The Hypograph Index of a curve x is the proportion of curves in the sample
that are below x.

Implements methods for functional data analysis based on the epigraph
and hypograph indices. These methods transform
functional datasets, whether in one or multiple dimensions, into multivariate
datasets. The transformation involves applying the epigraph, hypograph, and
their modified versions to both the original curves and their first and second
derivatives. The calculation of these indices is tailored to the dimensionality
of the functional dataset, with special considerations for dependencies between
dimensions in multidimensional cases. This approach extends traditional multivariate
data analysis techniques to the functional data setting. A key application of
this package is the EHyClus method, which enhances clustering analysis for
functional data across one or multiple dimensions using the epigraph and
hypograph indices. See Pulido et al. (2023) <doi:10.1007/s11222-023-10213-7>
and Pulido et al. (2024) <doi:10.48550/arXiv.2307.16720>.

Belen Pulido

ehymet

Methodologies for Functional Data Based on the Epigraph and
Hypograph Indices

Jose Ignacio Diez

HI function

<dl><dt>curves</dt>
<dd><code>matrix</code> where each row represents a curve, and each column
represents values along the curve or <code>array</code> with dimension
\(n \times p \times q\) with \(n\) curves, \(p\) values along the curve, and
\(q\) dimensions.</dd>
<dt>...</dt>
<dd>Ignored.</dd></dl>

Arguments

Hypograph Index (HI) for a functional dataset — HI

<dl>

<dt>curves</dt>
<dd><code>matrix</code> where each row represents a curve, and each column
represents values along the curve or <code>array</code> with dimension
\(n \times p \times q\) with \(n\) curves, \(p\) values along the curve, and
\(q\) dimensions.</dd>


<dt>...</dt>
<dd>Ignored.</dd>

</dl>

HI: Hypograph Index (HI) for a functional dataset

Description

Usage

Value

Arguments

Examples