Introduction
Creating synthetic datasets is essential for testing algorithms and validating results in Formal Concept Analysis. However, simple uniform random generation (where every cell has a fixed probability of being 1) often fails to capture the structure of real-world data.
fcaR now implements advanced generation methods,
allowing for more realistic and controllable simulations.
1. Dirichlet Distribution for Realistic Data
Real-world contexts often have “clumpy” or “sparse” rows. Some objects have many attributes, while others have very few. A uniform distribution creates rows that are all roughly the same size (Binomial distribution).
To mimic real variability, we use a Dirichlet Distribution to sample the probability of an object having attributes.
# Uniform Context (Standard)
# All objects have roughly 20% of attributes
fc_uni <- RandomContext(n_objects = 20, n_attributes = 10, density = 0.2, distribution = "uniform")
# Dirichlet Context (Realistic)
# Some objects will be empty, some full, some in between.
# alpha = 0.1 -> High skewness (Very sparse or very dense rows)
# alpha = 1.0 -> Uniform distribution of row sizes
fc_dir <- RandomContext(n_objects = 20, n_attributes = 10, distribution = "dirichlet", alpha = 0.2)
# Compare Row Sums
barplot(rowSums(fc_uni$incidence()), main = "Uniform: Row Sums", ylim = c(0, 10))
2. Randomization via Edge Swapping
When performing statistical analysis on a concept lattice, we often ask: “Is this pattern significant, or could it happen by chance?”.
To answer this, we need to compare our context against a “random null model”. The most robust null model is a random matrix that preserves:
- The number of attributes per object (Row sums).
- The frequency of each attribute (Column sums).
This is achieved by Edge Swapping (also known as the Curveball algorithm). It swaps connections without altering the marginal sums.
data(planets)
fc <- FormalContext$new(planets)
# Original Marginals
orig_col_sums <- colSums(fc$incidence())
print(orig_col_sums)
#> small medium large near far moon no_moon
#> 5 2 2 4 5 7 2
# Randomize using Swap
fc_random <- randomize_context(fc, method = "swap")
# Verify Marginals are preserved
new_col_sums <- colSums(fc_random$incidence())
print(new_col_sums)
#> small medium large near far moon no_moon
#> 5 2 2 4 5 7 2
# But the structure is different
print(all(fc$incidence() == fc_random$incidence()))
#> [1] FALSEThis allows you to generate 1000 randomized versions of your data and check if your concept stability or support is statistically significant.