Constructs low-dimensional embeddings from a Higher-Order Network (HON) that preserve higher-order dependencies. Uses exponentially-decaying matrix powers of the HON transition matrix followed by truncated SVD.
Arguments
- hon
A
net_honobject frombuild_hon, or a square weighted adjacency matrix.- dim
Integer. Embedding dimension (default 32).
- max_power
Integer. Maximum walk length for neighborhood computation (default 10). Higher values capture longer-range structure.
Value
An object of class net_honem with components:
- embeddings
Numeric matrix (n_nodes x dim) of node embeddings.
- nodes
Character vector of node names.
- singular_values
Numeric vector of top singular values.
- explained_variance
Proportion of variance explained.
- dim
Embedding dimension used.
- max_power
Maximum power used.
- n_nodes
Number of nodes embedded.
Details
HONEM is parameter-free and scalable — no random walks, skip-gram, or hyperparameter tuning required.
References
Saebi, M., Ciampaglia, G. L., Kazemzadeh, S., & Meyur, R. (2020). HONEM: Learning Embedding for Higher Order Networks. Big Data, 8(4), 255–269.
Examples
# \donttest{
trajs <- list(c("A","B","C","D"), c("A","B","D","C"),
c("B","C","D","A"), c("C","D","A","B"))
hon <- build_hon(trajs, max_order = 2)
emb <- build_honem(hon, dim = 4)
print(emb)
#> HONEM: Higher-Order Network Embedding
#> Nodes: 4
#> Dimensions: 3
#> Max power: 10
#> Variance explained: 94.6%
plot(emb)
# }