%0 Journal Article %T Note on the Rademacher-Walsh Polynomial Basis Functions %A Hamse Y. Mussa %A Jonathan D. Tyzack %A Robert C. Glen %J Journal of Mathematics Research %D 2013 %I %R 10.5539/jmr.v5n1p114 %X Over the years, one of the methods of choice to estimate probability density functions for a given random variable (defined on binary input space) has been the expansion of the estimation function in Rademacher-Walsh Polynomial basis functions. For a set of $L$ features (often considered as an ``$L$-dimensional binary vector''), the Rademacher-Walsh Polynomial approach requires $2^{L}$ basis functions. This can quickly become computationally complicated and notationally clumsy to handle whenever the value of $L$ is large. In current pattern recognition applications it is often the case that the value of $L$ can be 100 or more. In this paper we show that the expansion of the probability density function estimation in Rademacher-Walsh Polynomial basis functions is equivalent to the expansion of the estimation function in a set of Dirac kernel functions. The latter approach is not only able to eloquently allay the computational bottle--neck and notational awkwardness mentioned above, but may also be naturally neater and more ``elegant'' than the Rademacher-Walsh Polynomial basis function approach even when this latter approach is computationally feasible. %U http://www.ccsenet.org/journal/index.php/jmr/article/view/24995