KfoldCV_delta: Cross-validation for selecting delta
In bingx1990/LOVE: Overlapping clustering based on latent factor models

KfoldCV_delta uses nfolds cross-validation to select delta.

KfoldCV_delta(
  X,
  delta = NULL,
  ndelta = 50,
  q = 2,
  exact = FALSE,
  nfolds = 10,
  max_pure = NULL
)

`X`	A n by p data matrix.
`delta`	The grid of leading constant of δ.
`ndelta`	Integer. The length of the grid of `delta`.
`q`	Either `2` or `Inf` to specify the type of score.
`exact`	Logical. Only active for compute the `Inf` score. If TRUE, compute the `Inf` score exactly via solving a linear program. Otherwise, use approximation to compute `Inf` score.
`nfolds`	The number of folds. Default is 10.
`max_pure`	A numeric value between (0, 1] specifying the maximal proportion of pure variables. Default is NULL. When not specified, `max_pure` = 1 if n > p, `max_pure` = 0.8 otherwise.

A list of objects including:

foldid The indices of observations used for cv.
delta_min The value of delta that has the minimum cv error.
delta_1se The smallest and largest value of delta such that the cv errors are wihtin one standard error of the minimum cv error.
delta The used delta sequence.
cv_mean The averaged cv errors.
cv_sd The standard errors of cv errors.
est_pure A list including:
- K The cardinality of parallel rows.
- I The index of parallel rows.
- I_part The partition of parallel rows.
score The score matrix.
moments The crossproduct matrix R'R.