Package 'DLFM'

Description

This dataset contains information about credit card applications. All attribute names and values have been changed to meaningless symbols to protect confidentiality. The dataset includes a mix of continuous and categorical attributes, with some missing values.

Usage

data(Australian)

Format

A data frame with 690 rows and 15 columns representing different features related to credit card applications.

• A1: Categorical - 0, 1 (formerly: a, b)

• A2: Continuous

• A3: Continuous

• A4: Categorical - 1, 2, 3 (formerly: p, g, gg)

• A5: Categorical - 1 to 14 (formerly: ff, d, i, k, j, aa, m, c, w, e, q, r, cc, x)

• A6: Categorical - 1 to 9 (formerly: ff, dd, j, bb, v, n, o, h, z)

• A7: Continuous

• A8: Categorical - 1, 0 (formerly: t, f)

• A9: Categorical - 1, 0 (formerly: t, f)

• A10: Continuous

• A11: Categorical - 1, 0 (formerly: t, f)

• A12: Categorical - 1, 2, 3 (formerly: s, g, p)

• A13: Continuous

• A14: Continuous

• A15: Class attribute - 1, 2 (formerly: +, -)

Examples

# Load the dataset
data(Australian)

# Print the first few rows of the dataset
print(head(Australian))

Description

The data set contain the ratio of retained earnings (RE) to total assets, and the ratio of earnings before interests and taxes (EBIT) to total assets of 66 American firms recorded in the form of ratios. Half of the selected firms had filed for bankruptcy.

Usage

data(bankruptcy)

Format

A data frame with the following variables:

Y

The status of the firm: 0 bankruptcy or 1 financially sound;

RE

Ratio of retained earnings to total assets;

EBIT

Ratio of earnings before interests and taxes to total assets

Examples

data(bankruptcy)

Description

This dataset contains original clinical cases reported by Dr. Wolberg. The data are grouped chronologically, reflecting the time periods when the samples were collected. The dataset includes various attributes related to breast cancer diagnosis.

Usage

data(Breast)

Format

A data frame with 699 rows and several columns representing different features related to breast cancer diagnosis.

• Sample_code_number: Identification number for the sample.

• Clump_Thickness: 1-10

• Uniformity_of_Cell_Size: 1-10

• Uniformity_of_Cell_Shape: 1-10

• Marginal_Adhesion: 1-10

• Single_Epithelial_Cell_Size: 1-10

• Bare_Nuclei: 1-10 (some values may be missing or revised)

• Bland_Chromatin: 1-10

• Normal_Nucleoli: 1-10

• Mitoses: 1-10

• Class: 2 (benign) or 4 (malignant)

Examples

# Load the dataset
data(Breast)

# Print the first few rows of the dataset
print(head(Breast))

Description

Computes a normalized distance between the subspaces spanned by the columns of two factor loading matrices Ahat (estimated) and A1 (true/reference). The metric is based on the projection matrix of A1, regularized to avoid singularity, and is scaled by the number of factors m and squared number of variables p^2 to lie in $[0,1]$.

Usage

calculate_DAA(Ahat, A1, m, p)

Arguments

Details

The distance is defined as

$D(A_{\mathrm{est}}, A_{\mathrm{true}}) = \sqrt{1 - \frac{1}{m p^2} \, \mathrm{Re}\left( \mathrm{tr}\left( A_{\mathrm{est}}^\top (A_{\mathrm{true}} A_{\mathrm{true}}^\top + \epsilon I)^{-1} A_{\mathrm{true}} A_{\mathrm{true}}^\top A_{\mathrm{est}} \right) \right)},$

where $\epsilon = 10^{-6}$ is a small ridge parameter to ensure invertibility of $A_{\mathrm{true}} A_{\mathrm{true}}^\top$.

Value

A scalar in $[0,1]$ representing the discrepancy between the column spaces of Ahat and A1. A value of 0 indicates identical subspaces; values closer to 1 indicate greater discrepancy.

Examples

set.seed(123)
p <- 10; m <- 3
# True loading matrix (orthonormal columns)
A_true <- qr.Q(qr(matrix(rnorm(p * m), p, m)))
# Slightly perturbed estimate
A_est <- A_true + matrix(rnorm(p * m, sd = 0.05), p, m)
A_est <- qr.Q(qr(A_est))  # re-orthogonalize

calculate_DAA(A_est, A_true, m, p)

Description

This dataset contains measurements related to the slump test of concrete, including input variables (concrete ingredients) and output variables (slump, flow, and compressive strength).

Usage

concrete

Format

A data frame with 103 rows and 10 columns.

• Cement: Amount of cement (kg in one M^3 concrete).

• Slag: Amount of slag (kg in one M^3 concrete).

• Fly_ash: Amount of fly ash (kg in one M^3 concrete).

• Water: Amount of water (kg in one M^3 concrete).

• SP: Amount of superplasticizer (kg in one M^3 concrete).

• Coarse_Aggr: Amount of coarse aggregate (kg in one M^3 concrete).

• Fine_Aggr: Amount of fine aggregate (kg in one M^3 concrete).

• SLUMP: Slump of the concrete (cm).

• FLOW: Flow of the concrete (cm).

• Compressive_Strength: 28-day compressive strength of the concrete (MPa).

Examples

# Load the dataset
data(concrete)

# Print the first few rows of the dataset
print(head(concrete))

Description

Performs comprehensive factor model testing in distributed environment across multiple nodes, including joint tests (Wald, GRS, PY), individual asset t-tests, and False Discovery Rate control.

Usage

Dfactor.tests(ret, fac, n1, K, q.fdr = 0.05)

Arguments

Value

A list containing the following components:

Examples

set.seed(42)
T <- 120
N <- 100  # Larger dataset for distributed testing
K_factors <- 3
fac <- matrix(rnorm(T * K_factors), T, K_factors)
beta <- matrix(rnorm(N * K_factors), N, K_factors)
alpha <- rep(0, N)
alpha[1:10] <- 0.4 / 100  # 10 non-zero alphas
eps <- matrix(rnorm(T * N, sd = 0.02), T, N)
ret <- alpha + fac %*% t(beta) + eps

# Distributed testing with 4 nodes, each handling 25 assets
results <- Dfactor.tests(ret, fac, n1 = 25, K = 4, q.fdr = 0.05)

# View combined results
cat("Total significant assets after FDR:", results$total_power_proxy, "\n")
cat("Combined results across all nodes:\n")
print(summary(results$combined_alpha))

Description

Distributed general unilateral loading principal component

Usage

DGulPC(data, m, n1, K)

Arguments

Value

AU1,AU2,DU3,Shat

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
DGulPC(data,m=3,n1=128,K=2)

Description

Apply IPC in a distributed manner across K nodes.

Usage

DIPC(data, m, eta, K)

Arguments

Value

List with per-node results and aggregated averages.

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- DIPC(data, m, eta=0.8, K=5)

Description

Distributed principal component

Usage

DPC(data, m, n1, K)

Arguments

Value

Ahat,Dhat,Sigmahathat

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
DPC(data,m=3,n1=128,K=2)

Description

Distributed projection principal component

Usage

DPPC(data, m, n1, K)

Arguments

Value

Apro,pro,Sigmahathatpro

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
DPPC(data,m=3,n1=128,K=2)

Description

The distributed stochastic approximation principal component for handling online data sets with highly correlated data across multiple nodes.

Usage

DSAPC(data, m, eta, n1, K)

Arguments

Value

Asa, Dsa (lists containing results from each node)

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
DSAPC(data=data, m=3, eta=0.8, n1=128, K=2)

Description

Extracts the estimated factor loading matrix $A$ and the diagonal noise covariance matrix $D$ from the output of online_sir_lfm. The subspace estimate B_hat is truncated or padded to have exactly m columns, used as $A$, and $D$ is obtained by subtracting the factor covariance contribution from the sample covariance matrix, with a lower bound on the diagonal entries to ensure positivity.

Usage

estimate_AD_from_OSDR(data, res, m)

Arguments

Value

A list with components:

Examples

## Not run: 
set.seed(123)
n <- 500; p <- 20; m <- 3
B_true <- qr.Q(qr(matrix(rnorm(p * m), p, m)))
f <- matrix(rnorm(n * m), n, m)
eps <- matrix(rexp(n * p, rate = 1) - 1, n, p) # Laplace noise
X <- f %*% t(B_true) + eps

# Run online SIR
res <- online_sir_lfm(X, K_true = m, method = "gradient", verbose = FALSE)

# Estimate A and D from the result
AD <- estimate_AD_from_OSDR(X, res, m)
print(head(AD$A_est))
print(diag(AD$D_est)[1:5])

## End(Not run)

Description

Performs comprehensive factor model testing including joint tests (Wald, GRS, PY), individual asset t-tests, and False Discovery Rate control.

Usage

factor.tests(ret, fac, q.fdr = 0.05)

Arguments

Value

A list containing the following components:

Examples

set.seed(42)
T <- 120
N <- 25
K <- 3
fac <- matrix(rnorm(T * K), T, K)
beta <- matrix(rnorm(N * K), N, K)
alpha <- rep(0, N)
alpha[1:3] <- 0.4 / 100  # 3 non-zero alphas
eps <- matrix(rnorm(T * N, sd = 0.02), T, N)
ret <- alpha + fac %*% t(beta) + eps
results <- factor.tests(ret, fac, q.fdr = 0.05)

# View results
cat("Wald test p-value:", results$p_Wald, "\n")
cat("GRS test p-value:", results$p_GRS, "\n")
cat("PY test p-value:", results$p_PY, "\n")
cat("Significant assets after FDR:", results$power_proxy, "\n")

Description

This function performs Factor Analysis via Principal Component (FanPC) on a given data set. It calculates the estimated factor loading matrix (AF), specific variance matrix (DF), and the mean squared errors.

Usage

FanPC(data, m)

Arguments

Value

AF,DF,SigmahatF

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- FanPC(data, m)
print(results)

Description

Calculates the Frobenius norm of a matrix, defined as the square root of the sum of squares of all its entries. This is the standard Euclidean norm when the matrix is treated as a vector.

Usage

frobenius.norm(M)

Arguments

Value

A non-negative scalar representing the Frobenius norm of M.

Examples

M <- matrix(1:6, nrow = 2)
frobenius.norm(M)

Description

This function simulates data from a Lapalce factor model and applies the FarmTest for multiple hypothesis testing. It calculates the false discovery rate (FDR) and power of the test.

Usage

Ftest(
  data,
  p1,
  alpha = 0.05,
  K = -1,
  alternative = c("two.sided", "less", "greater")
)

Arguments

Value

A list containing the following elements:

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
p1=40
results <- Ftest(data, p1)
print(results$FDR)
print(results$Power)

Description

Generates a matrix of independent draws from a multivariate asymmetric Laplace distribution. Each row is $\epsilon = \alpha W + Z\sqrt{W}$, where $W \sim \text{Exp}(1)$ independent of $Z \sim N_p(0, \Sigma)$. The parameter $\alpha$ controls the asymmetry (skewness) in each coordinate.

Usage

generate_asymmetric_laplace(n, p, alpha, Sigma)

Arguments

Value

An n x p matrix where each row is a draw from the multivariate asymmetric Laplace distribution with shift vector alpha and scale matrix Sigma.

Examples

set.seed(123)
p <- 3
alpha <- c(0.5, -0.3, 0.2)
Sigma <- diag(p)
X <- generate_asymmetric_laplace(100, p, alpha, Sigma)
pairs(X)

Description

Generates a matrix of independent draws from a multivariate symmetric Laplace distribution. Each row is an independent observation of a $p$-dimensional random vector $\epsilon = Z\sqrt{W}$, where $Z \sim N_p(0, \Sigma_L)$ and $W \sim \text{Exp}(1)$ independent of $Z$.

Usage

generate_multivariate_laplace(n, p, Sigma_L)

Arguments

Value

An n x p matrix where each row is a draw from the multivariate symmetric Laplace distribution with scale matrix $\Sigma_L$.

Examples

set.seed(123)
p <- 3
Sigma_L <- diag(p)
X <- generate_multivariate_laplace(100, p, Sigma_L)
pairs(X)

Description

Generates a matrix of independent draws from a multivariate skew Laplace distribution with location vector $\alpha$, scale matrix $\Sigma$, and skewness parameter $\gamma$. Each observation is constructed as $\epsilon = \alpha + \gamma V + \sqrt{V} Z$, where $V \sim \text{Gamma}((p+1)/2, 1/2)$ and $Z \sim N_p(0, \Sigma)$ independent of $V$.

Usage

generate_skew_laplace(n, p, alpha, gamma, Sigma)

Arguments

Value

An n x p matrix where each row is a draw from the specified multivariate skew Laplace distribution.

Examples

set.seed(123)
p <- 3
alpha <- c(0.1, -0.2, 0.0)
gamma <- c(0.5, 0.3, -0.4)
Sigma <- diag(p)
X <- generate_skew_laplace(100, p, alpha, gamma, Sigma)
pairs(X)

Description

General unilateral loading principal component

Usage

GulPC(data, m)

Arguments

Value

AU1,AU2,DU3,SigmaUhat

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
GulPC(data=data,m=5)

Description

This dataset contains information about heart disease diagnosis, including various clinical attributes and the presence of heart disease in patients. The dataset is commonly used for classification tasks to predict the presence of heart disease.

Usage

data(Heart)

Format

A data frame with multiple rows and 14 columns representing different features related to heart disease diagnosis.

• age: Age in years (integer).

• sex: Sex (1 = male; 0 = female) (categorical).

• cp: Chest pain type (categorical).

• trestbps: Resting blood pressure (in mm Hg on admission to the hospital) (integer).

• chol: Serum cholesterol in mg/dl (integer).

• fbs: Fasting blood sugar > 120 mg/dl (1 = true; 0 = false) (categorical).

• restecg: Resting electrocardiographic results (categorical).

• thalach: Maximum heart rate achieved (integer).

• exang: Exercise-induced angina (1 = yes; 0 = no) (categorical).

• oldpeak: ST depression induced by exercise relative to rest (integer).

• slope: The slope of the peak exercise ST segment (categorical).

• ca: Number of major vessels (0-3) colored by fluoroscopy (integer).

• thal: Thalassemia (3 = normal; 6 = fixed defect; 7 = reversible defect) (categorical).

• num: Diagnosis of heart disease (angiographic disease status) (integer).

Examples

# Load the dataset
data(Heart)

# Print the first few rows of the dataset
print(head(Heart))

Description

This dataset contains radar returns from the ionosphere, collected by a system in Goose Bay, Labrador. The dataset is used for classifying radar returns as 'good' or 'bad' based on the presence of structure in the ionosphere.

Usage

data(ionosphere)

Format

A data frame with multiple rows and 35 columns representing different features related to radar returns.

• Attribute1: Continuous feature.

• Attribute2: Continuous feature.

• Attribute3: Continuous feature.

• Attribute4: Continuous feature.

• Attribute5: Continuous feature.

• Attribute6: Continuous feature.

• Attribute7: Continuous feature.

• Attribute8: Continuous feature.

• Attribute9: Continuous feature.

• Attribute10: Continuous feature.

• ...: Additional continuous features (up to Attribute34).

• Class: Binary classification target ('good' or 'bad').

Examples

# Load the dataset
data(ionosphere)

# Print the first few rows of the dataset
print(head(ionosphere))

Description

The incremental principal component can handle online data sets with highly correlated.

Usage

IPC(data, m, eta)

Arguments

Value

Ai,Di

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
IPC(data=data,m=3,eta=0.8)

Description

The Iris dataset is a classic and widely-used dataset in the field of machine learning and statistics. It contains measurements of sepal length, sepal width, petal length, and petal width for three species of iris plants. The dataset is commonly used for classification tasks.

Usage

data(Iris)

Format

A data frame with 150 rows and 5 columns representing different features of iris plants.

• Sepal.Length: Sepal length in centimeters (continuous).

• Sepal.Width: Sepal width in centimeters (continuous).

• Petal.Length: Petal length in centimeters (continuous).

• Petal.Width: Petal width in centimeters (continuous).

• Species: Species of iris plant (categorical): Iris Setosa, Iris Versicolor, or Iris Virginica.

Examples

# Load the dataset
data(Iris)

# Print the first few rows of the dataset
print(head(Iris))

Description

The function is to generate Laplace factor model data. The function supports various distribution types for generating the data, including: - 'truncated_laplace': Truncated Laplace distribution - 'log_laplace': Univariate Symmetric Log-Laplace distribution - 'Asymmetric Log_Laplace': Log-Laplace distribution - 'Skew-Laplace': Skew-Laplace distribution

Usage

LFM(n, p, m, distribution_type)

Arguments

Value

A list containing the following elements:

Examples

n <- 1000
p <- 10
m <- 5
sigma1 <- 1
sigma2 <- matrix(c(1,0.7,0.7,1), 2, 2)
distribution_type <- "Asymmetric Log_Laplace"
results <- LFM(n, p, m, distribution_type)
print(results)

Description

A questionnaire survey on consumers' purchase intention toward new energy vehicles (NEVs) and its influencing factors. The dataset includes (i) household vehicle purchase history, (ii) attitudes toward policy/product/economic/firm factors measured on a 5-point Likert scale, and (iii) demographic information.

Usage

new_energy_vehicle

Format

A data frame with 520 rows and multiple variables:

household_ice_owned

Whether the household has purchased an internal-combustion (fuel) vehicle (single choice).

household_nev_owned

Whether the household has purchased a new energy vehicle (single choice).

policy_subsidy_intention

Effect of subsidy policies (e.g., toll exemptions, lower purchase price, low-interest loans) on NEV purchase intention (Likert 5-point).

policy_license_intention

Effect of license-plate policies (e.g., free registration, road-restriction privileges) on NEV purchase intention (Likert 5-point).

environmental_intention

Effect of environmental concerns on NEV purchase intention (Likert 5-point).

infrastructure_intention

Effect of charging infrastructure convenience on NEV purchase intention (Likert 5-point).

driving_experience_factor

Effect of driving experience (product factor) on NEV purchase intention (Likert 5-point).

battery_performance_factor

Effect of battery performance (range, lifespan, capacity, charging efficiency) on NEV purchase intention (Likert 5-point).

safety_factor

Effect of safety and technology maturity/reliability on NEV purchase intention (Likert 5-point).

depreciation_cost_factor

Effect of depreciation/durability concerns (economic factor) on NEV purchase intention (Likert 5-point).

purchase_cost_factor

Effect of purchase price (economic factor) on NEV purchase intention (Likert 5-point).

charging_cost_factor

Effect of charging cost (economic factor) on NEV purchase intention (Likert 5-point).

maintenance_cost_factor

Effect of maintenance/repair cost (economic factor) on NEV purchase intention (Likert 5-point).

service_factor

Effect of firm service (pre-sales and after-sales) on NEV purchase intention (Likert 5-point).

brand_factor

Effect of brand (firm factor) on NEV purchase intention (Likert 5-point).

technology_advantage_factor

Effect of perceived technological advantages (firm factor) on NEV purchase intention (Likert 5-point).

purchase_intent

Stated intention to purchase an NEV (Likert 5-point).

recommend_intent

Willingness to recommend NEVs to others (Likert 5-point).

repurchase_intent

Willingness to prioritize buying an NEV next time (Likert 5-point).

gender

Gender (single choice).

age

Age group (single choice).

education

Education level (single choice).

occupation

Occupation (single choice).

hukou

Household registration type (rural/urban; single choice).

household_income

Average monthly household income (categorical; single choice).

Details

The Likert scale options are: A = Strongly disagree, B = Disagree, C = Neutral, D = Agree, E = Strongly agree.

Source

Consumer survey dataset on NEV purchase intention and influencing factors.

Description

Implements an online SIR algorithm tailored for LFM data, using a proxy response constructed from the current subspace estimate and robust updates to handle heavy-tailed noise. The algorithm supports two optimization methods: gradient-based updates and perturbation-based updates.

Usage

online_sir_lfm(
  X,
  K_true = NULL,
  K_max = NULL,
  c_robust = 1.345,
  eta = "auto",
  method = "gradient",
  verbose = FALSE
)

Arguments

Value

A list with:

Examples

set.seed(123)
n <- 500; p <- 20; m <- 3
B_true <- qr.Q(qr(matrix(rnorm(p * m), p, m)))
f <- matrix(rnorm(n * m), n, m)
eps <- matrix(rexp(n * p, rate = 1) - 1, n, p) # Asymmetric Laplace-like noise
X <- f %*% t(B_true) + eps

# Using gradient method (default)
out_grad <- online_sir_lfm(X, K_true = m, verbose = TRUE)

# Using perturbation method
out_pert <- online_sir_lfm(X, K_true = m, method = "perturbation", verbose = TRUE)

Description

Implements an online SIR-based sufficient dimension reduction method tailored for Laplace Factor Models (LFM) with symmetric, asymmetric, or skewed error structures. Supports distributed deployment via local updates and global aggregation.

Usage

osdr_lfm(
  X,
  Y = NULL,
  laplace_type = c("symmetric", "asymmetric", "skewed"),
  K_max = NULL,
  H = NULL,
  method_svd = c("gradient", "perturbation"),
  is_distributed = FALSE,
  node_id = 1,
  sync_interval = 50,
  verbose = FALSE
)

Arguments

Value

list with B_hat (p x K_est), K_est, lambda_trace, and (if distributed) local_B.

Examples

set.seed(42)
n <- 600; p <- 30; m <- 4
A <- qr.Q(qr(matrix(rnorm(p * m), p, m)))
F <- matrix(rnorm(n * m), n, m)
eps <- matrix(rexp(n * p) - rexp(n * p), n, p)
X <- F %*% t(A) + eps

out <- osdr_lfm(X, laplace_type = "asymmetric", K_max = 6, verbose = TRUE)
cat("Estimated K:", out$K_est, "\n")

Description

Principal component

Usage

PC(data, m)

Arguments

Value

Ahat, Dhat, Sigmahat

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
PC(data,m=5)

Description

Projection principal component

Usage

PPC(data, m)

Arguments

Value

Apro, Dpro, Sigmahatpro

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
PPC(data=data,m=5)

Description

This dataset contains protein sequences and their corresponding secondary structures, including beta-sheets (E), helices (H), and coils (_).

Usage

protein

Format

A data frame with multiple rows and columns representing protein sequences and their secondary structures.

• Sequence: Amino acid sequence (using 3-letter codes).

• Structure: Secondary structure of the protein (E for beta-sheet, H for helix, _ for coil).

• Parameters: Additional parameters for neural networks (to be ignored).

• Biophysical_Constants: Biophysical constants (to be ignored).

Examples

# Load the dataset
data(protein)

# Print the first few rows of the dataset
print(head(protein))

Description

This dataset contains travel reviews from TripAdvisor.com, covering destinations in 11 categories across East Asia. Each traveler's rating is mapped to a scale from Terrible (0) to Excellent (4), and the average rating for each category per user is provided.

Usage

review

Format

A data frame with multiple rows and 12 columns.

• User_ID: Unique identifier for each user (Categorical).

• Art_Galleries: Average user feedback on art galleries.

• Dance_Clubs: Average user feedback on dance clubs.

• Juice_Bars: Average user feedback on juice bars.

• Restaurants: Average user feedback on restaurants.

• Museums: Average user feedback on museums.

• Resorts: Average user feedback on resorts.

• Parks_Picnic_Spots: Average user feedback on parks and picnic spots.

• Beaches: Average user feedback on beaches.

• Theaters: Average user feedback on theaters.

• Religious_Institutions: Average user feedback on religious institutions.

Examples

# Load the dataset
data(review)

# Print the first few rows of the dataset
print(head(review))

Description

This dataset contains measurements of riboflavin (vitamin B2) production by Bacillus subtilis, a Gram-positive bacterium commonly used in industrial fermentation processes. The dataset includes $n = 71$ observations with $p = 4088$ predictors, representing the logarithm of the expression levels of 4088 genes. The response variable is the log-transformed riboflavin production rate.

Usage

data(riboflavin)

Format

y

Log-transformed riboflavin production rate (original name: q_RIBFLV). This is a continuous variable indicating the efficiency of riboflavin production by the bacterial strain.

x

A matrix of dimension $71 \times 4088$ containing the logarithm of the expression levels of 4088 genes. Each column corresponds to a gene, and each row corresponds to an observation (experimental condition or time point).

Examples

# Load the riboflavin dataset
data(riboflavin)

# Display the dimensions of the dataset
print(dim(riboflavin$x))
print(length(riboflavin$y))

Description

This dataset is a subset of the riboflavin production data by Bacillus subtilis, containing $n = 71$ observations. It includes the response variable (log-transformed riboflavin production rate) and the 100 genes with the largest empirical variances from the original dataset.

Usage

data(riboflavinv100)

Format

y

Log-transformed riboflavin production rate (original name: q_RIBFLV). This is a continuous variable indicating the efficiency of riboflavin production by the bacterial strain.

x

A matrix of dimension $71 \times 100$ containing the logarithm of the expression levels of the 100 genes with the largest empirical variances.

Examples

# Load the riboflavinv100 dataset
data(riboflavinv100)

# Display the dimensions of the dataset
print(dim(riboflavinv100$x))
print(length(riboflavinv100$y))

Description

The stochastic approximation principal component can handle online data sets with highly correlated.

Usage

SAPC(data, m, eta)

Arguments

Value

Asa,Dsa

Examples

library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
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)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
SAPC(data=data,m=3,eta=0.8)

Description

This dataset contains sonar signals bounced off a metal cylinder (mines) and a roughly cylindrical rock. The task is to classify whether the signal is from a mine or a rock based on the sonar signal patterns.

Usage

data(Sonar)

Format

A data frame with 208 rows and 61 columns representing different features of sonar signals.

• Attribute1: Continuous feature representing energy within a frequency band.

• Attribute2: Continuous feature representing energy within a frequency band.

• Attribute3: Continuous feature representing energy within a frequency band.

• ...: Additional continuous features (up to Attribute60).

• Class: Categorical target variable ('M' for mine, 'R' for rock).

Examples

# Load the dataset
data(Sonar)

# Print the first few rows of the dataset
print(head(Sonar))

Description

This dataset contains information about coupon recommendations made to drivers in a vehicle, including various contextual features and the outcome of whether the coupon was accepted.

Usage

vehicle

Format

A data frame with multiple rows and 27 columns representing different features related to coupon recommendations.

• destination: Driver's destination - No Urgent Place, Home, Work.

• passanger: Passengers in the car - Alone, Friend(s), Kid(s), Partner.

• weather: Current weather - Sunny, Rainy, Snowy.

• temperature: Temperature in Fahrenheit - 55, 80, 30.

• time: Time of day - 2PM, 10AM, 6PM, 7AM, 10PM.

• coupon: Type of coupon - Restaurant(<$20), Coffee House, Carry out & Take away, Bar, Restaurant($20-$50).

• expiration: Coupon expiration - 1d (1 day), 2h (2 hours).

• gender: Driver's gender - Female, Male.

• age: Driver's age group - 21, 46, 26, 31, 41, 50plus, 36, below21.

• maritalStatus: Driver's marital status - Unmarried partner, Single, Married partner, Divorced, Widowed.

• has_Children: Whether the driver has children - 1, 0.

• education: Driver's education level - Some college - no degree, Bachelors degree, Associates degree, High School Graduate, Graduate degree (Masters or Doctorate), Some High School.

• occupation: Driver's occupation - Various categories including Unemployed, Student, etc.

• income: Driver's income range - Various ranges such as $37500 - $49999, $62500 - $74999, etc.

• Bar: Frequency of bar visits per month - never, less1, 1~3, gt8, nan4~8.

• CoffeeHouse: Frequency of coffeehouse visits per month - never, less1, 4~8, 1~3, gt8, nan.

• CarryAway: Frequency of getting take-away food per month - n4~8, 1~3, gt8, less1, never.

• RestaurantLessThan20: Frequency of visiting restaurants with average expense <$20 per month - 4~8, 1~3, less1, gt8, never.

• Restaurant20To50: Frequency of visiting restaurants with average expense $20-$50 per month - 1~3, less1, never, gt8, 4~8, nan.

• toCoupon_GEQ15min: Driving distance to the coupon location greater than 15 minutes - 0, 1.

• toCoupon_GEQ25min: Driving distance to the coupon location greater than 25 minutes - 0, 1.

• direction_same: Whether the coupon location is in the same direction as the current destination - 0, 1.

• direction_opp: Whether the coupon location is in the opposite direction of the current destination - 1, 0.

• Y: Whether the coupon was accepted - 1, 0.

Examples

# Load the dataset
data(vehicle)

# Print the first few rows of the dataset
print(head(vehicle))

Description

This dataset contains the annual spending amounts of wholesale customers on various product categories, along with their channel and region information.

Usage

wholesale

Format

A data frame with 440 rows and 8 columns.

• FRESH: Annual spending (m.u.) on fresh products.

• MILK: Annual spending (m.u.) on milk products.

• GROCERY: Annual spending (m.u.) on grocery products.

• FROZEN: Annual spending (m.u.) on frozen products.

• DETERGENTS_PAPER: Annual spending (m.u.) on detergents and paper products.

• DELICATESSEN: Annual spending (m.u.) on delicatessen products.

• CHANNEL: Customers' channel - Horeca (Hotel/Restaurant/Café) or Retail channel (Nominal).

• REGION: Customers' region - Lisbon, Oporto or Other (Nominal).

Examples

# Load the dataset
data(wholesale)

Description

The Wine dataset contains the results of a chemical analysis of wines grown in the same region in Italy but derived from three different cultivars. The analysis determined the quantities of 13 constituents found in each of the three types of wines. This dataset is commonly used for classification tasks to determine the origin of wines based on their chemical properties.

Usage

data(Wine)

Format

A data frame with 178 rows and 14 columns representing different features of wines.

• Class: Categorical target variable indicating the type of wine (1, 2, or 3).

• Alcohol: Continuous feature representing the alcohol content.

• Malic_acid: Continuous feature representing the malic acid content.

• Ash: Continuous feature representing the ash content.

• Alcalinity_of_ash: Continuous feature representing the alcalinity of ash.

• Magnesium: Integer feature representing the magnesium content.

• Total_phenols: Continuous feature representing the total phenols content.

• Flavanoids: Continuous feature representing the flavanoids content.

• Nonflavanoid_phenols: Continuous feature representing the nonflavanoid phenols content.

• Proanthocyanins: Continuous feature representing the proanthocyanins content.

• Color_intensity: Continuous feature representing the color intensity.

• Hue: Continuous feature representing the hue.

• OD280_OD315_of_diluted_wines: Continuous feature representing the OD280/OD315 of diluted wines.

• Proline: Continuous feature representing the proline content.

Examples

# Load the dataset
data(Wine)

# Print the first few rows of the dataset
print(head(Wine))

Description

This dataset contains the hydrodynamic characteristics of sailing yachts, including design parameters and performance metrics.

Usage

yacht_hydrodynamics

Format

A data frame with 308 rows and 7 columns.

• Residuary Resistance: Residuary resistance per unit weight of displacement (performance metric).

• Longitudinal Position of Center of Buoyancy: Longitudinal position of the center of buoyancy.

• Prismatic Coefficient: Prismatic coefficient.

• Length-Displacement Ratio: Length-displacement ratio.

• Beam-Draft Ratio: Beam-draft ratio.

• Length-Beam Ratio: Length-beam ratio.

• Froude Number: Froude number.

Examples

# Load the dataset
data(yacht_hydrodynamics)

# Print the first few rows of the dataset
print(head(yacht_hydrodynamics))