Overview of the Functional Data Explorer Platform
Functional data can be defined as data that are recorded over a continuous domain, where a set of measurements form a curve or image. Often, the domain is time and the sets of measurements are defined by an ID variable. A functional data observation for ID level i at a specific point t on the domain is written as fi(t). The Functional Data Explorer platform enables you to explore and analyze functional data.
The form of functional data can be dense or sparse. Dense functional data occur when observations are on the same equally spaced grid of points for all levels of the ID variable. Sparse functional data occur when ID levels have different numbers of observations that are unequally spaced across the domain. The Functional Data Explorer platform can handle both forms of functional data.
Although functional data can be expressed in many ways, it can generally be classified into the following two cases:
• The response of interest, f(t), has a functional form.
• There are one or more covariates, f(t)’s, that have functional forms. These are sometimes referred to as functional or signal processes.
The Functional Data Explorer platform is useful as an exploratory tool for any type of functional data. However, the strength of the platform is taking many functional processes (that might be associated with a scalar response) and extracting key features to use in further modeling. This can be done by first fitting a functional model to the data using a B-spline, P-spline, or Fourier basis model. Then, a functional principal components analysis (functional PCA) is performed on the functional model. Results from the functional PCA, such as the functional principal component (FPC) scores, are saved and used for feature extraction and analysis in another modeling platform, such as the Generalized Regression personality of the Fit Model platform. Alternatively, you can specify a set of supplementary variables and fit a generalized regression model within the FDE platform to determine how these variables affect the response.
For more information about functional data analysis, see Ramsay and Silverman (2005).