pECV (version 1.0.1)

estimate_C: Estimate constraint constant C for continuous data

Description

Data-driven estimation of the constraint constant C in alternating maximization algorithm for continuous data using truncated SVD approach. This function decomposes the data matrix and estimates C based on the maximum row norms.

Usage

estimate_C(X, qmax = 8, safety = 1.2)

Value

A list containing:

qmax

Truncation rank used

safety

Safety parameter applied

C_norm_hat

Original maximum row norm

C_est

Final conservative estimate of C

a_norms

Row norms of factor matrix A

b_norms

Row norms of factor matrix B

Arguments

X

n x p continuous data matrix

qmax

Rank for truncated SVD (default 8)

safety

Safety parameter for conservative estimation (default 1.2)

Details

The function performs the following steps: 1. Computes truncated SVD of X with rank qmax 2. Constructs factor matrices A = U * sqrt(D) and B = V * sqrt(D) 3. Calculates row 2-norms for matrices A and B 4. Takes the maximum norm and multiplies by safety parameter

For count data, it is recommended to transform the data using log(X + 1) before applying this function.

Examples

# Example 1: Continuous data
set.seed(123)
n <- 100; p <- 50; q <- 3
theta_true <- matrix(runif(n * q), n, q)
A_true <- matrix(runif(p * q), p, q)
X <- theta_true %*% t(A_true) + matrix(rnorm(n * p, sd = 0.5), n, p)

# Estimate C
C_result <- estimate_C(X, qmax = 5)
print(C_result$C_est)

# Example 2: Count data (apply log transformation)
lambda <- exp(theta_true %*% t(A_true))
X_count <- matrix(rpois(n * p, lambda = as.vector(lambda)), n, p)
X_transformed <- log(X_count + 1)
C_count <- estimate_C(X_transformed, qmax = 5)
print(C_count$C_est)