ProjectionPathExplorer: Exploring Visual Patterns in Projected Decision-making Paths

In problem-solving, a path towards a 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 bemade 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.

Automated summary

In problem-solving, paths to solutions can be seen as sequences of decisions that can be visualized through dimensionality reduction. By analyzing patterns in these trajectories, general statements about problem-solving tasks and strategies can be made, which is crucial for understanding human and machine decisions in various application domains.