Using mathematical morphology for unsupervised classification of functional data

摘要

This paper is concerned with the unsupervised classification of functional data by using mathematical morphology. Different morphological operators are used to extract relevant structures of the functions (considered as sets through their subgraph representations). These operators can be considered as prepro-cessing tools whose outputs are also functional data. We explore some dissimilarity measures and clustering methods for the classification of the transformed data. Our approach is illustrated through a detailed analy-sis of two data sets. These techniques, which have mainly been used in image processing, provide a flexible and robust toolbox for improving the results in unsupervised functional data classification.