Functional Modeling of High-Dimensional Data: A Manifold Learning Approach

This paper introduces stringing via Manifold Learning (ML-stringing), an alternative to the original based on Unidimensional Scaling (UDS). Our proposal is framed within a wider class of methods that map high-dimensional observations infinite space functions, allowing use Functional Data Analysis (FDA). Stringing handles general data as scrambled realizations unknown stochastic process. Therefore, essential feature method rearrangement observed values. Motivated by linear nature UDS and increasing number applications biosciences (e.g., functional modeling gene expression arrays single nucleotide polymorphisms, or classification neuroimages) we aim recover more complex relations between predictors through ML. In simulation studies, it shown ML-stringing achieves higher-quality orderings that, in general, this leads improvements representation data. The versatility our also illustrated with application colon cancer study deals arrays. shows feasible UDS-based version. Also, opens window new contributions field FDA