relative perturbations

[[concept]]

Relative Perturbations modulo permutations

$E(S,\tilde{S})=\{D:P^{T}SP=S+DS+SD,P\in \mathcal{P}\}$

given $\tilde{S}$, the error is $E$ with the smallest norm ie $\tilde{E}=\arg {\min }_{D\in E(S,\tilde{S})}||D||$ ie $||\tilde{E}||=d(S,\tilde{S})$

where $d(\cdot )$ is the operator distance modulo permutations.

NOTE

• dilation takes into account edge weights, but cannot model edge additions and deletions
• additive perturbations can model edge additions and deletions, but do not take into account edge weights
• relative perturbations take into account both edge weights and additions/deletions

Mentions

TABLE
FROM [[]]
 
FLATTEN choice(contains(artist, this.file.link), 1, "") + choice(contains(author, this.file.link), 1, "") + choice(contains(director, this.file.link), 1, "") + choice(contains(source, this.file.link), 1, "") as direct_source
 
WHERE !direct_source