Clustering of Functional Data via Ensemble of Random Projections

Clustering functional data presents challenges due to its infinite-dimensional nature. A common strategy to represent functions in a finite space is to consider basis function decomposition, where each curve is represented by a linear combination of basis functions; however, the need for accurate representation may still lead to high-dimensional embedding, making traditional clustering methods inadequate. In this work, we propose using Random Projections (RPs) to reduce dimensionality while approximately preserving distances. Specifically, we propose to employ an ensemble approach that aggregates multiple clustering solutions from different projections, enhancing stability and accuracy. Its capability of recovering the true cluster membership is illustrated on a real data application.