PGraphD*: Methods for Drift Detection and Localisation Using Deep Learning Modelling of Business Processes

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. 2022 Jun 30;24(7):910. doi: 10.3390/e24070910

Algorithm 2 PGraphDD-SS: concept drift detection using similarity score

Require:
Event stream: $S$ , LSTM model: $μ$ , Threshold: $ϕ$
1:
$s i m S c o r e \leftarrow []$ , $D r i f t L o g \leftarrow []$
2:
$e \leftarrow f e t c h (e v e n t S t r e a m)$
3:
$w \leftarrow w i n S i z e$ {the window size}
4:
$p a r t s \leftarrow s p l i t L o g (e, w)$
5:
for alli in range(0, parts) do
6:
$j \leftarrow i + 1$
7:
if $i = p a r t s - 1$ then
8:
$j \leftarrow 0$
9:
$R \leftarrow p a r t (i)$ , $D \leftarrow p a r t (j)$
10:
end if
11:
while $w \neq 0$ do
12:
$p r e p a r e (R, D)$ {compile and train two lstm model on the reference and detection window}
13:
$μ_{1}^{'} \leftarrow (μ, R)$ , $μ_{2}^{'} \leftarrow (μ, D)$
14:
{Make predictions for both}
15:
$R_{p r e d} \leftarrow p r e d i c t (μ_{1}^{'}, R)$
16:
$D_{p r e d} \leftarrow p r e d i c t (μ_{2}^{'}, D)$
17:
{build next event prediction probability matrices, construct graphs}
18:
$P_{i j}^{R} \leftarrow g e n e r a t e (P r e d_P r o b_M a t, R_{p r e d})$
19:
$P_{i j}^{D} \leftarrow g e n e r a t e (P r e d_P r o b_M a t, D_{p r e d})$
20:
$G^{R} \leftarrow d r a w G r a p h (i, o, N, E, P_{i j}^{R}, R_{p r e d})$
21:
$G^{D} \leftarrow d r a w G r a p h (i, o, N, E, P_{i j}^{D}, D_{p r e d})$
22:
{generate adjacency matrices, measure similarity score}
23:
$A_{i j}^{R} \leftarrow g e n e r a t e (a d j a c e n c y_m a t r i x, G^{R})$
24:
$A_{i j}^{D} \leftarrow g e n e r a t e (a d j a c e n c y_m a t r i x, G^{D})$
25:
$p \leftarrow p e r f o r m a n c e ()$
26:
$s i m S c o r e \leftarrow p . g e t S c o r e ()$
27:
$M \leftarrow 0$ {set a counter of non-zero values}
28:
$M \leftarrow g e t M (A_{i j}^{R}, A_{i j}^{D})$
29:
$a b s o l u t e V a l \leftarrow (A_{i j}^{R} - A_{i j}^{D})$
30:
$s u m V a l \leftarrow a b s o l u t e V a l . a b s () . s u m () . s u m ()$
31:
$s i m S c o r e \leftarrow 1 - s u m V a l / M$
32:
if $s i m S c o r e \leq ϕ$ then
33:
$p r i n t (‘ ‘ d r i f t f o u n d i n w i n d o w^{''} + s t r (j))$
34:
{change point detected and reported}
35:
end if
36:
$R e p o r t \leftarrow (i, j, s i m S c o r e)$
37:
end while
38:
end for