Attribute Exploration of Discrete Temporal Transitions

TL;DR

This paper extends formal concept analysis to analyze discrete temporal transitions, enabling the exploration of temporal dependencies in biological data and other domains through an adapted attribute exploration algorithm.

Contribution

It introduces a novel adaptation of the attribute exploration algorithm for relational contexts involving temporal transitions, applicable to biological and other complex systems.

Findings

Successfully applied to a gene regulatory network example

Demonstrated ability to analyze temporal dependencies

Provided insights into biological time series data

Abstract

Discrete temporal transitions occur in a variety of domains, but this work is mainly motivated by applications in molecular biology: explaining and analyzing observed transcriptome and proteome time series by literature and database knowledge. The starting point of a formal concept analysis model is presented. The objects of a formal context are states of the interesting entities, and the attributes are the variable properties defining the current state (e.g. observed presence or absence of proteins). Temporal transitions assign a relation to the objects, defined by deterministic or non-deterministic transition rules between sets of pre- and postconditions. This relation can be generalized to its transitive closure, i.e. states are related if one results from the other by a transition sequence of arbitrary length. The focus of the work is the adaptation of the attribute exploration algorithm to such a relational context, so that questions concerning temporal dependencies can be asked during the exploration process and be answered from the computed stem base. Results are given for the abstract example of a game and a small gene regulatory network relevant to a biomedical question.