We develop dynamic dimensionality reduction based on the appro ximationof the standard inner-product. The innerproduct, by itself, is used as a distance measure in a wide area of applications such as document databases, eg latent semantic indexing (LSI). A first order approximation to the inner-product is usually obtained from the Cauchy-Schw arz inequality. The method proposed in this paper refines such an appro ximation by using higher order pow er symmetric functions of the components of the v ectors, which are pow ers of the p-norms of the vectors for p= 1 2::: m. We sho w how to compute fixed coefficients that work as universal weights based on the moments of the probability density function assumed for the distribution of the components of the input vectors in the data set. Our experiments on synthetic and document data show that with this technique, the similarity between tw o objects in high dimensional space for certain applications can be accurately approximated by a significantly low er dimensional representation.