Arithmetic precision of the Generalized Hebbian Algorithm for hardware implementation

The principal component analysis (PCA) is a data mining methodology to express multivariate data comprehensively. The PCA reduces the dimension of data set, but its computational complexity easily gets large depending on the input factors. In this paper, we evaluate calculation accuracy of the PCA for hardware implementation. As a PCA learning algorithm, the generalized Hebbian algorithm (GHA) is adopted under the assumption of targeting field programmable gate arrays (FPGAs). With the aim of verification of the errors and required accuracy to reduce necessary hardware resources. The GHA is implemented by software in C language using input graphical images. The relationship between the three parameters, the number of principal components, mantissa bit width, and the errors, was found by comparing the output principal component images with the originals. This result will be applied to the implementation of circuit on hardware.