Struct EmbeddingGeometry 

pub struct EmbeddingGeometry {
    pub n_rows: usize,
    pub h: usize,
    pub common_mode_cos: f32,
    pub mean_pairwise_cos: f32,
    pub eff_rank_raw: f32,
    pub eff_rank_centered: f32,
    pub eff_rank_double_centered: f32,
    pub max_abs_corr: f32,
    pub max_vif: f32,
}

Geometry of an embedding table, measured once and handed to the caller to report. A struct of measured scalars; nothing here decides anything.

Fields

n_rows: usize

Rows measured (units: cells, genes, modules).

h: usize

Columns (the embedding dimension h).

common_mode_cos: f32

Mean |cos| between a row and the mean direction over rows. → 1 means every row is essentially the same direction plus a small residual; → 0 means the rows are spread about the origin.

mean_pairwise_cos: f32

SIGNED mean cosine over distinct row pairs, zero-norm rows excluded. Computed in closed form from the sum of unit rows, so it is one O(n·h) pass rather than n² pairs. A balanced cloud reads −1/(n−1), not 0.

eff_rank_raw: f32

Participation ratio (Σλ)² / Σλ² of the uncentered Gram EᵀE/n, in [1, h].

READ THIS AS VARIANCE CONCENTRATION, NOT USEFUL DIMENSIONALITY. A low value says the variance is carried by few directions; it does not say the remaining dims are noise. On real fits this has read under 3 of 16 while the dims beyond the first few still recovered cell type well above a null. Low-variance directions can carry ample signal, and reading this field as a capacity estimate is a mistake that has already been made once.

eff_rank_centered: f32

Same, for the column-centered Gram. Much larger than Self::eff_rank_raw ⇒ the apparent low rank is a mean offset (a common mode), not a genuine collapse.

eff_rank_double_centered: f32

Same, after DOUBLE centering: each row’s mean across its h columns removed, then each column’s mean. A log-simplex dictionary is log β_gk = (per-gene share) + (module/topic content) − (per-topic partition), and the two offsets dominate its variance: column centering leaves the per-gene share, row centering leaves the per-topic constant, and either alone reads near 1 with a huge Self::max_vif. Removing both leaves the topic-specific content, which is what “how many directions do the topics use” means for such a table. For an embedding it removes a per-unit depth-like offset the same way. Row centering projects out the all-ones direction, so a genuinely full-rank table reads h − 1 here, not h. No VIF is reported for it: the row-centered columns sum to zero, so their correlation matrix is singular by construction.

max_abs_corr: f32

Largest |correlation| between two distinct dims.

max_vif: f32

Largest variance-inflation factor diag(C⁻¹) over dims (1 = orthogonal). Above ~5, per-dim readouts stop being trustworthy on their own.

Trait Implementations

impl Clone for EmbeddingGeometry

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for EmbeddingGeometry

impl Debug for EmbeddingGeometry

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for EmbeddingGeometry

fn default() -> Self

Returns the “default value” for a type.

impl PartialEq for EmbeddingGeometry

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for EmbeddingGeometry