Compact Flow Diagrams for State Sequences

TL;DR

This paper presents methods for creating compact flow diagrams to summarize large sets of state sequences, offering intuitive visualizations and algorithms for small datasets, along with heuristics for larger datasets, demonstrated through sports analysis.

Contribution

It introduces the concept of compact flow diagrams for state sequences and provides algorithms and heuristics for their construction, addressing computational complexity issues.

Findings

Efficient algorithms for small datasets

Heuristics for large datasets

Successful application to sports data

Abstract

We introduce the concept of compactly representing a large number of state sequences, e.g., sequences of activities, as a flow diagram. We argue that the flow diagram representation gives an intuitive summary that allows the user to detect patterns among large sets of state sequences. Simplified, our aim is to generate a small flow diagram that models the flow of states of all the state sequences given as input. For a small number of state sequences we present efficient algorithms to compute a minimal flow diagram. For a large number of state sequences we show that it is unlikely that efficient algorithms exist. More specifically, the problem is W[1]-hard if the number of state sequences is taken as a parameter. We thus introduce several heuristics for this problem. We argue about the usefulness of the flow diagram by applying the algorithms to two problems in sports analysis. We evaluate the performance of our algorithms on a football data set and generated data.