# Glossary of Common Terms¶

This glossary contains concepts and API elements specific to the functional data analysis setting or for the package scikit-fda. If the term you are looking is not listed here, it may be a more generally applicable term listed in the scikit-learn Glossary of Common Terms and API Elements.

## General Concepts¶

codomain

The set of allowed output values of a function. Note that the set of actual output values, called the image, can be a strict subset of the codomain.

curve
trajectory

A functional data object whose domain and codomain are both the set of real numbers ($$\mathbb{R}$$). Thus, its dim_domain and dim_codomain attributes shall both be 1.

domain

The set of possible input values of a function.

domain range

The valid range where a function can be evaluated. It is a Python sequence that contains, for each dimension of the domain, a tuple with the minimum and maximum values for that dimension. Usually used in plotting functions and as the domain of integration for this function.

FDA
Functional Data Analysis

The branch of statistics that deals with curves, surfaces or other objects varying over a a continuum (functional data objects).

functional data

A collection of functional data objects. Represented by a FData object.

functional data object
functional data objects
functional object
functional objects

An object of study of Functional Data Analysis. It is a function between $$\mathbb{R}^p$$ and $$\mathbb{R}^q$$. Usually represented by a FData object of length 1, but in some cases regular Python callables are also accepted.

functional observation
functional observations

An observed functional data object, represented as a FData object of length 1.

image

The set of actual ouput values that a function takes. It must be a (non necessarily strict) subset of the codomain.

multivariate functional data

Often used for functional data where each functional data object is a vector-valued function.

multivariate object
multivariate objects

An object of study of multivariate statistics. It is a vector of possibly related variables, represented as a 1d array.

operator
operators

Function whose domain is a set of functions.

vector-valued function

A functional data object that outputs vectors, that is, its codomain has dimension greater than 1.