Fuzzy clustering of sampled functions

Fuzzy clustering algorithms perform cluster analysis on a data set that consists of feature attribute vectors. In the context of multiple sampled functions, a set of samples (e.g. a time series) becomes a single datum. We show how the already known algorithms can be used to perform fuzzy cluster analysis on this kind of data sets by replacing the conventional prototypes with sets of prototypes. This approach allows reusing the known algorithms and works also with other data than sampled functions. Furthermore, to reduce the computational costs in case of single-input/single-output functions we present a new fuzzy clustering algorithm, which uses for the first time a more complex input data type (data points aggregated to data-lines instead of raw data). The new alternating optimisation algorithm performs duster analysis directly on this more compact representation of the sampled functions