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Soft topic membership from the spectral embedding

Source: R/text_topics.R
hg_membership.Rd

Turns a hard partition into a membership of every document in every topic. The documents are placed in the spectral embedding of the hypergraph Laplacian that hg_cluster() cuts (the same type and edge_weights), each topic's centre is the mean position of its documents, and the membership of a document in a topic is the fuzzy c-means weight with fuzziness 2: the inverse squared distance to that centre, normalised over the topics. A document at a centre has membership 1 there; a document halfway between two centres has 0.5 in each. The values sum to one over the topics, so their level depends on the number of topics k: the uniform value is 1 / k, and with many topics even a clearly assigned document has a modest membership. Read them as ratios between topics (a document with 0.15 and 0.11 in two topics is 1.4 times closer to the first), not as probabilities of belonging.

Usage

hg_membership(
  hg,
  clusters,
  type = c("zhou", "random_walk"),
  edge_weights = NULL
)

# S3 method for class 'hypernets_membership'
plot(x, ...)

Arguments

hg

The document hypergraph the clustering was computed on.

clusters

The tidy table returned by hg_cluster() (columns node, cluster), or a named vector of cluster labels.

type, edge_weights

Passed to hg_cluster() to reproduce the embedding the partition was cut in (defaults as there).

x

A table returned by the verb.

...

Unused; for S3 consistency.

Value

A base data.frame of class hypernets_membership, one row per document and topic: node, cluster (the hard label), topic, membership (rows of one document sum to one). plot() draws, per topic, the distribution of its documents' membership in it: a topic whose documents sit near 1 is compact, one whose documents spread towards 0.5 overlaps its neighbours. Raises hypernets_bad_input for unknown node names.

References

Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum.

Examples

hg <- text_hypergraph(c(
  cooking_1 = "simmer the soup with onions and carrots",
  cooking_2 = "this soup recipe needs salt on a cold night",
  space_1 = "the telescope revealed a distant galaxy and stars",
  space_2 = "astronomers aimed the telescope at the stars all night"
), stop_words = c("the", "with", "and", "a", "this", "at", "on", "all"))
topics <- hg_cluster(hg, k = 2, seed = 1)
hg_membership(hg, topics)
#>        node   cluster     topic  membership
#> 1 cooking_1 Cluster 1 Cluster 1 0.981830203
#> 2 cooking_1 Cluster 1 Cluster 2 0.018169797
#> 3 cooking_2 Cluster 1 Cluster 1 0.971963064
#> 4 cooking_2 Cluster 1 Cluster 2 0.028036936
#> 5   space_1 Cluster 2 Cluster 1 0.005819465
#> 6   space_1 Cluster 2 Cluster 2 0.994180535
#> 7   space_2 Cluster 2 Cluster 1 0.007346161
#> 8   space_2 Cluster 2 Cluster 2 0.992653839