sfa_project: Semantic Projection onto Bipolar Axes

In semanticfa: Semantic Factor Analysis of Language Model Embeddings

Semantic Projection onto Bipolar Axes

Description

Places each item on a continuous scale defined by two opposing text poles (Grand et al. 2022). An axis is built as the direction from a "low" pole to a "high" pole (e.g. mild -> severe, passive -> active); every item is then projected onto that line. Unlike factor grouping (which says which construct an item belongs to), projection says where along a named dimension the item falls — useful for checking that a scale's items span a full range of intensity/severity, ordering items, or locating items on an interpretable axis.

Usage

sfa_project(
  x,
  axes,
  normalize = TRUE,
  pole_embeddings = NULL,
  embed = NULL,
  model = NULL
)

Arguments

x	An "sfa" object, or a numeric item-embedding matrix (n_items x dim) with item rownames.
axes	A named list of axes. Each element defines the two poles, as either a named character vector c(low = "...", high = "...") or a list list(low = c(...phrases...), high = c(...phrases...)) (multiple phrases per pole are averaged, which is more robust).
normalize	Logical. If TRUE (default), rescale each item's projection so 0 = the low pole and 1 = the high pole (values may fall outside 0 to 1). The 0-to-1 pole convention is this package's convenience, not from Grand et al., whose projections are unbounded inner products. If FALSE, return the raw cosine projection in the range -1 to 1.
pole_embeddings	Optional named list (one entry per axis) of precomputed pole embeddings, each a list with low and high numeric matrices/vectors. Use when x carries no embedding backend.
embed, model	Embedding backend/model for the pole text. Default to the backend/model recorded on x.

Details

This uses the cosine of each item against the pole-difference axis (a length-normalized variant of Grand et al.'s raw inner-product projection), so scores are comparable across items of differing embedding norm. As in Grand et al., a bipolar (two-pole) axis is what gives a diagnostic direction; a single pole is far less informative.

Value

An object of class "sfa_projection": a list with the item-by-axis scores matrix, the axis definitions, and normalize.

References

Grand, G., Blank, I. A., Pereira, F., & Fedorenko, E. (2022). Semantic projection recovers rich human knowledge of multiple object features from word embeddings. Nature Human Behaviour, 6(7), 975–987. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1038/s41562-022-01316-8")}

See Also

sfa_anchor

Examples

data(big5)
fit <- sfa(
  data.frame(code = big5$codes, item = big5$items,
             factor = big5$factors, scoring = big5$scoring),
  embeddings = big5$embeddings, scoring = big5$scoring, nfactors = 5)

# project items onto a neuroticism -> extraversion axis using precomputed poles
poles <- list(NtoE = list(
  low  = big5$embeddings[big5$factors == "Neuroticism", ],
  high = big5$embeddings[big5$factors == "Extraversion", ]))
pr <- sfa_project(fit, axes = list(NtoE = c(low = "neurotic", high = "extraverted")),
                  pole_embeddings = poles)
head(round(pr$scores, 2))

## Not run: 
# with a live embedding backend, name the poles in words and they are embedded:
sfa_project(fit, axes = list(severity = c(low = "mild", high = "severe")))

## End(Not run)

semanticfa documentation built on Sept. 2, 2026, 1:07 a.m.