SAPC_TFM: Stochastic Approximation Principal Component Analysis

In TFM: Sparse Online Principal Component for Truncated Factor Model

Stochastic Approximation Principal Component Analysis

Description

This function calculates several metrics for the SAPC method, including the estimated factor loadings and uniquenesses, and various error metrics comparing the estimated matrices with the true matrices.

Usage

SAPC_TFM(x, m, A, D, p)

Arguments

x	The data used in the SAPC analysis.
m	The number of common factors.
A	The true factor loadings matrix.
D	The true uniquenesses matrix.
p	The number of variables.

Value

A list of metrics including:

Asa	Estimated factor loadings matrix obtained from the SAPC analysis.
Dsa	Estimated uniquenesses vector obtained from the SAPC analysis.
MSESigmaA	Mean squared error of the estimated factor loadings (Asa) compared to the true loadings (A).
MSESigmaD	Mean squared error of the estimated uniquenesses (Dsa) compared to the true uniquenesses (D).
LSigmaA	Loss metric for the estimated factor loadings (Asa), indicating the relative error compared to the true loadings (A).
LSigmaD	Loss metric for the estimated uniquenesses (Dsa), indicating the relative error compared to the true uniquenesses (D).

Examples

library(MASS)
library(relliptical)
library(SOPC)

SAPC_MSESigmaA <- c()
SAPC_MSESigmaD <- c()
SAPC_LSigmaA <- c()
SAPC_LSigmaD <- c()

p <- 10
m <- 5
n <- 2000

mu <- t(matrix(rep(runif(p, 0, 1000), n), p, n))
mu0 <- as.matrix(runif(m, 0))
sigma0 <- diag(runif(m, 1))
F <- matrix(mvrnorm(n, mu0, sigma0), nrow = n)
A <- matrix(runif(p * m, -1, 1), nrow = p)

lower <- c(rep(-0.5, p - 3), -5, -5, -Inf)
upper <- c(rep(0.5, p - 3), 5, 5, Inf)
Sigma <- diag(runif(p, 0, 1))
mut <- runif(p, 0, 10)
trnor <- rtelliptical(n, mut, Sigma, lower, upper, dist = "Normal")
epsilon <- matrix(trnor, nrow = n)
D <- Sigma

data <- mu + F %*% t(A) + epsilon

result <- SAPC_TFM(data, m = m, A = A, D = D, p = p)

SAPC_MSESigmaA <- result$MSESigmaA
SAPC_MSESigmaD <- result$MSESigmaD
SAPC_LSigmaA <- result$LSigmaA
SAPC_LSigmaD <- result$LSigmaD

data_K <- data.frame(
  n = n,
  MSEA = SAPC_MSESigmaA,
  MSED = SAPC_MSESigmaD,
  LSA = SAPC_LSigmaA,
  LSD = SAPC_LSigmaD
)

print(data_K)

TFM documentation built on April 16, 2025, 5:10 p.m.