dppca

dppca is an R package for differentially private principal component analysis (PCA) visualization. It estimates private PC directions, scree values, and two-dimensional score histograms, and uses these quantities to create loading plots, scree plots, score plots, variable plots, and biplots.

The package supports standalone analyses with dp_loading(), dp_scree(), and dp_score(), as well as a shared PCA workflow with dp_pca(). The fitting functions return S3 objects that can be inspected with summary() and visualized with plot().

Installation

Install the released package from CRAN:

install.packages("dppca")

To use the latest development code shown in the tutorials, install from GitHub:

# install.packages("remotes")
remotes::install_github("yejinjo0220/dppca")
library(dppca)

Quick start: one fit, five PCA visualizations

The integrated dp_pca() function estimates a private PC direction matrix once and reuses it for private scree and score estimation. It requires one scree estimator ("clipped", "pmwm", or "huber") and one score histogram estimator ("add" or "sparse").

library(dppca)
data("gau", package = "dppca")
X <- gau  # 1,000 observations, 20 numeric variables

set.seed(123)
pca_fit <- dp_pca(
  X,
  privacy = privacy_control(eps = 6, delta = 1e-4),
  scree = list(
    k = 5,
    method = "clipped",
    control = clipped_control(C_clip = 3)
  ),
  score = list(method = "add", bins = c(10, 10)),
  axes = c(1, 2)
)

pca_fit
summary(pca_fit)

set.seed(456)
pca_plots <- plot(pca_fit)  # Five DP panels

By default, plot(pca_fit) displays PVE, a score histogram, a loading vector plot, a variable plot, and a biplot.

Inspect the returned results

Component Description
pca_fit$directions Private PC directions (columns of an orthonormal matrix).
pca_fit$scree Estimated variances along the retained private directions.
pca_fit$pve Proportions of estimated variation over the retained components.
pca_fit$frame Privately estimated two-dimensional score frame.
pca_fit$hist Private pooled score histogram.
pca_fit$score_groups Per-group histograms, when a group is provided.
pca_fit$metadata Dimensions, selected axes, methods, and privacy allocations.
pca_fit$nonprivate Optional ordinary PCA reference; NULL by default.

You can choose individual panels and their display settings without refitting:

set.seed(456)
selected_plots <- plot(
  pca_fit,
  display = c("score", "biplot"),
  score = list(type = "sample"),
  biplot = list(alpha = 0, labels = TRUE),
  sampling = sampling_control(method = "uniform", sample_size = 300),
  center = TRUE,  # Shared by score and biplot (default)
  variables = 10,
  base_size = 12
)

# The individual ggplot objects are also stored:
selected_plots$private$plots$score
selected_plots$private$plots$biplot

The variables argument defaults to the 10 variables with the largest Euclidean norms of their private loading coefficients on the displayed two PC axes. The same selected variables are reused in loading, variable, and biplot panels.

Optional non-private comparison

To compare against ordinary PCA, add non_private = TRUE to the initial dp_pca() call and fit again. Then, plot(pca_fit) automatically draws the ordinary reference page first, followed by the DP page.

Standalone estimators and plots

The standalone workflows offer additional method and display choices.

Function What it estimates Plot interface
dp_loading() Private PC directions plot(fit, type = "vector"), "point", or "heatmap"
dp_scree() Private scree and PVE with one or more of clipped, PMWM, and Huber methods plot(fit, type = "scree") or "pve"
dp_score() Two-dimensional additive and/or sparse score histograms plot(fit, type = "histogram") or "sample"
dp_pca() Shared directions, scree, and histogram for five plots plot(fit, display = "all") or selected panel names

Private loading directions

loading_fit <- dp_loading(
  X,
  privacy = privacy_control(eps = 3, delta = 1e-4)
)

loading_fit$directions
loading_plot <- plot(loading_fit, type = "vector", variables = 10)

Scree / PVE

scree_fit <- dp_scree(
  X,
  k = 5,
  privacy = privacy_control(eps = 3, delta = 1e-4),
  method = "clipped",
  control = clipped_control(C_clip = 3)
)

summary(scree_fit)
plot(scree_fit, type = "pve")

For multiple methods, dp_scree() also accepts method = c("clipped", "pmwm", "huber") with suitable method-specific controls.

Score histograms and synthetic samples

score_fit <- dp_score(
  X,
  privacy = privacy_control(eps = 3, delta = 1e-4),
  bins = c(10, 10),
  method = c("add", "sparse")
)

summary(score_fit)
set.seed(456)
score_plots <- plot(
  score_fit,
  type = c("histogram", "sample"),
  center = FALSE,  # Optional: disable the default display centering
  sampling_control = sampling_control(method = "uniform", sample_size = 300)
)

By default, center = TRUE translates the displayed private score coordinates by the midpoint of the private frame. Set center = FALSE to leave those coordinates unshifted. This affects the plot, not the stored frame or histogram probabilities. Grouped score plots use the same center option.

Grouped PCA visualizations

A grouping column is excluded from PCA features and used to color synthetic score points and form group histograms. The gau_g dataset contains the same 20 numeric features as gau, plus a group label:

data("gau_g", package = "dppca")

set.seed(123)
group_fit <- dp_pca(
  gau_g,
  privacy = privacy_control(eps = 6, delta = 1e-4),
  scree = list(k = 5, method = "clipped",
               control = clipped_control(C_clip = 3)),
  score = list(method = "add", bins = c(10, 10)),
  group = "group"
)

set.seed(456)
plot(group_fit, display = c("score", "biplot"),
     score = list(type = "sample"), center = FALSE)

Standalone grouped score analysis is available with dp_score(..., group = "group").

Privacy note: For the grouped histogram privacy argument, group labels and the group partition are assumed public and fixed. Private sampled points are not original score records.

Privacy-budget allocation

privacy_control() specifies the total (eps, delta) and optional named split. If no split is given, each fitting function uses an equal allocation among its required components:

Fitting function Budget components Implicit allocation
dp_loading() loading 100%
dp_scree() loading, scree 50% / 50%
dp_score() loading, score 50% / 50%
dp_pca() loading, scree, score 1/3 each

For example, customize the integrated budget as follows:

privacy <- privacy_control(
  eps = 6,
  delta = 1e-4,
  split = c(loading = 0.2, scree = 0.4, score = 0.4)
)

privacy$total
privacy$budgets

The selected score epsilon allocation is further divided 35% for the private frame and 65% for the histogram; its delta allocation is assigned to the histogram.

Example datasets

Dataset Shape Description
gau 1,000 × 20 Five synthetic Gaussian clusters with numeric features V1–V20.
gau_g 1,000 × 21 The same observations and features, plus the group column.
vowel 990 × 14 British English vowel data: 10 acoustic measurements and four categorical descriptors.

The vowel dataset originates from the UCI Machine Learning Repository and is distributed under the terms described in its package documentation. See ?vowel for the data source and license. Dataset details and preprocessing examples are provided in the Getting Started tutorial.

Tutorials and theory

The practical tutorials are:

For the mathematics, see PCA Background, DP Directions Methodology, DP Scree Methodology, DP Score Methodology, and DP PCA Visualization Methodology.

For complete argument descriptions, use the R help pages: ?dp_loading, ?dp_scree, ?dp_score, ?dp_pca, and the corresponding plot.* methods. The development implementation is available on GitHub.

Online Shiny app

Explore the dppca visualizations interactively in your browser, without installing R:

Launch the online DP-PCA Shiny app

See the Shiny App guide for the available analyses, data options, and privacy considerations.

References