WPCMS: Weighted Principal Curve Metric Scaling

In ElenaTuzhilina/PoisMS: Principal Curve based chromatin reconstruction

Description

WPCMS function calculates the Weighted Principal Curve Metric Scaling solution for a contact matrix Z (e.g. representing a Hi-C contact matrix after some proper transformation applied) and a spline basis matrix H. The optimal solution is found via minimizing the weighted Frobenius norm

|| W x (Z - D^2(X) + β) ||

w.r.t. Θ subject to the smooth curve constraint X = HΘ. Here D(X) refers to the matrix of pairwise distances. The spatial coordiantes of the resulting reconstruction are presented in X.

Usage

WPCMS(
  Z,
  H,
  W = matrix(1, nrow(Z), ncol(Z)),
  beta0 = -min(Z),
  Theta0 = matrix(rnorm(ncol(H) * 3), ncol(H), 3),
  update_beta = TRUE,
  eps = 1e-06,
  maxiter = 100,
  verbose = FALSE
)

Arguments

Z	a square symmetric matrix.
H	a spline basis matrix. By default assumed to have orthogonal columns. If not, orthogonalization should be done via QR decomposition.
W	a weights matrix, same dimension as Z. By default equal weights W = 1 are assumed.
Theta0	an initialization for spline basis coefficient matrix Theta. By defaul Theta0 = matrix(rnorm(ncol(H) * 3), ncol(H), 3), i.e. a random initialization is considered.
update_beta	If update_beta = TRUE, then the algorithm finds an optimal intercept value. If update_beta = TRUE, then the intercept is considered to be fixed and set to beta0.
eps	a positive convergence tolerance.
maxiter	an integer giving the maximal number of iterations.
verbose	logical. If TRUE, the WPCMS loss after each iteration is printed.

Value

A list containing the WPCMS problem solution:

• Theta – the matrix of spline parameters.

• X – the resulting conformation reconstruction.

• beta – the resulting intercept value.

• loss – the resulting value of the WPCMS loss.

• iter – the total number of iterations.

• plot – the list of WPCMS plots: 'loss' corresponds to loss vs. iteration plot, 'intercept' represents beta vs. iteration plot.

Examples

data(C)

#transform contact counts to distances
Z = 1/(C+1)

#create spline basis matrix
H = splines::bs(1:ncol(C), df = 5)

#orthogonalize H using QR decomposition
H = qr.Q(qr(H))

#run WPCMS with equal weights; optimize intercept 
WPCMS(Z, H)$X

#run WPCMS with random weights; fixed intercept
W = matrix(runif(length(Z)), dim(Z))
WPCMS(Z, H, W, beta = 1)$X

ElenaTuzhilina/PoisMS documentation built on Dec. 11, 2020, 1:29 a.m.