Package 'LFM'

Australian

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))

---

Bankruptcy data

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)

---

Breast

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))

---

Concrete Slump Test Data

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))

---

Distributed general unilateral loading principal component

Description

Distributed general unilateral loading principal component

Usage

DGulPC(data, m, n1, K)

Arguments

data	is a total data set
m	is the number of principal component
n1	is the length of each data subset
K	is the number of nodes

Value

AU1,AU2,DU3,Shat

Examples

library(LFM)
data_from_package <- Wine
data_a <- Wine
DGulPC(data_a,m=3,n1=128,K=2)

---

Distributed projection principal component

Description

Distributed projection principal component

Usage

DPPC(data, m, n1, K)

Arguments

data	is a total data set
m	is the number of principal component
n1	is the length of each data subset
K	is the number of nodes

Value

Apro,pro,Sigmahathatpro

Examples

library(LFM)
data_from_package <- Wine
data_a <- Wine
DPPC(data_a,m=3,n1=128,K=2)

---

Factor Model Testing with Wald, GRS, PY tests and FDR control

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

ret	A T × N matrix representing the excess returns of N assets at T time points.
fac	A T × K matrix representing the returns of K factors at T time points.
q.fdr	The significance level for FDR (False Discovery Rate) testing, defaulting to 5%.

Value

A list containing the following components:

alpha	N-vector of estimated alphas for each asset
tstat	N-vector of t-statistics for testing individual alphas
pval	N-vector of p-values for individual alpha tests
Wald	Wald test statistic for joint alpha significance
p_Wald	p-value for Wald test
GRS	GRS test statistic (finite-sample F-test)
p_GRS	p-value for GRS test
PY	Pesaran and Yamagata test statistic
p_PY	p-value for PY test
reject_fdr	Logical vector indicating which assets have significant alphas after FDR correction
fdr_p	Adjusted p-values using Benjamini-Hochberg procedure
power_proxy	Number of significant assets after FDR correction

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")

---

Apply the FanPC method to the Laplace factor model

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

data	A matrix of input data.
m	is the number of principal component

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)

---

Apply the Farmtest method to the Laplace factor model

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

data	A matrix or data frame of simulated or observed data from a Laplace factor model.
p1	The number or proportion of non-zero hypotheses.
alpha	The significance level for controlling the false discovery rate (default: 0.05).
K	The number of factors to estimate (default: -1, meaning auto-detect).
alternative	The alternative hypothesis: "two.sided", "less", or "greater" (default: "two.sided").

Value

A list containing the following elements:

FDR	The false discovery rate, which is the proportion of false positives among all discoveries (rejected hypotheses).
Power	The statistical power of the test, which is the probability of correctly rejecting a false null hypothesis.
PValues	A vector of p-values associated with each hypothesis test.
RejectedHypotheses	The total number of hypotheses that were rejected by the FarmTest.
reject	Indices of rejected hypotheses.
means	Estimated means.

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)

---

Apply the GulPC method to the Laplace factor model

Description

This function performs General Unilateral Loading Principal Component (GulPC) analysis on a given data set. It calculates the estimated values for the first layer and second layer loadings, specific variances, and the mean squared errors.

Usage

GulPC(data, m)

Arguments

data	A matrix of input data.
m	is the number of first layer principal component

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
results <- GulPC(data, m)
print(results)

---

Heart

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))

---

ionosphere Data

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))

---

Apply the IPC method to the Laplace factor model

Description

This function performs Incremental Principal Component Analysis (IPC) on the provided data. It updates the estimated factor loadings and uniquenesses as new data points are processed, calculating mean squared errors and loss metrics for comparison with true values.

Usage

IPC(data, m, eta)

Arguments

data	The data used in the IPC analysis.
m	is the number of principal component
eta	is the proportion of online data to total data

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
results <- IPC(data, m, eta=0.1)
print(results)

---

Iris Data

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))

---

Generate Laplace factor models

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

n	An integer specifying the sample size.
p	An integer specifying the sample dimensionality or the number of variables.
m	An integer specifying the number of factors in the model.
distribution_type	A character string indicating the type of distribution to use for generating the data.

Value

A list containing the following elements:

data	A numeric matrix of the generated data.
A	A numeric matrix representing the factor loadings.
D	A numeric matrix representing the uniquenesses, which is a diagonal matrix.

Examples

library(MASS)
library(matrixcalc)
library(relliptical)
n <- 1000
p <- 10
m <- 5
sigma1 <- 1
sigma2 <- matrix(c(1,0.7,0.7,1), 2, 2)
distribution_type <- "truncated_laplace"
results <- LFM(n, p, m, distribution_type)
print(results)

---

Apply the OPC method to the Laplace factor model

Description

This function computes Online Principal Component Analysis (OPC) for the provided input data, estimating factor loadings and uniquenesses. It calculates mean squared errors and sparsity for the estimated values compared to true values.

Usage

OPC(data, m, eta)

Arguments

data	is a highly correlated online data set
m	is the number of principal component
eta	is the proportion of online data to total data

Value

Ao,Do

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 <- OPC(data, m, eta=0.1)
print(results)

---

Apply the traditional principal component method to the Laplace factor model

Description

This function performs Principal Component Analysis (PCA) on a given data set to reduce dimensionality. It calculates the estimated values for the loadings, specific variances, and the covariance matrix.

Usage

PC1(data, m = m)

Arguments

data	The total data set to be analyzed.
m	The number of principal components to retain in the analysis.

Value

Ahat, Dhat

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 <- PC1(data, m)
print(results)

---

Apply the PC method to the Laplace factor model

Description

This function performs principal component analysis (PCA) on a given data set to reduce dimensionality. It calculates the estimated values for the loadings, specific variances, and the covariance matrix.

Usage

PC2(data, m)

Arguments

data	The total data set to be analyzed.
m	The number of principal components to retain in the analysis.

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
results <- PC2(data, m)
print(results)

---

Apply the PPC method to the Laplace factor model

Description

This function computes Perturbation Principal Component Analysis (PPC) for the provided input data, estimating factor loadings and uniquenesses. It calculates mean squared errors and loss metrics for the estimated values compared to true values.

Usage

PPC1(data, m)

Arguments

data	A matrix of input data.
m	The number of principal components.

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
results <- PPC1(data, m)
print(results)

---

Apply the PPC method to the Laplace factor model

Description

This function performs Projected Principal Component Analysis (PPC) on a given data set to reduce dimensionality. It calculates the estimated values for the loadings, specific variances, and the covariance matrix.

Usage

PPC2(data, m)

Arguments

data	The total data set to be analyzed.
m	The number of principal components.

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
results <- PPC2(data, m)
print(results)

---

Protein Secondary Structure Data

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))

---

Review

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))

---

Riboflavin Production Data

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))

---

Riboflavin Production Data (Top 100 Genes)

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))

---

Generate Random Variables from the Laplace Distribution

Description

Generates random samples from the Laplace (double exponential) distribution with location parameter 0 and scale parameter b.

The probability density function is

$f(x)=\frac{1}{2b}\exp\left(-\frac{|x|}{b}\right),$

where $b>0$ is the scale parameter.

Random numbers are generated using the inverse transform method.

Usage

rlaplace(n, b = 1)

Arguments

n	An integer specifying the number of observations to generate.
b	A positive numeric value specifying the scale parameter of the Laplace distribution. The default value is 1.

Details

If $X \sim Laplace(0,b)$, then

$E(X)=0,$

and

$Var(X)=2b^2.$

This function is used internally by the Laplace Factor Model (LFM) package for generating Laplace-distributed error terms.

Value

A numeric vector of length n containing random observations from the Laplace distribution.

Examples

set.seed(123)

x <- rlaplace(1000)

mean(x)
var(x)

hist(x,
     breaks = 30,
     main = "Laplace Random Sample",
     xlab = "x")

---

Apply the SAPC method to the Laplace factor model

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(data, m, eta)

Arguments

data	The data used in the SAPC analysis.
m	is the number of principal component
eta	is the proportion of online data to total data

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
results <- SAPC(data, m, eta=0.1)
print(results)

---

Sonar

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))

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Apply the SOPC method to the Laplace factor model

Description

This function calculates various metrics for the sprase online principle component (SOPC) analysis on the Laplace factor model.

Usage

SOPC(data, m, gamma,eta)

Arguments

data	A numeric matrix containing the data used in the SOPC analysis.
m	is the number of principal component
gamma	is a sparse parameter
eta	is the proportion of online data to total data

Value

Aso,Dso

Examples

library(MASS)
library(matrixcalc)
library(LaplacesDemon)
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 <- SOPC(data, m, gamma=0.03, eta=0.1)
print(results)

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Apply the SPC method to the Laplace factor model

Description

This function performs Sparse Principal Component Analysis (SPC) on the input data. It estimates factor loadings and uniquenesses while calculating mean squared errors and loss metrics for comparison with true values.

Usage

SPC(data, m, gamma)

Arguments

data	The data used in the SPC analysis.
m	is the number of principal component
gamma	is a sparse parameter

Value

A list containing:

As	Estimated factor loadings, a matrix of estimated factor loadings from the SPC analysis.
Ds	Estimated uniquenesses, a vector of estimated uniquenesses corresponding to each variable.

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 <- SPC(data, m, gamma=0.03)
print(results)

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In Vehicle Coupon Recommendation Data

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))

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Wholesale Customers Data

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)

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Wine Data

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))

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Yacht Hydrodynamics Data

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))

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