We use IceCube's high-statistics, neutrino-induced, through-going muon samples to search for astrophysical neutrino sources. Specifically, we analyze the arrival directions of IceCube's highest energy neutrinos. These high-energy events allow for a good angular reconstruction of their origin. Additionally, they have a high probability to come from an astrophysical source. On average, 8 neutrino events that satisfy these selection criteria are detected per year. Using these neutrino events as a source catalog, we present a search for the production sites of cosmic neutrinos. In this contribution we explore a time-dependent analysis, and present preliminary 3$\sigma$ discovery potential fluences of $\approx 2.7 \cdot 10^{-2} \rm{GeV}/\rm{cm}^2$. We construct the fluences using expectation maximization.