A roundoff error analysis of the Oja´s subspace rule

This paper deals with the effects of finite precision data representation and arithmetic in principal component analysis (PCA) networks. PCA or Karhunen Loeve transform (KLT) is a statistical method that determines an optimal linear transformation of input vectors of a stationary stochastic process. The PCA networks are single layer linear neural networks that use some versions of Oja´s (1989) learning rule. The paper concentrates on the errors which will arise during learning if fixed point data representation and arithmetic are used. It gives analytical results based on the additive noise model of quantization. In the analysis all three components of the finite precision effects are considered: (i) the error due to the input data quantization, (ii) the error caused by finite precision representation of the weights of the network, and (iii) the effects of the finite precision arithmetic. The results can be used directly to determine the required word-lengths for special hardware implementation of the neural net