Designing a Streaming Algorithm for Outlier Detection in Data Mining—An Incremental Approach

. 2020 Feb 26;20(5):1261. doi: 10.3390/s20051261

Algorithm 1 Incremental LOF Update (Dataset S, Point

p_{n}

)

if $Δ p_{n} < ε$ then
$S_{u p d a t e_k_d i s t a n c e}$ = Compute $r - k^{t h} (p_{n}) \cup p_{n}$ ;
Update(S, $p_{n}$ );
$S_{u p d a t e_l r d}$ = Compute ${[k - R N N (S, p_{n}) - k - N N (S, p_{n})]} \cup p_{n}$ ;
for all $p \in S_{u p d a t e_k_d i s t a n c e s}$ do
Compute $k - d i s t a n c e (S, p)$ ;
for all $q \in k - N N (S, p)$ do
if $p \in k - N N (S, q)$ then
$r e a c h - d i s t (q, p) = k - d i s t a n c e (S, p)$ ;
$S_{u p d a t e_l r d} \cup q$ ;
end if
end for
end for
$S_{u p d a t e_L O F} = S_{u p d a t e_l r d}$ ;
for all $p \in S_{u p d a t e_l r d}$ do
Compute $k - N N (S, p)$ ;
for all $q \in k - N N (S, p)$ do
Get/Compute $r e a c h - d i s t (p, q)$ using Equation (15);
end for
Update $l r d (p)$ using Equation (16);
$S_{u p d a t e_L O F} \cup k - R N N (p)$ ;
end for
for all $p \in S_{u p d a t e_L O F}$ do
Get $l r d (p)$ ;
for all $q \in k - N N (S, p)$ do
Get $l r d (q)$ ;
end for
Update $L O F (p)$ using Equation (17);
end for
else
Deletion(S, $p_{n}$ );
Insertion(S, $p_{n}$ );
end if