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Functional Data Class

fdClass.Rd

The fdClass class represents an element of functional data.

  • Data objects are constructed using matrices, where columns represent grid points (user-defined or NULL) and rows represent observations.

  • Users can assign both smoothing and sparsity parameters.

  • If the smoothing parameter is set to zero, no smoothing is applied. Otherwise, users can specify a fixed smoothing value or provide a vector of values, which will be optimized using generalized cross-validation (GCV).

Usage

fdClass(data, argval = NULL, Smoothing_parameter = 0, Sparsity_parameter = 0)

Arguments

data

A matrix representing the data, with rows indicating observations and columns representing grid points.

argval

A vector of grid points, it assigns grid points to the columns, with a length equal to the number of columns in the data. If NULL, grid points are automatically assigned from 0 to 1.

Smoothing_parameter

: Smoothing parameter for columns. It can be:

  • A fixed number representing the smoothing parameter.

  • A vector of numerical values, which will undergo generalized cross-validation (GCV) to determine the optimal value.

  • Set to 0 for no smoothing.

  • If NULL, it analyzes a sequence of 2^seq(-30, 5, length.out = 10) and attempts to tune it.

Sparsity_parameter

  • A fixed number representing the level of sparsity for columns, or a vector of numerical values that will undergo cross-validation (CV) to determine the optimal value.

  • For no sparsity, set it to 0.

  • If NULL, the sparsity parameter will be tuned automatically.

Examples

# Example for Functional Data (fd)
fd_data <- matrix(rnorm(100), nrow = 10, ncol = 10)  # 10 rows, 10 columns
fd_object <- fdClass(data = fd_data,
                     argval = seq(0, 1, length.out = 10),  # Grid points for columns
                     Smoothing_parameter = 0.5,  # Custom smoothing parameter
                     Sparsity_parameter = 2)  # Custom sparsity parameter

# Display the created fd object
print(fd_object)
#> Functional Data (fdClass) Object
#> -----------------------------------
#> Dimensions: 10 x 10
#> Smoothing Parameter: 0.5 
#> Sparsity Parameter: 2 
#> GridPoints_v: 0 0.1111111 0.2222222 ... 0.8888889 1 
#> -----------------------------------
#> First few rows and columns of the data:
#>              V1         V2          V3         V4         V5
#> [1,] -0.9487057  1.3364468 -0.03705146 -1.1376128  0.2253395
#> [2,]  0.4768438 -0.8603562  0.81005379 -1.4372467 -0.7299152
#> [3,] -0.7952016  0.6665378 -0.49935541 -0.4941435 -1.2224871
#> [4,]  0.2343269 -1.4215347  0.94803159  0.8408018  0.4068052
#> [5,] -1.2224511  1.1700562 -0.17424596  0.7915341 -0.7510122
print(attr(fd_object, "GridPoints_v"))  # Display grid points for columns
#>  [1] 0.0000000 0.1111111 0.2222222 0.3333333 0.4444444 0.5555556 0.6666667
#>  [8] 0.7777778 0.8888889 1.0000000
print(attr(fd_object, "Smoothing_parameter"))  # Display smoothing parameter
#> [1] 0.5