  In problem-solving, a path towards solutions can be viewed as a sequence of
decisions. The decisions, made by humans or computers, describe a trajectory
through a high-dimensional representation space of the problem. By means of
dimensionality reduction, these trajectories can be visualized in
lower-dimensional space. Such embedded trajectories have previously been
applied to a wide variety of data, but analysis has focused almost exclusively
on the self-similarity of single trajectories. In contrast, we describe
patterns emerging from drawing many trajectories -- for different initial
conditions, end states, and solution strategies -- in the same embedding space.
We argue that general statements about the problem-solving tasks and solving
strategies can be made by interpreting these patterns. We explore and
characterize such patterns in trajectories resulting from human and
machine-made decisions in a variety of application domains: logic puzzles
(Rubik's cube), strategy games (chess), and optimization problems (neural
network training). We also discuss the importance of suitably chosen
representation spaces and similarity metrics for the embedding.
