Circadian Patterns Recognition in Ecosystems by Wavelet Filtering and Fuzzy Clustering

This paper presents a method for extracting representative patterns from a set of data representing circadian cycles. The analysis is based on a combination of wavelet filtering and fuzzy clustering. The data are first processed with a discrete wavelet decomposition in order to filter out the noise and isolate the relevant circadian cycle. It is shown that the second level decomposition yields the best cycle approximation, filtering out measurement noise and other artefacts and preserving the main cycle features. From the filtered data the following discriminating features are extracted: minimum and maximum daily values, and the slope of the line passing through these extreme points. These features are then processed with a fuzzy clustering algorithm, in order to isolate significant behaviours. The Fuzzy Maximum Likelihood Estimates (FMLE) method was used for its variable metric, being able to conform the cluster shape and volume to the data. This combined algorithm is applied to the physico-chemical data from the Orbetello lagoon with the aim of detecting ecologically meaningful behaviours. The results show that relevant daily patterns are indeed isolated and in particular combination of variables leading to the dystrophic crisis are correctly interpreted. The relevance of the selected patterns is confirmed by their distribution over the calendar day, which corresponds to a clear seasonal patterns.