ASALSAN is a new algorithm for computing three-way DEDICOM, which is a linear algebra model for analyzing intrinsically asymmetric relationships, such as trade among nations or the exchange of emails among individuals, that incorporates a third mode of the data, such as time. ASALSAN is unique because it enables computing the three-way DEDICOM model on large, sparse data. A nonnegative version of ASALSAN is described as well. When we apply these techniques to adjacency arrays arising from directed graphs with edges labeled by time, we obtain a smaller graph on latent semantic dimensions and gain additional information about their changing relationships over time. We demonstrate these techniques on international trade data and the Enron email corpus to uncover latent components and their transient behavior. The mixture of roles assigned to individuals by ASALSAN showed strong correspondence with known job classifications and revealed the patterns of communication between these roles. Changes in the communication pattern over time, e.g., between top executives and the legal department, were also apparent in the solutions.