Embedding of a higher-order network (HONEM)

Low-dimensional node embedding of a higher-order network that preserves its higher-order dependencies: exponentially decaying powers of the network's transition matrix, followed by a truncated singular value decomposition.

Usage

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

Arguments

hon

A net_hon from hon(), or a square weighted adjacency matrix.

dim

Integer. Embedding dimension, capped at the number of nodes minus one. Default 32.

max_power

Integer. Longest walk length in the neighbourhood matrix. Default 10.

Value

A net_honem object. Read it with hg_get(): the node coordinates (what = "embeddings", the default) or the variance per dimension ("variance").

References

Saebi, M., Ciampaglia, G. L., Kaplan, L. M., & Chawla, N. V. (2020). HONEM: Learning embedding for higher order networks. Big Data, 8(4), 255–269. doi:10.1089/big.2019.0169

See also

hon()

Examples

seqs <- list(c("a", "b", "c", "a", "b", "c"), c("x", "b", "d", "x", "b", "d"),
             c("a", "b", "c", "a", "b", "c"), c("x", "b", "d", "x", "b", "d"))
emb <- honem(hon(seqs, max_order = 2), dim = 2)
hg_get(emb)
#>     node      dim1          dim2
#> 1      a -0.366535 -4.082483e-01
#> 2 a -> b -0.428539 -4.082483e-01
#> 3      b -0.428539  2.578122e-15
#> 4      c -0.366535 -4.082483e-01
#> 5      d -0.366535  4.082483e-01
#> 6      x -0.366535  4.082483e-01
#> 7 x -> b -0.428539  4.082483e-01