Functional SOM for variable-length signal windows

Functional data, often sampled at high frequency, lead to high-dimensional vectors. The curse of dimensionality makes the latter difficult to handle with standard data analysis tools. Functional data analysis tools take profit of the functional nature of data by projecting them on a smooth basis. This paper shows how to extend functional Self-Organizing Maps (SOM) to signal windows having different lengths. This technique may be applied for example on signal sampled regularly, but for which the duration of each signal is varying; an example concerns electrocardiography (ECG), where the signal is usually cut according to the variable period between two heart beats.