The persistent/zig-zag persistent intervals provide a meaningful topological summary of a given filtration/sequence of spaces. However, there often arises the need to compute sparse generators for these intervals which serve to "track" the features corresponding to the intervals. We will address this problem on two aspects: 1) simplification of the data in order to reduce the computational complexity while preserving the desired topological features , and 2) computing a specific summand decomposition of the given persistent/zig-zag module where the summands result in the desired generators. Further, given a choice of a set of filtrations, we will present meaningful ways to choose the right filtration where the resulting bar-code reflects some underlying geometric features.