Air Quality Data Set (UCI)

Description

Measurements of air quality variables in an Italian city collected over several months in 2004–2005. The data includes hourly averaged responses from chemical sensors embedded in an air quality chemical multi-sensor device.

Usage

data(AirQuality)

Format

A data frame with 9358 observations on the following 15 variables. Some variable names use parentheses, which may need to be quoted with backticks in R.

• Date: Date (in DD/MM/YYYY format)

• Time: Time (in HH.MM.SS format)

• CO.GT.: Carbon Monoxide concentration (mg/m³)

• PT08.S1.CO.: Sensor 1 response

• NMHC.GT.: Non-methane hydrocarbons (µg/m³)

• C6H6.GT.: Benzene concentration (µg/m³)

• PT08.S2.NMHC.: Sensor 2 response

• NOx.GT.: Nitric oxide concentration (ppb)

• PT08.S3.NOx.: Sensor 3 response

• NO2.GT.: Nitrogen dioxide concentration (µg/m³)

• PT08.S4.NO2.: Sensor 4 response

• PT08.S5.O3.: Sensor 5 response

• T: Temperature (°C)

• RH: Relative Humidity (%)

• AH: Absolute Humidity

Some variables contain missing values coded as -200.

Details

The dataset contains air quality data recorded in a densely populated area of an Italian city between March 2004 and February 2005. The data were collected using an array of chemical sensors and meteorological instruments.

This dataset is frequently used for tasks such as missing value imputation, time series analysis, regression, and machine learning model evaluation.

Source

De Vito, S., Massera, E., Piga, M., Martinotto, L., & Di Francia, G. (2008).\ UCI Machine Learning Repository: Air Quality Data Set.\ Available at: https://archive.ics.uci.edu/ml/datasets/Air+Quality

References

De Vito, S., Massera, E., Piga, M., Martinotto, L., & Di Francia, G. (2008).\ Semi-Supervised Learning Techniques in Artificial Olfaction: A Novel Approach to Classification Problems and Drift Counteraction.\ IEEE Sensors Journal, 8(12), 2030–2038.

Examples

data(AirQuality)

# Replace missing values (-200) with NA
AirQuality[AirQuality == -200] <- NA

# Check if there are non-NA values before plotting
if (sum(!is.na(AirQuality$CO.GT.)) > 0) {
  plot(AirQuality$CO.GT., type = "l", ylab = "CO (mg/m³)",
       main = "Hourly CO Concentration")
} else {
  message("No non-NA values in CO.GT. column to plot")
}

Distributed Fan Principal Component Analysis

Description

This function performs distributed Fan-type principal component analysis on a numeric dataset split across multiple nodes.

Usage

DFanPC(data, m, n1, K)

Arguments

Value

A list with the following components:

AF

List of estimated loading matrices for each node.

DF

List of diagonal residual variance matrices for each node.

SigmahatF

List of covariance matrices for each node.

Examples

set.seed(123)
data <- matrix(rnorm(500), nrow = 100, ncol = 5)
DFanPC(data = data, m = 3, n1 = 20, K = 5)

Distributed Gao Principal Component Analysis

Description

Performs distributed Gao-type principal component analysis on a numeric dataset split across multiple nodes.

Usage

DGaoPC(data, m, n1, K)

Arguments

Value

A list with the following components:

AG1

List of estimated loading matrices for the first-stage components for each node.

AG2

List of estimated loading matrices for the second-stage components for each node.

DG3

List of diagonal residual variance matrices for each node.

sGhat

List of covariance matrices of reconstructed data for each node.

Examples

set.seed(123)
data <- matrix(rnorm(500), nrow = 100, ncol = 5)
DGaoPC(data = data, m = 3, n1 = 20, K = 5)

Distributed Gul Principal Component Analysis

Description

Performs distributed Gul-type principal component analysis on a numeric dataset split across multiple nodes.

Usage

DGulPC(data, m, n1, K)

Arguments

Value

A list with the following components:

AU1

List of estimated first-stage loading matrices for each node.

AU2

List of estimated second-stage loading matrices for each node.

DU3

List of diagonal residual variance matrices for each node.

shat

List of covariance matrices of reconstructed data for each node.

Examples

set.seed(123)
data <- matrix(rnorm(500), nrow = 100, ncol = 5)
DGulPC(data = data, m = 3, n1 = 20, K = 5)

Distributed Principal Component Analysis

Description

Performs distributed principal component analysis on a numeric dataset split across multiple nodes. Estimates loading matrices, residual variances, and covariance matrices for each node.

Usage

DPC(data, m, n1, K)

Arguments

Value

A list with the following components:

Ahat

List of estimated loading matrices for each node.

Dhat

List of diagonal residual variance matrices for each node.

Sigmahat

List of covariance matrices for each node.

Examples

set.seed(123)
data <- matrix(rnorm(500), nrow = 100, ncol = 5)
DPC(data = data, m = 3, n1 = 20, K = 5)

Distributed Probabilistic Principal Component Analysis

Description

Performs distributed probabilistic principal component analysis (PPC) on a numeric dataset split across multiple nodes. Estimates loading matrices, residual variances, and covariance matrices for each node using a probabilistic approach.

Usage

DPPC(data, m, n1, K)

Arguments

Value

A list with the following components:

Apro

List of estimated loading matrices for each node.

Dpro

List of diagonal residual variance matrices for each node.

Sigmahatpro

List of covariance matrices for each node.

Examples

set.seed(123)
data <- matrix(rnorm(500), nrow = 100, ncol = 5)
DPPC(data = data, m = 3, n1 = 20, K = 5)

Distributed Sparse Principal Component Analysis

Description

Performs distributed sparse principal component analysis (DSPC) on a numeric dataset split across multiple nodes. Estimates sparse loading matrices, residual variances, and covariance matrices for each node.

Usage

DSPC(data, m, gamma, n1, K)

Arguments

Value

A list with the following components:

Aspro

List of sparse loading matrices for each node.

Dspro

List of diagonal residual variance matrices for each node.

Sigmahatpro

List of covariance matrices for each node.

Examples

set.seed(123)
data <- matrix(rnorm(500), nrow = 100, ncol = 5)
DSPC(data = data, m = 3, gamma = 0.03, n1 = 20, K = 5)

Nutrimouse: Gene, Lipid and Grouping Data

Description

A data frame containing gene expression, lipid measurements, and grouping variables (diet and genotype) for 40 mice from a nutrigenomics study.

Usage

data(Nutrimouse)

Format

A data frame with 40 observations on 143 variables:

• 120 numeric variables for gene expression

• 21 numeric variables for lipid measurements

• 2 categorical variables: diet and genotype

Details

This dataset was created for integrative analysis of transcriptomic and lipidomic responses of mice to different diets and genotypes.

All numeric variables (genes and lipids) are centered and scaled. The categorical variables indicate the experimental design: five diet types and two genotypes.

This format is convenient for regression, classification, and dimension reduction techniques requiring a single data frame.

Source

Extracted from the mixOmics package, based on: \ Martin, P. G. P., et al. (2007). A systems biology approach to the study of gene expression and lipid metabolism in mice fed high-fat diets. Journal of Lipid Research, 48(2), 360–377.

References

González, I., Déjean, S., Martin, P. G. P., and Baccini, A. (2009). CCA: An R package to extend canonical correlation analysis. Journal of Statistical Software, 23(12), 1–14.

Examples

data(Nutrimouse)

# View structure
str(Nutrimouse)

# Boxplot of a gene across diets
boxplot(Nutrimouse[,1] ~ Nutrimouse$diet, main = "Gene 1 Expression by Diet")

# PCA on all numeric variables (excluding factors)
nutri_numeric <- Nutrimouse[, sapply(Nutrimouse, is.numeric)]
pca_result <- prcomp(nutri_numeric, scale. = TRUE)

# PCA plot
plot(pca_result$x[,1:2], col = as.numeric(Nutrimouse$diet), pch = 19)
legend("topright", legend = levels(Nutrimouse$diet), col = 1:5, pch = 19)

Parkinson's Disease Voice Features Dataset

Description

A dataset containing biomedical voice measurements from people with Parkinson's disease and healthy controls. The goal is to analyze voice signal features for detecting and monitoring Parkinson's disease.

Usage

data(Parkinsons_Features)

Format

A data frame with 5,876 observations on 22 variables. Each row corresponds to a voice recording from a subject.

All features are numerical except for identifiers and categorical variables.

Details

This dataset was collected from subjects with Parkinson's disease and healthy controls. Multiple biomedical voice measurements were recorded over time to evaluate disease progression.

The features include various jitter, shimmer, noise, and entropy measures extracted from sustained vowel phonations.

The dataset is widely used for classification and regression models aiming to predict Parkinson's disease severity or presence.

Source

UCI Machine Learning Repository: Parkinson's Disease Classification Data Set \ https://archive.ics.uci.edu/ml/datasets/Parkinsons+Telemonitoring

References

Tsanas, A., Little, M.A., McSharry, P.E., & Ramig, L.O. (2010). Accurate telemonitoring of Parkinson's disease progression by noninvasive speech tests. IEEE Transactions on Biomedical Engineering, 57(4), 884–893.

Examples

data(Parkinsons_Features)

if (all(startsWith(names(Parkinsons_Features), "V"))) {
  colnames(Parkinsons_Features) <- Parkinsons_Features[1, ]
  Parkinsons_Features <- Parkinsons_Features[-1, ]
}

Parkinsons_Features[] <- lapply(Parkinsons_Features, type.convert, as.is = TRUE)

summary(Parkinsons_Features$motor_UPDRS)
boxplot(motor_UPDRS ~ sex, data = Parkinsons_Features,
        main = "Motor UPDRS by Sex", ylab = "Motor UPDRS")

The SFM function is to generate Skew Factor Models data.

Description

The function supports various distribution types for generating the data, including: Skew-Normal Distribution, Skew-Cauchy Distribution, Skew-t Distribution.

Usage

SFM(n, p, m, xi, omega, alpha, distribution_type)

Arguments

Value

A list containing:

Examples

library(MASS)
library(SOPC)
library(sn)
library(matrixcalc)
library(psych)
n <- 100
p <- 10
m <- 5
xi <- 5
omega <- 2
alpha <- 5
distribution_type <- "Skew-Normal Distribution"
X <- SFM(n, p, m, xi, omega, alpha, distribution_type)

The sparse online principal component can not only process online data sets, but also obtain a sparse solution of online data sets.

Description

The sparse online principal component can not only process online data sets, but also obtain a sparse solution of online data sets.

Usage

SOPC(data, m, gamma, eta)

Arguments

Value

Aso,Dso

The sparse principal component can obtain sparse solutions of the eigenmatrix to better explain the relationship between principal components and original variables.

Description

The sparse principal component can obtain sparse solutions of the eigenmatrix to better explain the relationship between principal components and original variables.

Usage

SPC(data, m, gamma)

Arguments

Value

As,Ds

calculate_errors Function

Description

This function calculates the Mean Squared Error (MSE) and relative error for factor loadings and uniqueness estimates obtained from factor analysis.

Usage

calculate_errors(data, A, D)

Arguments

Value

A named vector containing:

Examples

set.seed(123) # For reproducibility
# Define dimensions
n <- 10  # Number of samples
p <- 5   # Number of factors

# Generate matrices with compatible dimensions
A <- matrix(runif(p * p, -1, 1), nrow = p)  # Factor loadings matrix (p x p)
D <- diag(runif(p, 1, 2))  # Uniquenesses matrix (p x p)
data <- matrix(runif(n * p), nrow = n)  # Data matrix (n x p)

# Calculate errors (only if SOPC is installed)
if (requireNamespace("SOPC", quietly = TRUE)) {
  errors <- calculate_errors(data, A, D)
  print(errors)
}

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

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")

Piedmont wines data

Description

Data refer to chemical properties of 178 specimens of three types of wine produced in the Piedmont region of Italy.

Usage

data(wines)

Format

A data frame with 178 observations on the following 28 variables.

Details

The data represent 27 chemical measurements on each of 178 wine specimens belonging to three types of wine produced in the Piedmont region of Italy. The data have been presented and examined by Forina et al. (1986) and were freely accessible from the PARVUS web-site until it was active. These data or, more often, a subset of them are now available from various places, including some R packages. The present dataset includes all variables available on the PARVUS repository, which are the variables listed by Forina et al. (1986) with the exception of ‘Sulphate’. Moreover, it reveals the undocumented fact that the original dataset appears to include also the vintage year; see the final portion of the ‘Examples’ below.

Source

Forina, M., Lanteri, S. Armanino, C., Casolino, C., Casale, M. and Oliveri, P. V-PARVUS 2008: an extendible package of programs for esplorative data analysis, classification and regression analysis. Dip. Chimica e Tecnologie Farmaceutiche ed Alimentari, Università di Genova, Italia. Web-site (not accessible as of 2014): ‘⁠http://www.parvus.unige.it⁠’

References

Forina M., Armanino C., Castino M. and Ubigli M. (1986). Multivariate data analysis as a discriminating method of the origin of wines. Vitis 25, 189–201.

Examples

data(wines)
pairs(wines[,c(2,3,16:18)], col=as.numeric(wines$wine))
#
code <- substr(rownames(wines), 1, 3)
table(wines$wine, code)
#
year <- as.numeric(substr(rownames(wines), 6, 7))
table(wines$wine, year)
# coincides with Table 1(a) of Forina et al. (1986)