Getting Started with dppca

This guide covers the essentials for getting started with dppca: installing and loading the package, understanding its example datasets, preparing your own data, and allocating privacy budgets with privacy_control(). If you are looking for a particular visualization, use the guide below to choose a tutorial and its corresponding theory article.

Choose a starting point

The tutorials explain how to use dppca in R, while the methodology articles describe the statistical concepts and methods. For an introduction to ordinary PCA, see PCA Background.

What you want to do	Tutorial	Methodology
Explore private PC directions and their coefficients	DP Loading Plot	DP Directions Methodology
Examine scree values and proportions of variance explained (PVE)	DP Scree Plot	DP Scree Methodology
Visualize private score distributions and compare groups	DP Score Plot	DP Score Methodology
Explore loading, scree, score, variable, and biplot views in one workflow	DP PCA Visualization	DP PCA Visualization Methodology

For complete argument descriptions and return values, see Functions.

1. Install and load the package

Install the released version of dppca from CRAN:

install.packages("dppca")

Alternatively, install the development version from GitHub:

install.packages("remotes")  # Only needed once
remotes::install_github("yejinjo0220/dppca")

Once installed, load the package:

library(dppca)

2. Prepare your input data

In dppca, rows represent observations and columns represent variables. Numeric features are used for PCA. For functions supporting group (such as dp_score() and dp_pca()), a data frame may also contain categorical columns; the selected grouping column is excluded from PCA features. Other non-numeric columns are not included in the PCA calculation.

The private PCA method implemented in dppca is based on pairwise differences of observations and therefore does not require explicit centering. Also, if standardization is needed, it should be performed before applying dppca. When standardization involves estimating parameters from sensitive data, the preprocessing must satisfy differential privacy, and its privacy budget must be included in the total privacy budget.

3. Explore the Example Datasets

The dppca package provides several example datasets for demonstrating its functions. These include numeric datasets and datasets containing categorical variables for grouped visualizations.

Dataset	Rows	Columns	What it contains
`gau`	1,000	20	Numeric variables `V1`–`V20` from five synthetic Gaussian clusters, with 200 observations per cluster.
`gau_g`	1,000	21	The same 20 numeric variables plus the character label `group`, with values `group1`–`group5`.
`vowel`	990	14	Ten acoustic measurements and four categorical columns describing British English vowel observations.

The Gaussian clusters differ in means and covariance scales. gau_g adds grouping labels to the observations in gau; it is not a separate sample.

3.1. Gaussian data

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

dim(gau)
#> [1] 1000   20
dim(gau_g)
#> [1] 1000   21
head(gau[, 1:4, drop = FALSE])
#>           V1         V2          V3         V4
#> 1  0.7019527 -0.2136231 -0.36868434 -0.8423263
#> 2  0.3361815  1.1978761  0.97822807  0.1018881
#> 3  0.7498257  0.2318031 -0.30707361 -0.8979258
#> 4 -0.8008823 -0.5028415 -0.05840928  1.3939254
#> 5 -0.1227414  0.6304571  0.35253375 -2.4865239
#> 6  0.6642886  0.9572975 -0.18232763  0.4012941
table(gau_g$group)
#> 
#> group1 group2 group3 group4 group5 
#>    200    200    200    200    200

The variables V1–V20 are numeric features. The group column in gau_g identifies five groups and can be used as a categorical label in analyses that support grouping.

For more details about the datasets, see the documentation for gau and gau_g.

3.2. Vowel data

The vowel dataset contains 990 observations of spoken British English vowels from 15 speakers, covering 11 vowel categories. Each observation consists of ten numeric acoustic measurements (F0–F9) and four categorical variables (Split, Speaker, Sex, and Class).

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

numeric_columns <- vapply(vowel, is.numeric, logical(1))
dim(vowel)
#> [1] 990  14
names(vowel)[numeric_columns]
#>  [1] "F0" "F1" "F2" "F3" "F4" "F5" "F6" "F7" "F8" "F9"
names(vowel)[!numeric_columns]
#> [1] "Split"   "Speaker" "Sex"     "Class"
table(vowel$Class)
#> 
#>  0  1  2  3  4  5  6  7  8  9 10 
#> 90 90 90 90 90 90 90 90 90 90 90

The variables in the dataset are summarized below.

Columns	Role
`F0`–`F9`	Ten numeric acoustic features used for PCA.
`Split`	Training/test-set label.
`Speaker`	Speaker identifier, with 15 levels.
`Sex`	Speaker descriptor.
`Class`	Vowel category, with 11 levels. This variable can be used for grouped score visualizations.

For more details about the dataset, see the documentation for vowel.

4. Set and Allocate the Privacy Budget

The privacy_control() function specifies the privacy budget for PCA estimation in dppca. The privacy parameters, eps and delta, are allocated to three components:

Component	Purpose
`loading`	Estimation of private principal component directions.
`scree`	Estimation of private scree values and PVE.
`score`	Construction of private score visualizations.

The dppca package provides three functions for individual analyses: dp_loading(), dp_scree(), and dp_score(). The dp_pca() function combines these analyses into a single workflow. Since these functions involve different estimation steps, the required privacy budget components depend on the function used.

4.1. Default privacy budget allocation

The total privacy budget can be specified using eps and delta:

privacy <- privacy_control(
  eps = 6,
  delta = 1e-4
)

When split is omitted, the fitting function automatically divides the total budget equally among its required components.

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

For example, when the specified total budget is eps = 6 and delta = 1e-4:

dp_loading() allocates the entire budget to direction estimation.
dp_scree() and dp_score() allocate epsilon 3 and delta 5e-5 to each of their two components.
dp_pca() allocates epsilon 2 and delta 1e-4 / 3 to each of its three components.

The total budget and its allocations can be inspected using:

privacy$total
#>   eps delta 
#> 6e+00 1e-04
privacy$budgets
#> $loading
#>          eps        delta 
#> 2.000000e+00 3.333333e-05 
#> 
#> $scree
#>          eps        delta 
#> 2.000000e+00 3.333333e-05 
#> 
#> $score
#>          eps        delta 
#> 2.000000e+00 3.333333e-05

The total field contains the overall budget, and budgets contains its component allocations.

4.2. Customize the budget allocation

To change the default allocation, use the split argument to specify the proportion of the total budget assigned to each component. The proportions must be positive, named, and sum to one. The same proportions are applied to both epsilon and delta.

For example, to allocate more budget to scree and score estimation in dp_pca():

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

pca_privacy_custom$budgets
#> $loading
#>     eps   delta 
#> 1.20000 0.00002 
#> 
#> $scree
#>     eps   delta 
#> 2.40000 0.00004 
#> 
#> $score
#>     eps   delta 
#> 2.40000 0.00004

Similarly, for dp_score(), a different allocation can be specified as follows:

score_privacy_custom <- privacy_control(
  eps = 6,
  delta = 1e-4,
  split = c(loading = 0.4, score = 0.6)
)

score_privacy_custom$budgets
#> $loading
#>     eps   delta 
#> 2.40000 0.00004 
#> 
#> $score
#>     eps   delta 
#> 3.60000 0.00006

4.3. Specify individual component budgets

Alternatively, epsilon and delta can be specified separately for each component, without using a total budget or split.

pca_privacy_absolute <- privacy_control(
  loading = c(eps = 2, delta = 2e-5),
  scree   = c(eps = 3, delta = 3e-5),
  score   = c(eps = 5, delta = 5e-5)
)

pca_privacy_absolute$total
#>   eps delta 
#> 1e+01 1e-04

In this example, the total budget is epsilon 10 and delta 1e-4. Unlike the proportional allocation approach, this allows epsilon and delta to have different allocation proportions.

The total-budget and individual-component approaches should not be combined in a single call.

5. Next steps

With the package installed, the input data prepared, and the privacy budget specified, you are ready to explore differentially private PCA visualizations. Start with the DP Loading Plot Tutorial to estimate and visualize private PC directions, or choose another tutorial from the overview.

Next: DP Loading Plot
Tutorial overview: Choose a starting point