1. An associative vector storage system, comprising: an encoding engine that takes input vectors, and generates transformed coefficients for a tunable number of iterations, wherein each iteration performs a complete transformation to obtain coefficients, thereby performing a process of iterative transformations, wherein said encoding engine selects a subset of coefficients from the coefficients generated by the process of iterative transformations to form an approximation vector with reduced dimension; a data store that stores the approximation vectors with a corresponding set of meta data containing information about how the approximation vectors are generated, wherein the meta data includes at least one of the number of iterations, a projection map, quantization, or statistical information associated with each approximation vector; and a search engine that uses a comparator module to perform similarity search between the approximation vectors and a query vector in a transformed domain, wherein said search engine uses the meta data in a distance calculation of the similarity search.