Differentially Private Principal Component Analysis and Visualization

Provides tools for differentially private principal component analysis (PCA) and visualization. Includes private principal component directions, scree and proportion of variance explained (PVE) estimates, and two-dimensional private score histograms with synthetic sampled points. Supports additive and sparse histogram mechanisms, group-wise score visualizations, and optional non-private comparisons. An integrated workflow produces loading plots, scree plots, score plots, variable plots, and biplots from shared private PCA estimates. An interactive 'shiny' application is also provided. Private direction estimation is based on Kim and Jung (2025) . Private scree estimation draws on Dwork and Roth (2014) , Ramsay and Spicker (2025) , and Yu, Ren and Zhou (2024) . Private score frames use unbounded quantile mechanisms from Durfee (2023) . Private score histograms use methods related to Wasserman and Zhou (2010) and Karwa and Vadhan (2018) .

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

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.

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:

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

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:

• Getting Started: installation, datasets, preprocessing, and privacy budgets.
• DP Loading Plot: private PC directions and loading displays.
• DP Scree Plot: clipped, PMWM, and Huber estimation; scree and PVE.
• DP Score Plot: histogram methods, synthetic points, and grouped scores.
• DP PCA Visualization: five plots built from a shared fit.

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

• Kim, M. and Jung, S. (2025). Robust and Differentially Private Principal Component Analysis. Statistical Analysis and Data Mining: An ASA Data Science Journal, 18(6), e70053. https://doi.org/10.1002/sam.70053
• Dwork, C. and Roth, A. (2014). The Algorithmic Foundations of Differential Privacy. Foundations and Trends in Theoretical Computer Science, 9(3–4), 211–407. https://doi.org/10.1561/0400000042
• Ramsay, K. and Spicker, D. (2025). Improved subsample-and-aggregate via the private modified winsorized mean. arXiv:2501.14095.
• Yu, M., Ren, Z., and Zhou, W.-X. (2024). Gaussian differentially private robust mean estimation and inference. Bernoulli, 30(4), 3059–3088.
• Nissim, K., Raskhodnikova, S., and Smith, A. (2007). Smooth Sensitivity and Sampling in Private Data Analysis. In STOC ’07, 75–84. https://doi.org/10.1145/1250790.1250803
• Wasserman, L. and Zhou, S. (2010). A Statistical Framework for Differential Privacy. Journal of the American Statistical Association, 105(489), 375–389. https://doi.org/10.1198/jasa.2009.tm08651
• Karwa, V. and Vadhan, S. P. (2017). Finite Sample Differentially Private Confidence Intervals. arXiv:1711.03908.