generate_projection_indexes: Generate projection index sets

In focus: Online Changepoint Detection in Univariate and Multivariate Data Streams

Generate projection index sets

Description

Generates projection index sets for high-dimensional multivariate detectors using circular combinations.

Usage

generate_projection_indexes(D, p)

Arguments

D	Integer. Total number of dimensions.
p	Integer. Projection subset size (number of dimensions per projection).

Details

This function generates systematic projection sets for use with multivariate detectors. The circular combination approach ensures good coverage of the dimensional space while keeping the number of projections manageable.

Value

A list of integer vectors. Each element is a vector of 0-based column indices representing one projection.

Examples

# Generate 2-dimensional projections from 5 dimensions
proj <- generate_projection_indexes(D = 5, p = 2)
print(proj)

# Use with multivariate detector
det <- detector_create(type = "multivariate", dim_indexes = proj)
set.seed(42)
p <- 5

# Create data: changepoint at t=1000
Y_multi <- rbind(
    matrix(rnorm(1000 * p, mean = -1, 1), ncol = p),
    matrix(rnorm(500 * p, mean = 1.2), ncol = p)
)

# Full multivariate detection
system.time(
res_multi <- focus_offline(Y_multi, threshold = Inf,
                           type = "multivariate", family = "gaussian")
)

# Low-dimensional projection approximation
dim_indexes <- generate_projection_indexes(5, 2)
system.time(
res_multi_approx <- focus_offline(Y_multi, threshold = Inf,
                                  type = "multivariate", family = "gaussian",
                                  dim_indexes = dim_indexes)
)

# Verify similarity
all.equal(res_multi$stat, res_multi_approx$stat)

focus documentation built on March 30, 2026, 5:08 p.m.