Declarative Bias in Equation Discovery
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In this paper, we present a method for pattern selection in collections of patterns discovered in multivariate time-series. Because our data is continuous in nature, the pattern language we consider is somewhat out of the ordinary, compared to the common discrete patterns considered in the data mining field. An equation discovery system is employed to generate either regular algebraic equations, or more complex differential equations. As the equation discovery system generates a collection of equations per target variable, and we require equations for each variable, we are dealing with an abundance of equations, quite likely with serious levels of redundancy. The method presented here selects a subset of equations by considering to what extent the different variables are covered by the selected equations, while optimising the relevance of variables within the equations. As such, the equation selection method returns a concise set of equations, that captures the dependencies between the different time-series well, while minimizing redundancy. The work in this paper is inspired by the new InfraWatch project, which deals with high-resolution sensor data from a highway bridge. The 145 sensors (sensing structural characteristics such as stretch, vibration and temperature) are distributed fairly densely over the bridge, such that adjacent sensors are likely to show correlated signals. Especially in an exploratory setting, one would be interested in a small collection of prototype sensors with associated equations for how these prototypes are related to other sensors in the vicinity. In the experimental section, we demonstrate how the sensors can be modeled by (differential) equations, and how the equation selection method picks relevant equations that models structural properties of the bridge sensibly.