From High-dimensional to Functional Data: Stringing Via Manifold Learning

Abstract

The study of high-dimensional data is becoming a common trend in modern research. Recently, stringing emerged as a methodology to treat high-dimensional sample vectors as realizations of smooth stochastic processes. Under the hypothesis of noisy and order-perturbed measurements, stringing introduces smooth transitions between predictors and takes advantage of Functional Data Analysis (FDA) to study the data. Once a functional representation is achieved, it is possible to visualize intrinsic patterns, or fit functional regression models.We propose manifold learning as an alternative to multidimensional scaling in the reordering step. In a simulation study we show that our proposal achieves smaller relative order errors, and that it can recover more complex relationships between predictors.