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FQPCA (Functional Quantile Principal Component Analysis)

Source: R/fqpca.R
fqpca.Rd

Solves the functional quantile principal component analysis methodology

Usage

fqpca(
  data,
  colname = NULL,
  npc = 2,
  quantile.value = 0.5,
  periodic = TRUE,
  splines.df = 10,
  splines.method = "conquer",
  penalized = FALSE,
  lambda.ridge = 0,
  tol = 0.001,
  max.iters = 20,
  verbose = FALSE,
  seed = NULL
)

Arguments

data

An \((N \times T)\) matrix, a tf object from the tidyfun package or a data.frame containing the functional data as a tf column.

colname

The name of the column containing the functional data. Use only if data is a dataframe and colname is a column in the dataframe.

npc

The number of estimated components.

quantile.value

The quantile considered.

periodic

Boolean indicating if the data is expected to be periodic (start coincides with end) or not.

splines.df

Degrees of freedom for the splines.

splines.method

Method used in the resolution of the splines quantile regression model. It currently accepts the methods c('conquer', 'quantreg').

penalized

Boolean indicating if the smoothness should be controlled using a second derivative penalty. This functionality is experimental.

lambda.ridge

Hyper parameter controlling the penalization on the second derivative of the splines. It has effect only with penalized=TRUE and method='conquer'.

tol

Tolerance on the convergence of the algorithm.

max.iters

Maximum number of iterations.

verbose

Boolean indicating the verbosity.

seed

Seed for the random generator number.

Value

fqpca_object

Examples


n.obs = 150
n.time = 144

# Generate scores
c1.vals = rnorm(n.obs)
c2.vals = rnorm(n.obs)

# Generate pc's
pc1 = sin(seq(0, 2*pi, length.out = n.time))
pc2 = cos(seq(0, 2*pi, length.out = n.time))

# Generate data
Y <- c1.vals * matrix(pc1, nrow = n.obs, ncol=n.time, byrow = TRUE) +
c2.vals * matrix(pc2, nrow = n.obs, ncol=n.time, byrow = TRUE)

# Add noise
Y <- Y + matrix(rnorm(n.obs * n.time, 0, 0.4), nrow = n.obs)

# Add missing observations
Y[sample(n.obs*n.time, as.integer(0.2*n.obs*n.time))] <- NA

results <- fqpca(data = Y, npc = 2, quantile.value = 0.5, seed=1)

intercept <- results$intercept
loadings <- results$loadings
scores <- results$scores