Create iterated graph-geodesic iKNN graphs — create.iterated.iknn.graphs • dgraphs

Constructs G0 with create.iknn.graphs(), then constructs G1, G2, ..., Gm by repeatedly applying create.geodesic.iknn.graph() to each graph in the k.values sequence. This implements the iterated nerve rule

$$\{i,j\} \in E(G_{t+1}) \iff kNN_{G_t}(i) \cap kNN_{G_t}(j) \ne \emptyset,$$

with edge length

$$\ell_{t+1}(i,j) = d_{G_t}(i,j).$$

Usage

create.iterated.iknn.graphs(
  X,
  k.values,
  n.iterations = 3L,
  small.component = c("error", "truncate"),
  max.path.edge.ratio.deviation.thld = 0,
  path.edge.ratio.percentile = 0.5,
  threshold.percentile = 0,
  pca.dim = 100,
  variance.explained = 0.99,
  verbose = TRUE,
  knn.cache.path = NULL,
  knn.cache.mode = c("none", "read", "write", "readwrite")
)

Arguments

X: Numeric matrix with rows as observations and columns as features.
k.values: Strictly increasing integer vector of neighborhood sizes, each between 1 and n - 1.
n.iterations: Non-negative integer number of geodesic rebuilds after G0. The default 3 returns G0, G1, G2, and G3.
small.component: Component-size policy forwarded to every geodesic rebuild.
max.path.edge.ratio.deviation.thld, path.edge.ratio.percentile, threshold.percentile: Initial G0 pruning arguments forwarded to create.iknn.graphs(). The default deviation and quantile thresholds are zero so that G0 is the unpruned iKNN 1-skeleton.
pca.dim, variance.explained, verbose, knn.cache.path, knn.cache.mode: Additional arguments forwarded to create.iknn.graphs() for the initial G0 construction.

Value

A list of class "iterated_iknn_graphs" with entries:

k.values: Integer vector of requested k values.
n_iterations: Number of geodesic rebuilds after G0.
initial_graphs: The "iknn_graphs" object returned by create.iknn.graphs() for G0.
graphs: Nested list named G0, G1, ...; each entry is a named list of graph objects for k.values.
summary: Data frame with one row per iteration and k.

Examples

set.seed(1)
X <- matrix(rnorm(30), ncol = 2)
out <- create.iterated.iknn.graphs(X, k.values = seq.int(2, 3), n.iterations = 1,
    verbose = FALSE)
out$summary
#>   iteration graph k n_vertices n_edges n_ccomp mean_degree min_degree
#> 1         0    G0 2         15      37       1    4.933333          3
#> 2         0    G0 3         15      58       1    7.733333          5
#> 3         1    G1 2         15      37       1    4.933333          3
#> 4         1    G1 3         15      58       1    7.733333          5
#>   max_degree
#> 1          8
#> 2         10
#> 3          8
#> 4         10