Before revision:  We first apply our technique to a variety of synthetic and real-world datasets with known strange attractors, and we use established and novel measures of attractor fidelity to show that our method successfully reconstructs attractors better than existing techniques . We then use our technique to discover dynamical attractors in datasets ranging from patient electrocardiograms, to household electricity usage, to eruptions of the Old Faithful geyser---demonstrating diverse applications of our technique for exploratory data analysis.
After revision:  We first apply our technique to a variety of synthetic and real-world datasets with known strange attractors, and we use established and novel measures of attractor fidelity to show that our method successfully reconstructs attractors better than existing techniques , and that it creates consistent, predictive representations of even stochastic systems. We conclude by using our technique to discover dynamical attractors in datasets ranging from patient electrocardiograms, to household electricity usage, to eruptions of the Old Faithful geyser---demonstrating diverse applications of our technique for exploratory data analysis.