reconstructIndicators: Reconstruct the indicators using encoding

In cfda: Categorical Functional Data Analysis

Reconstruct the indicators using encoding

Description

The reconstruction formula is:

1^{x}(t) = p^x(t) ( 1 + \sum_{i\geq 1} z_i*a_i^x(t)

)

with z_i, the i-th principal component, encoding a_i^x = \sum_j \alpha_{(x, j)} * \phi_j(t) and p^x(t) = 1 / (\sum_{i \geq 1} a_i^x(t)^2)

Usage

reconstructIndicators(
  x,
  nComp = NULL,
  timeValues = NULL,
  propMinEigenvalues = 1e-04
)

Arguments

x	output of compute_optimal_encoding function
nComp	number of components to use for the reconstruction. By default, all are used.
timeValues	vector containing time values at which compute the indicators. If NULL, the time values from the data
propMinEigenvalues	Only if nComp = NULL. Minimal proportion used to estimate the number of non-null eigenvalues

Value

a data.frame with columns: time, id, state1, ..., stateK, state. state1 contains the estimated indicator values for the first state. state contains the state with the maximum values of all indicators

Author(s)

Quentin Grimonprez

See Also

plotIndicatorsReconstruction

Examples

set.seed(42)
# Simulate the Jukes-Cantor model of nucleotide replacement
K <- 3
Tmax <- 1
d_JK <- generate_Markov(n = 100, K = K, Tmax = Tmax)
d_JK2 <- cut_data(d_JK, Tmax)

# create basis object
m <- 20
b <- create.bspline.basis(c(0, Tmax), nbasis = m, norder = 4)

# compute encoding
encoding <- compute_optimal_encoding(d_JK2, b, computeCI = FALSE, nCores = 1)

indicators <- reconstructIndicators(encoding)

# we plot the first path and its reconstructed indicators
iInd <- 3
plotData(d_JK2[d_JK2$id == iInd, ])

plotIndicatorsReconstruction(indicators, id = iInd)

# the column state contains the state associated with the greatest indicator.
# So, the output can be used with plotData function
plotData(remove_duplicated_states(indicators[indicators$id == iInd, ]))

cfda documentation built on April 3, 2025, 9:21 p.m.