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Principal Component Analysis for Vertically Partitioned Data

Source: R/ds.vertPCA.R
ds.vertPCA.Rd

Performs PCA on vertically partitioned data using the privacy-preserving correlation matrix computed via Homomorphic Encryption.

Usage

ds.vertPCA(
  data_name = NULL,
  variables = NULL,
  n_components = NULL,
  cor_result = NULL,
  log_n = 12,
  log_scale = 40,
  datasources = NULL
)

Arguments

data_name

Character string. Name of the (aligned) data frame on each server. Ignored if cor_result is provided.

variables

A named list where each name corresponds to a server name and each element is a character vector of variable names from that server. Ignored if cor_result is provided.

n_components

Integer. Number of principal components to return. Default is NULL (returns all).

cor_result

An existing ds.cor object from ds.vertCor. If provided, the MHE protocol is NOT re-run; the PCA is computed directly from this correlation matrix. This avoids running the expensive MHE protocol twice when you already have the correlation.

log_n

Integer. CKKS ring dimension parameter for MHE. Default is 12. Ignored if cor_result is provided.

log_scale

Integer. CKKS precision parameter for MHE. Default is 40. Ignored if cor_result is provided.

datasources

DataSHIELD connection object or list of connections. If NULL, uses all available connections. Ignored if cor_result is provided.

Value

A list with class "ds.pca" containing:

  • loadings: Matrix of variable loadings (n_vars x n_components)

  • eigenvalues: Eigenvalues for each component

  • variance_pct: Percentage of variance explained

  • cumulative_pct: Cumulative percentage explained

  • var_names: Variable names

  • n_obs: Number of observations

  • correlation: The correlation matrix used for PCA

Details

This function performs PCA using the correlation matrix obtained via Multiparty Homomorphic Encryption (MHE). The approach is:

  1. Compute the privacy-preserving correlation matrix using ds.vertCor (or reuse an existing one via the cor_result parameter)

  2. Perform eigen decomposition on the correlation matrix

  3. Extract loadings (eigenvectors) and eigenvalues

Since PCA on standardized data is equivalent to eigen decomposition of the correlation matrix, this gives correct loadings and variance explained.

Note on scores: This function does NOT return principal component scores because computing scores would require access to the raw data. If you need scores, you would need to compute them on each server using the loadings and aggregate the results (which is a separate operation).

Interpreting Loadings

Each column of the loadings matrix represents a principal component. The values show how much each variable contributes to that component:

  • Values close to 1 or -1 indicate strong contribution

  • Values close to 0 indicate weak contribution

  • Sign indicates direction of relationship

Security

This function inherits all security properties from ds.vertCor:

  • Individual observations are never exposed

  • The client cannot decrypt without all servers cooperating

  • Only aggregate statistics (correlation matrix) are revealed

See also

ds.vertCor for correlation analysis

Examples

if (FALSE) { # \dontrun{
vars <- list(
  server1 = c("age", "weight"),
  server2 = c("height", "bmi")
)

pca_result <- ds.vertPCA("D_aligned", vars, n_components = 3)

# Or reuse an existing correlation result (avoids running MHE again):
cor_result <- ds.vertCor("D_aligned", vars)
pca_result <- ds.vertPCA(cor_result = cor_result, n_components = 3)

# View variance explained
print(pca_result)

# Biplot of loadings for first two PCs
plot(pca_result$loadings[, 1], pca_result$loadings[, 2],
     xlim = c(-1, 1), ylim = c(-1, 1),
     xlab = paste0("PC1 (", round(pca_result$variance_pct[1], 1), "%)"),
     ylab = paste0("PC2 (", round(pca_result$variance_pct[2], 1), "%)"))
text(pca_result$loadings[, 1], pca_result$loadings[, 2],
     labels = pca_result$var_names, pos = 3)
abline(h = 0, v = 0, lty = 2)
} # }