Joint NMF clustering with an auxiliary vertex relation

Implements the two multi-view objectives in Section 6.3.2 of Hayashi et al. (2020). method = "joint" is Eq. 18 (J-NMF), jointly factorizing the edge-dependent incidence X and a vertex relation S. method = "joint_symmetric" is Eq. 19 (JS-NMF), jointly factorizing the representative-digraph similarity T = I - L and S. The paper uses a symmetric patent-citation indicator for S; any finite non-negative node-by-node relation matrix can be supplied here.

Usage

hg_joint_cluster(
  hg,
  relations,
  k,
  method = c("joint", "joint_symmetric"),
  alpha = 1,
  beta = 1,
  gamma = 1,
  type = c("random_walk", "zhou"),
  edge_weights = NULL,
  nstart = 10L,
  seed = NULL,
  max_iter = 500L,
  tol = 1e-06
)

Arguments

hg

A connected net_hg.

relations

A non-negative n_nodes by n_nodes numeric matrix. If it has dimnames, rows and columns are reordered to hg$nodes.

k

Number of clusters, between 2 and n_nodes - 1.

method

"joint" for J-NMF (Eq. 18) or "joint_symmetric" for JS-NMF (Eq. 19).

alpha

Non-negative symmetry penalty in JS-NMF.

beta

Non-negative agreement penalty between the content and relation vertex factors.

gamma

Non-negative weight of the auxiliary-relation loss.

type, edge_weights

Laplacian inputs for JS-NMF.

nstart

Number of random initializations.

seed

Optional integer initialization seed.

max_iter

Maximum multiplicative-update iterations.

tol

Relative objective tolerance.

Value

A net_hg_cluster object. Its $embedding is the fitted vertex factor M; $params contains all fitted factors, the objective trace and convergence diagnostics.

References

Hayashi, K., Aksoy, S. G., Park, C. H., & Park, H. (2020). Hypergraph random walks, Laplacians, and clustering. CIKM 2020, 495-504. doi:10.1145/3340531.3412034