SOPC_TFM: Sparse Online Principal Component Analysis

In TFM: Sparse Online Principal Component for Truncated Factor Model

Sparse Online Principal Component Analysis

Description

This function calculates various metrics for the Sparse Online Principal Component Analysis (SOPC) method. It estimates the factor loadings and uniquenesses while calculating mean squared errors and loss metrics for comparison with true values. Additionally, it computes the proportion of zero factor loadings in the estimated loadings matrix.

Usage

SOPC_TFM(data, m, p, gamma, eta, A, D)

Arguments

data	The data used in the SOPC analysis.
m	the number of common factors
p	the number of variables
gamma	Tuning parameter for the sparseness of the loadings matrix.
eta	Tuning parameter for the sparseness of the uniquenesses matrix.
A	The true A matrix.
D	The true D matrix.

Value

A list of metrics including:

Aso	Estimated factor loadings matrix obtained from the SOPC analysis.
Dso	Estimated uniquenesses vector obtained from the SOPC analysis.
MSEA	Mean squared error of the estimated factor loadings (Aso) compared to the true loadings (A).
MSED	Mean squared error of the estimated uniquenesses (Dso) compared to the true uniquenesses (D).
LSA	Loss metric for the estimated factor loadings (Aso), indicating the relative error compared to the true loadings (A).
LSD	Loss metric for the estimated uniquenesses (Dso), indicating the relative error compared to the true uniquenesses (D).
tauA	Proportion of zero factor loadings in the estimated loadings matrix (Aso), indicating the sparsity of the loadings.

Examples

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

SOPC_MSEA <- c()
SOPC_MSED <- c()
SOPC_LSA <- c()
SOPC_LSD <- c()
SOPC_TAUA <- c()

p = 10; m = 5
n = 2000  # Set n to 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)

# Sampling from the Truncated Normal distribution
lower = c(rep(-0.5, p - 3), -5, -5, -Inf)
upper = c(rep(0.5, p - 3), 5, 5, Inf)
Sigma = as.matrix(diag(rep(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

Z = data.frame(SOPC_TFM(data, m = m, p = p, gamma = 0.1, eta = 0.8, A = A, D = D))
SOPC_MSEA = c(SOPC_MSEA, Z$MSEA)
SOPC_MSED = c(SOPC_MSED, Z$MSED)
SOPC_LSA = c(SOPC_LSA, Z$LSA)
SOPC_LSD = c(SOPC_LSD, Z$LSD)
SOPC_TAUA = c(SOPC_TAUA, Z$tauA)

# Ensure the data frame has the correct column structure, even with one value
data_F = data.frame(n = rep(n, length(SOPC_MSEA)), MSEA = SOPC_MSEA, MSED = SOPC_MSED,
 LSA = SOPC_LSA, LSD = SOPC_LSD, tauA = SOPC_TAUA)
data_F

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