Measuring information-based complexity across scales using cluster analysis

Scaling of ecological data can present a challenge firstly because of the large amount of information contained in an ecological data set, and secondly because of the problem of fitting data to models that we want to use to capture structure. We present a measure of similarity between data collected at several scales using the same set of attributes. The measure is based on the concept of Kolmogorov complexity and implemented through minimal message length estimates of information content and cluster analysis (the models). The similarity represents common patterns across scales, within the model class. We thus provide a novel solution to the problem of simultaneously considering data structure, model fit and scale. The methods are illustrated in application to an ecological data set.