The functional mean-shift algorithm for mode hunting and clustering in infinite dimensions
This provides a method for clustering functional data in domains like neuroscience and forensics, but it appears incremental as it extends the mean-shift algorithm to functional contexts.
The paper tackles the problem of mode hunting and clustering for functional data by introducing the functional mean-shift algorithm, which estimates local modes and includes a bootstrap test for significance, with applications in spike sorting and signature verification.
We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data. We show that the algorithm can be used for cluster analysis of functional data. We propose a test based on the bootstrap for the significance of the estimated local modes of the surrogate density. We present two applications of our methodology. In the first application, we demonstrate how the functional mean-shift algorithm can be used to perform spike sorting, i.e. cluster neural activity curves. In the second application, we use the functional mean-shift algorithm to distinguish between original and fake signatures.