# ProjectionPathExplorer: Exploring Visual Patterns in Projected Decision-Making Paths

arXiv: https://arxiv.org/abs/2001.08372 · HTML: https://mlsanity.com/paper/2001.08372/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2020.

## Built on by (most cited first, 4 of 4)

- [EvolvED: Evolutionary Embeddings to Understand the Generation Process of Diffusion Models](https://mlsanity.com/paper/2406.17462/) (2024)
- [Abstracted Trajectory Visualization for Explainability in Reinforcement Learning](https://mlsanity.com/paper/2402.07928/) (2024)
- [Uncovering Temporal Patterns in Visualizations of High-Dimensional Data](https://mlsanity.com/paper/2403.19040/) (2024)
- [RePAIR: Predictive Self-Supervised Representation Learning in Chess](https://mlsanity.com/paper/2606.11860/) (2026)

## Abstract (arXiv)

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.