Package {nda}

Package of Generalized Network-based Dimensionality Reduction and Analyses

Description

The package of Generalized Network-based Dimensionality Reduction and Analysis (GNDA).

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona, Zahid Khan

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyan, Z. T., Kurbucz, M. T., & Katona, A. I. (2022). Network-based dimensionality reduction of high-dimensional, low-sample-size datasets. Knowledge-Based Systems, 109180.

Kosztyan, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

ndr, ndrlm, plot, biplot, summary, dCor.

COVID-19 case data for 138 countries and 18 variables

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Covid'19 of countries (2020), where the data frame has 138 observations of 18 variables.

Usage

data("COVID19_2020")

Format

A data frame with 138 observations 18 variables.

Source

Kurbucz, M. T. (2020). A joint dataset of official COVID-19 reports and the governance, trade and competitiveness indicators of World Bank group platforms. Data in brief, 31, 105881.

Examples

data(COVID19_2020)

CWTS Leiden University Ranking 2020 with 1,176 universities and 42 indicators

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

CWTS Leiden's 2020 dataset, where the data frame has 1176 observations of 42 variables.

Usage

data("CWTS_2020")

Format

A data frame with 1176 observations of 42 variables.

Source

CWTS Leiden Ranking 2020: https://www.leidenranking.com/ranking/2020/list

Examples

data(CWTS_2020)

Crimes in USA cities in 1990. Independent variables (X)

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Crimes in USA cities in 1990. Independent variables (X)

Usage

data("CrimesUSA1990.X")

Format

A data frame with 1994 observations 123 variables.

Source

UCI - Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/communities+and+crime

Examples

data(CrimesUSA1990.X)

Crimes in USA cities in 1990. Dependent variable (Y)

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Crimes in USA cities in 1990. Dependent variable (Y)

Usage

data("CrimesUSA1990.Y")

Format

A data frame with 1994 observations 1 variables.

Source

UCI - Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/communities+and+crime

Examples

data(CrimesUSA1990.Y)

Governmental and economic data for 138 countries and 2,161 variables

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Governmental and economic data of countries (2020), where the data frame has 138 observations of 2161 variables.

Usage

data("GOVDB2020")

Format

A data frame with 138 observations of 2161 variables.

Source

Kurbucz, M. T. (2020). A joint dataset of official COVID-19 reports and the governance, trade and competitiveness indicators of World Bank group platforms. Data in brief, 31, 105881.

Examples

data(GOVDB2020)

NUTS2 regional Industry 4.0 readiness data with 414 observations and 101 variables

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

NUTS2 regional development data (2020), where the data frame has 414 observations of 101 variables.

Usage

data("I40_2020")

Format

A data frame with 414 observations of 101 variables.

Source

Honti, G., Czvetko, T., and Abonyi, J. (2020). Data describing the regional Industry 4.0 readiness index. Data in Brief, 33, 106464.

Examples

data(I40_2020)

Biplot NDA Scores and Loadings

Description

Creates a printable two-dimensional biplot or a sequence of three-factor projections.

Usage

## S3 method for class 'nda'
biplot(x, main = NULL, dims = c(1, 2), view_3D = FALSE,
    triples = NULL, interactive = FALSE, angle = 45,
    point_cex = 0.7, label_cex = 0.9, ...)

Arguments

Value

An nda_biplot object; printing it renders the selected view or views.

Examples

fit <- ndr(swiss)
b <- biplot(fit, dims = c(1, 2))
b

Distance-Correlation Matrix

Description

Calculates distance correlation for two vectors or for every unique pair of matrix columns.

Usage

dCor(x, y = NULL, test = FALSE, adjust = "BH", alpha = NULL,
     parallel = FALSE, cores = 1L, R = 499L)

Arguments

Value

A coefficient or symmetric matrix when test = FALSE; otherwise a list with r and p.

Examples

x <- matrix(rnorm(80), 20, 4)
dCor(x)
## Not run: dCor(x, test = TRUE, R = 999)

Distance-Covariance Matrix

Description

Calculates distance covariance for two vectors or for every unique pair of matrix columns.

Usage

dCov(x, y = NULL, test = FALSE, adjust = "BH", alpha = NULL,
     parallel = FALSE, cores = 1L, R = 499L)

Arguments

Value

A covariance value or symmetric matrix when test = FALSE; otherwise a list with r and p.

Examples

x <- matrix(rnorm(80), 20, 4); dCov(x)

Generate Structured NDA Example Data

Description

Generates a noisy block matrix without constructing intermediate block-diagonal matrices.

Usage

data_gen(n, m, nfactors = 2, lambda = 1, sparse = FALSE,
         density = 1, seed = NULL)

Arguments

Value

A data frame, or a sparse matrix when sparse = TRUE.

Examples

dense <- data_gen(30, 10, nfactors = 2, seed = 1)
sparse <- data_gen(100, 40, nfactors = 4, sparse = TRUE, density = 0.5)

NDRLM Fitted Values

Description

Extracts fitted values from every response model.

Usage

## S3 method for class 'ndrlm'
fitted(object, ...)

Arguments

Value

A data frame with one column per fitted response.

Examples

X <- as.data.frame(freeny.x)
Y <- data.frame(y = freeny.y)
fit <- ndrlm(Y, X, optimize = FALSE)
fitted(fit)

KMO-Based Feature Selection

Description

Iteratively removes the indicator with the lowest measure of sampling adequacy until the requested overall KMO is reached.

Usage

fs.KMO(data, min_MSA = 0.5, cor.mtx = FALSE,
       max_iter = ncol(data) - 1L, ...)

Arguments

Value

Filtered data or correlation matrix. The final KMO result and removed variable names are stored in "KMO" and "removed" attributes.

Examples

filtered <- fs.KMO(swiss, min_MSA = 0.6)

Loading-Based Feature Selection

Description

Selects indicators from NDA, PCA, factor-analysis, and other objects that expose loadings, rotations, or variable coordinates. When the original model call is available, the model is refitted after every removal so that all later decisions use the current communalities and loadings.

Usage

fs.dimred(fn, DF, min_comm = 0.25, com_comm = 0.25, ...)

Arguments

Value

The final refitted model, preserving its original class, with dropped_low, dropped_com, and retained_DF (also available as remain_DF) added. The original fitted model is available as model.

Examples

pca <- prcomp(swiss, scale. = TRUE)
selected <- fs.dimred(pca, swiss)
colnames(selected$retained_DF)

Generalized Network-Based Dimensionality Reduction and Analysis

Description

Builds a squared-association network, detects indicator communities, and estimates one centrality-weighted latent variable per retained community.

Usage

ndr(r, covar = FALSE, cor_method = 1, cor_type = 1, min_R = 0,
    min_comm = 2, Gamma = 1, null_model_type = 4, mod_mode = 6,
    min_evalue = 0, min_communality = 0, com_communalities = 0,
    use_rotation = FALSE, rotation = "oblimin", weight = NULL,
    seed = NULL, parallel = FALSE, cores = 1L, sparsecalc = FALSE,
    membership = NULL,
    centrality = c("eigenvector", "authority", "hub", "pagerank"),
    standardized = TRUE, P_mat = NULL, test = FALSE,
    p_adjust = "BH", alpha = NULL, bootstrap = FALSE,
    n_boot = 200L, conf = 0.95)

Arguments

Details

The method follows three stages: construct a squared-association graph, detect network communities, and form standardized centrality-weighted latent scores. Partial and semipartial networks can be asymmetric. Null-model types 1–3 operate on nonnegative residual similarities; type 4 leaves the similarity matrix unchanged.

Value

An object of class nda. Important elements include scores, loadings, communality, uniqueness, membership, EVCs, R, correlation, modularity, reconstruction, and stats. The stats list contains indicator p-values, optional bootstrap intervals, retained and dropped indicators, community sizes, and null-model metadata. Scores are unavailable for association-matrix input, but reconstruction-consistent loadings, communalities, and a loading-based reconstructed association matrix are returned.

References

Kosztyan, Z. T., Kurbucz, M. T., and Katona, A. I. (2022). Network-based dimensionality reduction of high-dimensional, low-sample-size datasets. Knowledge-Based Systems, 109180. doi:10.1016/j.knosys.2022.109180.

Kosztyan, Z. T., Katona, A. I., Kurbucz, M. T., and Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. doi:10.1016/j.eswa.2023.121779.

Examples

fit <- ndr(swiss, cor_method = "spearman", centrality = "pagerank")
summary(fit)
scores <- predict(fit, swiss[1:3, ])

association <- cor(swiss)
fit_matrix <- ndr(association, covar = TRUE, membership = c(1, 1, 1, 2, 2, 2))
fit_matrix$loadings

## Not run: 
fit_boot <- ndr(swiss, cor_method = "distance", test = TRUE,
                bootstrap = TRUE, n_boot = 500, parallel = TRUE, cores = 4)

## End(Not run)

Network-Based Dimensionality Reduction and Regression

Description

Fits supervised models to original or NDA-reduced input and output variables, with optional NSGA-II tuning.

Usage

ndrlm(Y, X, latents = "in", dircon = FALSE, optimize = TRUE,
      target = "adj.r.square", rel_weight = FALSE, cor_method = 1,
      cor_type = 1, min_comm = 2, Gamma = 1, null_model_type = 4,
      mod_mode = 1, use_rotation = FALSE, rotation = "oblimin",
      pareto = FALSE, fit_weights = NULL,
      lower.bounds.x = rep(-100, ncol(X)),
      upper.bounds.x = rep(100, ncol(X)),
      lower.bounds.latentx = c(0, 0, 0, 0),
      upper.bounds.latentx = c(0.6, 0.6, 0.6, 0.3),
      lower.bounds.y = rep(-100, ncol(Y)),
      upper.bounds.y = rep(100, ncol(Y)),
      lower.bounds.latenty = c(0, 0, 0, 0),
      upper.bounds.latenty = c(0.6, 0.6, 0.6, 0.3),
      popsize = 20, generations = 30, cprob = 0.7, cdist = 5,
      mprob = 0.2, mdist = 10, seed = NULL,
      regression = c("lm", "ridge", "loess", "elastic_net"),
      model = NULL, alpha = 0.5, lambda = NULL, loess_span = 0.75,
      restarts = 1L, parallel = FALSE, cores = 1L,
      sparsecalc = FALSE, centrality = "eigenvector",
      standardized = TRUE, membership.X = NULL, membership.Y = NULL)

Arguments

Details

NDRLM is predictive and exploratory; its paths do not by themselves establish causal effects. Ridge and elastic net use glmnet. LOESS is intended for small predictor sets and does not provide linear-path significance tests. AIC and BIC for non-likelihood engines are residual-based approximations.

The class and structure of each element of fits depend on the selected regression engine. With regression = "lm", each fits[[i]] is a genuine lm object and can be passed directly to summary, coef, AIC, BIC, predict.lm, and lm.beta::lm.beta. The lm.beta package is meaningful only for ordinary least-squares fits; it must not be applied to ridge, elastic-net, or LOESS fits.

With regression = "ridge", "elastic_net", or "loess", each fits[[i]] is an NDRLM engine wrapper. It contains the engine name in method, the underlying fitted object in fit, and common fitted-value, residual, coefficient, and predictor metadata. Penalized fits additionally store the selected lambda, effective alpha, and standardized coefficients calculated on the complete training observations. The plot method applies the same standardization to ordinary least-squares fits, including compatible legacy lm objects. For engine-independent code, use summary, predict, fitted, residuals, and plot on the enclosing ndrlm object instead of relying on these internal fields.

The NDRLM methods retain backward compatibility with both legacy objects that stored ordinary least-squares fits directly and early 0.3.0 objects that wrapped ordinary least-squares fits. Newly fitted ordinary least-squares models use direct lm objects, while the newer non-lm engines retain their wrappers.

Value

An ndrlm object containing response-specific metrics, fitted NDA objects, optimized hyperparameters, training designs, NSGA-II results and an NSGA_trace evaluation history when optimization is enabled, and a response-named fits list. Elements of fits are lm objects for ordinary least squares and NDRLM engine wrappers for ridge, elastic net, and LOESS.

References

Kosztyan, Z. T., Kurbucz, M. T., Katona, A. I., and Khan, Z. Network-based dimensionality reduction and structural modeling.

Examples

X <- as.data.frame(freeny.x)
Y <- data.frame(income = freeny.y)

fit_lm <- ndrlm(Y, X, latents = "none", regression = "lm")
inherits(fit_lm$fits[[1]], "lm")
summary(fit_lm$fits[[1]])
predict(fit_lm, X[1:3, ])

if (requireNamespace("lm.beta", quietly = TRUE)) {
  summary(lm.beta::lm.beta(fit_lm$fits[[1]]))
}

if (requireNamespace("glmnet", quietly = TRUE)) {
  fit_ridge <- ndrlm(Y, X, latents = "none", regression = "ridge",
                     lambda = 0.1)
  fit_ridge$fits[[1]]$method
  predict(fit_ridge, X[1:3, ])
}

if (requireNamespace("glmnet", quietly = TRUE)) {
  fit_en <- ndrlm(Y, X, latents = "none", regression = "elastic_net",
                  alpha = 0.5, lambda = 0.1)
  predict(fit_en, X[1:3, ])
}

Fast Min-Max Normalization

Description

Rescales a numeric matrix or data frame globally, by row, or by column.

Usage

normalize(x, type = c("all", "row", "col"), range = c(0, 1),
          na.rm = TRUE)

Arguments

Details

A constant slice is mapped to the midpoint of range.

Value

A normalized object with the same matrix or data-frame form as x.

Examples

m <- matrix(rnorm(20), 5, 4)
normalize(m)
normalize(m, type = "row", range = c(-1, 1))

Partial Distance-Correlation Matrix

Description

Forms a partial distance-correlation matrix by inverting the distance-covariance matrix.

Usage

pdCor(x, test = FALSE, adjust = "BH", alpha = NULL,
      parallel = FALSE, cores = 1L)

Arguments

Details

When the distance-covariance matrix is singular, a Moore-Penrose generalized inverse is used. The optional p-values use a t approximation and should be interpreted as screening diagnostics.

Value

A matrix, or a list with matrices r and p when test = TRUE.

Examples

x <- matrix(rnorm(100), 20, 5); pdCor(x)

Plot an NDA Association Network

Description

Creates a printable static grid or interactive visNetwork network object. Assignment does not draw; printing the result draws it. The legacy igraph renderer remains available explicitly. Communities use a light qualitative node palette by default.

Usage

## S3 method for class 'nda'
plot(x, cuts = 0.3, interactive = FALSE, edgescale = 1,
    labeldist = -1.5, show_weights = FALSE, shapes = NULL,
    shape = "automatic", static.engine = c("grid", "igraph"),
    edge.color.links = TRUE, edge.colors = NULL,
    positive.color = "#009E73", negative.color = "#C62828",
    neutral.color = "grey65", positive.lty = 1, negative.lty = 1,
    neutral.lty = 1, edge.width.range = c(1, 6),
    edge.label.size = 10, edge.label.color = "#333333",
    edge.label.background = "#FFFFFFE6", edge.label.offset = 0.022,
    vertex.label.size = 12, vertex.label.color = "automatic",
    node.border.color = "#25313C",
    layout = "nicely", igraph_args = list(), visnetwork_args = list(), ...)

Arguments

Value

An object of class nda_plot; print it to render.

Examples

fit <- ndr(swiss)
p <- plot(fit, interactive = FALSE, show_weights = TRUE)
p

Plot an NDRLM Path Network

Description

Creates a layered, printable network of indicators, latent variables, and fitted regression links. A latent variable and its indicators share one community colour. A light qualitative node palette is used by default. Structural path labels and widths use standardized coefficients by default, including ridge and elastic-net fits. Legacy unnamed fits recover their response and standardization data from the fitted model.

Usage

## S3 method for class 'ndrlm'
plot(x, sig = 0.05, interactive = FALSE,
    show_edge_labels = TRUE, edge.label.size = 9,
    vertex.label.size = 11, edgescale = 1, shape = "automatic",
    standardized.paths = TRUE, layer.positions = NULL,
    node.lighten = 0.18, node.alpha = 0.90,
    static.engine = c("grid", "igraph"),
    positive.color = "#009E73", negative.color = "#C62828",
    loading.color = "grey60", positive.lty = 1, negative.lty = 1,
    loading.lty = 2, edge.width.range = c(1, 6),
    edge.label.color = "#333333",
    edge.label.background = "#FFFFFFE6", edge.label.offset = 0.022,
    node.border.color = "#25313C",
    igraph_args = list(), visnetwork_args = list(), ...)

Arguments

Value

An ndrlm_plot object; printing it renders the graph.

Examples

X <- as.data.frame(freeny.x)
Y <- data.frame(y = freeny.y)
p <- plot(ndrlm(Y, X, optimize = FALSE))
p

Predict NDA Scores

Description

Applies training feature standardization, indicator weights, retained centralities, latent-score scaling, and rotation to new rows.

Usage

## S3 method for class 'nda'
predict(object, newdata, ...)

Arguments

Value

A matrix with one predicted score column per latent variable. If newdata is NULL, training scores are returned.

Examples

fit <- ndr(swiss); predict(fit, swiss[1:4, ])

Predict from an NDRLM Model

Description

Transforms new independent variables with the fitted NDA model and predicts every fitted response.

Usage

## S3 method for class 'ndrlm'
predict(object, newdata = NULL, se.fit = FALSE,
    interval = c("none", "confidence", "prediction"), level = 0.95, ...)

Arguments

Value

A response-named data frame for ordinary predictions, or a response-named list when standard errors or intervals are requested.

Examples

X <- as.data.frame(freeny.x); Y <- data.frame(income = freeny.y)
fit <- ndrlm(Y, X, optimize = FALSE)
predict(fit, X[1:3, ])

Print an NDA Model

Description

Prints the NDA call, settings, modularity, community sizes, loadings, communalities, and dropped indicators.

Usage

## S3 method for class 'nda'
print(x, digits = getOption("digits"), ...)

Arguments

Value

x, invisibly.

Examples

fit <- ndr(swiss); print(fit)

Print an NDRLM Model

Description

Prints the reduction mode, regression engine, target metrics, and response-specific fits.

Usage

## S3 method for class 'ndrlm'
print(x, digits = getOption("digits"), ...)

Arguments

Value

x, invisibly.

Examples

X <- as.data.frame(freeny.x)
Y <- data.frame(y = freeny.y)
print(ndrlm(Y, X, optimize = FALSE))

NDRLM Residuals

Description

Extracts observed-minus-fitted residuals from every response model.

Usage

## S3 method for class 'ndrlm'
residuals(object, ...)

Arguments

Value

A data frame with one residual column per fitted response.

Examples

X <- as.data.frame(freeny.x)
Y <- data.frame(y = freeny.y)
fit <- ndrlm(Y, X, optimize = FALSE)
residuals(fit)

Semipartial Distance-Correlation Matrix

Description

Forms an asymmetric semipartial distance-correlation matrix from distance covariances.

Usage

spdCor(x, test = FALSE, adjust = "BH", alpha = NULL,
       parallel = FALSE, cores = 1L)

Arguments

Details

When the distance-covariance matrix is singular, a Moore-Penrose generalized inverse is used. The optional p-values use a t approximation and should be interpreted as screening diagnostics.

Value

A matrix, or a list with matrices r and p when test = TRUE.

Examples

x <- matrix(rnorm(100), 20, 5); spdCor(x)

Summarize an NDA Model

Description

Returns a printable summary without producing output during assignment.

Usage

## S3 method for class 'nda'
summary(object, digits = getOption("digits"), ...)

Arguments

Value

An object of class summary.nda containing settings, modularity, community sizes, loadings, communalities, uniquenesses, and inference statistics.

Examples

fit <- ndr(swiss); s <- summary(fit); s

Summarize an NDRLM Model

Description

Returns a printable regression and reduction summary without printing during assignment.

Usage

## S3 method for class 'ndrlm'
summary(object, digits = getOption("digits"), ...)

Arguments

Value

A summary.ndrlm object containing settings, variables, response metrics, fitted NDA objects, and regression fits.

Examples

X <- as.data.frame(freeny.x)
Y <- data.frame(y = freeny.y)
s <- summary(ndrlm(Y, X, optimize = FALSE))
s