elastic.depth

This functions calculates the elastic depth between set of functions in
\(R^1\)

depth

Performs alignment, PCA, and modeling of multidimensional and
unidimensional functions using the square-root velocity framework
(Srivastava et al., 2011 <doi:10.48550/arXiv.1103.3817> and Tucker et al., 2014
<DOI:10.1016/j.csda.2012.12.001>). This framework allows for elastic
analysis of functional data through phase and amplitude separation.

J Derek Tucker

fdasrvf

Elastic Functional Data Analysis

J. Derek Tucker

Aymeric Stamm

elastic.depth function

<dl><dt>f</dt>
<dd>matrix of sizes \(M \times N\), specifying values of \(N\)
function of \(M\) time points</dd>
<dt>time</dt>
<dd>vector of length \(M\), specifying the sample points of functions</dd>
<dt>lambda</dt>
<dd>controls amount of warping (default = <code>0</code>)</dd>
<dt>pen</dt>
<dd>alignment penalty (default = <code>"roughness"</code>) options are
second derivative (<code>"roughness"</code>), \(L^2\) distance of the warping
function from id (<code>"l2gam"</code>), \(L^2\) distance of the SRVF of the warping
function from that of id (<code>"l2psi"</code>), geodesic distance from id
(<code>"geodesic"</code>), and no penalty (<code>"none"</code>). <code>"norm"</code> is kept for backward
compatibility as an alias for <code>"l2gam"</code>. The penalty is weighted by
<code>lambda</code>, so it has no effect when <code>lambda = 0</code>.</dd>
<dt>parallel</dt>
<dd>run computation in parallel (default = <code>TRUE</code>)</dd></dl>

Arguments

Calculates elastic depth — elastic.depth

<dl>

<dt>f</dt>
<dd>matrix of sizes \(M \times N\), specifying values of \(N\)
function of \(M\) time points</dd>


<dt>time</dt>
<dd>vector of length \(M\), specifying the sample points of functions</dd>


<dt>lambda</dt>
<dd>controls amount of warping (default = <code>0</code>)</dd>


<dt>pen</dt>
<dd>alignment penalty (default = <code>"roughness"</code>) options are
second derivative (<code>"roughness"</code>), \(L^2\) distance of the warping
function from id (<code>"l2gam"</code>), \(L^2\) distance of the SRVF of the warping
function from that of id (<code>"l2psi"</code>), geodesic distance from id
(<code>"geodesic"</code>), and no penalty (<code>"none"</code>). <code>"norm"</code> is kept for backward
compatibility as an alias for <code>"l2gam"</code>. The penalty is weighted by
<code>lambda</code>, so it has no effect when <code>lambda = 0</code>.</dd>


<dt>parallel</dt>
<dd>run computation in parallel (default = <code>TRUE</code>)</dd>

</dl>

elastic.depth: Calculates elastic depth

Description

Usage

Value

Arguments

References

Examples