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TSB-UAD: An End-to-End Benchmark Suite for Univariate
Time-Series Anomaly Detection
13766
18
1980
958
126
10828
12
OPPORTUNITY IOPS SVDB Daphnet MGAB MITDB
Occupancy ECG GHL SensorScope NASA-MSL SMD
KDD21 NASA-SMAP NAB Genesis Dodgers YAHOO
red
13766
18 1980
126
958
90
92
10828
12
•
18
•
•
•
•
•
1200
0300 600 900
𝑃𝑜𝑖𝑛𝑡
𝑎𝑛𝑜𝑚𝑎𝑙𝑦
20
0510 15
𝑎𝑎𝑛𝑜𝑚𝑎𝑙𝑦 𝑜𝑢𝑡𝑠𝑖𝑑𝑒 𝑡ℎ𝑒
ℎ𝑒𝑎𝑙𝑡ℎ𝑦 𝑟𝑎𝑛𝑔𝑒
1200
0300 600 900
𝐶𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑣𝑒
𝑎𝑛𝑜𝑚𝑎𝑙𝑦
𝑐𝑎𝑛𝑜𝑚𝑎𝑙𝑦 𝑖𝑛𝑠𝑖𝑑𝑒 𝑡ℎ𝑒
ℎ𝑒𝑎𝑙𝑡ℎ𝑦 𝑟𝑎𝑛𝑔𝑒
20
0510 15
1200
0300 600 900
20
0510 15 20
0510 15
𝐶𝑜𝑛𝑡𝑒𝑥𝑡𝑢𝑎𝑙 𝑎𝑛𝑜𝑚𝑎𝑙𝑦
𝑏𝑎𝑛𝑜𝑚𝑎𝑙𝑦 𝑜𝑢𝑡𝑠𝑖𝑑𝑒 𝑡ℎ𝑒 𝑙𝑜𝑐𝑎𝑙
ℎ𝑒𝑎𝑙𝑡ℎ𝑦 𝑟𝑎𝑛𝑔𝑒
𝑎. 1 𝑇𝑖𝑚𝑒 𝑠𝑒𝑟𝑖𝑒𝑠
𝑎. 2 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝑐. 1 𝑇𝑖𝑚𝑒 𝑠𝑒𝑟𝑖𝑒𝑠
𝑐. 2 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝑏. 3
𝑏. 2
𝑏. 1 𝑇𝑖𝑚𝑒 𝑠𝑒𝑟𝑖𝑒𝑠
𝑃𝑜𝑖𝑛𝑡-𝑏𝑎𝑠𝑒𝑑 𝑆𝑒𝑞𝑢𝑒𝑛𝑐𝑒-𝑏𝑎𝑠𝑒𝑑
0
20
𝑉𝑎𝑙𝑢𝑒𝑠
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
100
300
1
18
18
1980
8
10
>0.8
•
•
∼
47
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
958 126
92
10828
12
10
=
ˆ
=
(ˆ
=|)
( + )/
2
=/−
<
=
20
=/
128
0
.
65
126 958
10
=(0, 1, ..., )
4.3.1 Global Transformations:
, ∈ [
1
, ]
0=
0
=
=1
=+ ··
∼ N (
0
,
1
), ∈ [
0
, ]
=+ ··
·
=+
5
= ()
=∗=F−1(F () F ())
1
2
=[0:/2∗1, /2:+1∗2]
4.3.2 Local Transformations:
4.3.3 Subsequence Transformations:
= /( +),
= /= /( + ),
= /= /( + ).
− =
2
· ·/( +).
1200
0300 600 900
𝑎𝑆𝑖𝑛𝑔𝑙𝑒 𝑎𝑛𝑜𝑚𝑎𝑙𝑦
1200
0300 600 900
𝑏𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑎𝑛𝑜𝑚𝑎𝑙𝑦
1200
0300 600 900
𝑏. 1 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑎𝑛𝑜𝑚𝑎𝑙𝑦
𝑏. 2 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑠𝑖𝑚𝑖𝑙𝑎𝑟 𝑎𝑛𝑜𝑚𝑎𝑙𝑦
𝐴
𝐴
𝐴
𝐴𝐴
1200
0300 600 900
𝑐𝑆𝑖𝑛𝑔𝑙𝑒 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑡𝑦
1200
0300 600 900
𝑑𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑡𝑦
1200
0300 600 900
𝑑. 1 𝐸𝑥𝑎𝑚𝑝𝑙𝑒 1
𝑑. 2 𝐸𝑥𝑎𝑚𝑝𝑙𝑒 2
𝐴
𝐴
𝐴𝐴
𝐴
𝑁
𝑁
𝑁
𝑁
𝑁
𝑁
𝑁
(, )
()=min∈−(, )
()=E∈−(, )
=
E∈[ ()]
E∈[ ()] .
=
E,∈ ,[(, )]
E,∈ ,[(, )]
=
min∈,∈ (, )
E,∈ ,[(, )]
12
13766
1980 18 958
126 10828 92
<
5%
(a) Measures standard
deviation
when we inject lag
(b) Measures standard
deviation when we
inject noise
(c) Measures standard
deviation when we vary
normal/abnormal ratio
0.4
0.3
0.2
0.1
0.0
Accuracy standard deviation
Precision
RPrecision
Recall
Rrecall
Precision@k
F
RF
AUC-PR
AUC-ROC
Precision
RPrecision
Recall
Rrecall
Precision@k
F
RF
AUC-PR
AUC-ROC
Precision
RPrecision
Recall
Rrecall
Precision@k
F
RF
AUC-PR
AUC-ROC
12 18
∈ [−
0
.
25
∗,
0
.
25
∗]
∈ [−
0
.
05
∗ ( () −
()),
0
.
05
∗ ( () − ())]
∈ [
0
.
01
,
0
.
2
]
12 18
=() +
3
∗()
0
1980
18
Dodgers MGAB SensorScope SMAP+MSL ECG NAB YAH OO
(a) NORMA: AUC(b) IForest: AUC
(b) 92 synthetic datasets:
(a.2) NORMA vs IForest(a.1) NORMA vs POLY
(a) 126 artificial datasets:
=
0
.
05
Dodgers MGAB SensorScope SMAP+MSL ECG NAB YAH OO
(a) NORMA: AUC(b) IForest: AUC