build_honem: Build HONEM Embeddings for Higher-Order Networks

In Nestimate: Network Estimation, Bootstrap, and Higher-Order Analysis

Build HONEM Embeddings for Higher-Order Networks

Description

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.

Usage

build_honem(hon, dim = 32L, max_power = 10L)

Arguments

hon	A net_hon object from build_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.

Details

HONEM is parameter-free and scalable — no random walks, skip-gram, or hyperparameter tuning required.

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.

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

seqs <- list(c("A","B","C","D"), c("A","B","C","A"), c("B","C","D","A"))
hem <- build_honem(build_hon(seqs, max_order = 2), dim = 2)


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)
plot(emb)

Nestimate documentation built on April 20, 2026, 5:06 p.m.