Table 1 Notation and symbols

c, d, e

Objects in set C

Z

Number of unique triplets in C

F(c)

High-dimensional feature vector

X(c)

Embedding vector

Λ^cd

Pairwise relationship in ℝ^N

δ ^cd

Pairwise relationship in ℝⁿ

Δ(c, d, e)

Triangle relationship (Defn. 1)

ψ^ES(ℝⁿ)

Embedding strength (Defn. 2)

${\widehat{ℝ}}^n$

True embedding (Defn. 3)

${\widehat{\delta }}^{cd}$

Pairwise relationship in ${\widehat{ℝ}}^n$

${\ddot{ℝ}}^n$

Strong embedding (Defn. 4)

${\dot{ℝ}}^n$

Weak embedding

${\widetilde{ℝ}}^n$

Consensus embedding (Defn. 5)

${\tilde{\delta }}^{cd}$

Pairwise relationship in ${\widetilde{ℝ}}^n$

M

Number of generated embeddings

K

Number of selected embeddings

R

Number of objects in C

$\tilde{\mathbf{X}}\left(c\right)$

Consensus embedding vector