# Functional Principal Component Analysis

### Description

Compute the functional PCA from a set of curves.

### Usage

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### Arguments

`x` |
The set of curves. |

`nbasisInit` |
The number of initial spline coefficients. |

`propVar` |
The proportion of explained variance. |

`reconstruct` |
Should the data be reconstruct after dimension reduction ? |

`varName` |
The name of the current functional variable. |

`verbose` |
Should the details be printed. |

### Details

The Functional PCA is performed in two steps. First we express each discretized curves as a linear combination of ‘nbasisInit’ spline basis functions. Then a multivariate PCA is computed on the spline coefficients. The final number of principal components is chosen such that the proportion of explained variance is larger than ‘propVar’.

### Value

A list with two components:

`design` |
The matrix of the principal components ; |

`smoothData` |
The reconstructed data if ‘reconstruct == TRUE’. |

### Author(s)

Baptiste Gregorutti

### References

Ramsay, J. O., and Silverman, B. W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

### See Also

`hardThresholding`

### Examples

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