Description Usage Arguments Details Value References See Also

This function calculates a smooth PCA representation based on the FCP_TPA
algorithm (see References) for functional data on two-dimensional domains. In
this case, the data can be interpreted as images with `S1 x S2`

pixels
(assuming `nObsPoints(funDataObject) = (S1, S2)`

), i.e. the total data
for `N`

observations can be represented as third order tensor of
dimension `N x S1 x S2`

.

1 2 3 4 5 6 7 8 | ```
fcptpaBasis(
funDataObject,
npc,
smoothingDegree = rep(2, 2),
alphaRange,
orderValues = TRUE,
normalize = FALSE
)
``` |

`funDataObject` |
An object of class |

`npc` |
An integer, giving the number of principal components to be calculated. |

`smoothingDegree` |
A numeric vector of length 2, specifying the degree of
the difference penalties inducing smoothness in both directions of the
image. Defaults to |

`alphaRange` |
A list of length 2 with entries |

`orderValues` |
Logical. If |

`normalize` |
Logical. If |

The smooth PCA of the tensor data is calculated via the `FCP_TPA`

function. Smoothness is induced by difference penalty matrices for both
directions of the images, weighted by smoothing parameters *α_v,
α_w*. The resulting eigenvectors can be interpreted in terms of
eigenfunctions and individual scores for each observation. See
`FCP_TPA`

for details.

`scores` |
A matrix of scores (coefficients) with dimension |

`B` |
A matrix containing the scalar product of all pairs of basis functions. |

`ortho` |
Logical, indicating whether the eigenfunctions are
orthonormal. Set to |

`functions` |
A functional data object, representing the functional principal component basis functions. |

`values` |
A vector of length |

G. I. Allen, "Multi-way Functional Principal Components Analysis", In IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2013.

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