output values. All weights for this
method can be computed in a single pass, and the resulting networks are more
accurate and more consistent on some standard problems than regular ELM
networks of the same size.
