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https://sites.google.com/site/yumakoizumiweb/
https://www.slideshare.net/yumakoizumi75/
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音響信号に対する異常音検知技術と応用
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n
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n ae di= 1
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complexity of the mode shapes increases with higher frequencies. The analysis of mode shapes of
all modes observed in this frequency range indicates that the deformation of the eggshell during
ARTICLE IN PRESS
Fig. 8. The lab-scale test arrangement for eggshell breakage inspection, with egg support by diabolo-shaped rollers (1),
the impacting rod (2) and the microphone (3), located at 90
from the impactor.
P. Coucke et al. / Journal of Sound and Vibration 266 (2003) 711–721720
P. Coucke, B. De Ketelaere, and J. De Baerdemaeker, ”Experimental analysis of the dynamic, mechanical
behaviour of a chicken egg,” Journal of Sound and Vibration , pp.711–721, 2003.
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音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
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音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
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Y. Koizumi, S. Saito, N. Harada, H. Uematsu, and K. Imoto, “ToyADMOS: A Dataset of Miniature-Machine Operating
Sounds for Anomalous Sound Detection,” in Proc. of WASPA, 2019.
GitHub: https://github.com/YumaKoizumi/ToyADMOS-dataset/
A
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https://github.com/YumaKoizumi/ToyADMOS-dataset/
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音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
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n ri o tso i
n 0 1 i e
n A E pr
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n
n
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n _ Ngr U N. 4
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0.6
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0.771
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0.720Anomaly-to-Normal Ratio
-10 dB -15 dB -20 dB
AUC
1 2 3
0.2
0.4
0.6
0.8
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0.793
0.864
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音響信号に対する異常音検知技術と応用
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n
Figure 3: Anomaly scores of RE (green dotted), SNP (blue dashed),
and BU (red solid). Yellow areas denote anomalous areas.
Table 1: KLD between oracle PDFs and estimated PDFs.
D(pa(x)kpb(x)) denotes the KLD between pa(x) and pb(x).
Cost-function D(p(x)kq✓(x)) D(U(x)kq✓(x))
J RE
✓ 1.395 0.913
J SNP
✓ 0.222 0.333
J BU
✓ 0.403 0.083
n
2/2
-3 -2 -1 0 1 2 3
0
1
2
3
4
5
Anomalyscore
x1 = 0.0latexit sha1_base64=l6BfYdy4qHCm7z8FfoaSKYRXs6E=AAACi3ichVG7SgNBFD1Z3/EVtRFsFkPEKtyI4AMFUQRLk7gmEiXsrqMu7ovdTVCDP2BrYaEWChbiB/gBNv6AhZ8glgo2Ft5sFkRFvcPMnDlzz505XM01DT8geoxJTc0trW3tHfHOru6e3kRf/6rvVDxdKLpjOl5RU31hGrZQAiMwRdH1hGpppihouwv1+0JVeL7h2CvBvis2LHXbNrYMXQ2YWtsrZ+RZmdJUTiR5DUP+CTIRSCKKZSdxi3VswoGOCiwI2AgYm1Dh8yghA4LL3AZqzHmMjPBe4BBx1lY4S3CGyuwur9t8KkWszed6TT9U6/yKydNjpYwUPdA1vdA93dATvf9aqxbWqP9ln3etoRVuufdoMP/2r8riPcDOp+oPhcbZf3sKsIXJ0IvB3tyQqbvUG/WrBycv+elcqjZCl/TM/i7oke7YoV191a+yIneKODco870dP4Eylp5KU3Y8OTcfdaodQxjGKLdjAnNYwjIUftbCMc5wLvVI49K0NNNIlWKRZgBfQlr8AMseka0=/latexitlatexit sha1_base64=l6BfYdy4qHCm7z8FfoaSKYRXs6E=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/latexit
x2latexit sha1_base64=CsC6TXnBtOG/TFQREwqdYhtS7Wk=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 sha1_base64=CsC6TXnBtOG/TFQREwqdYhtS7Wk=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
_ Rop Leu
n
n a _ g N / .
n y sd C y vt
n T
n y r i cR 1 l
n U 00 xeu op
n h 1. S n
4 B6 7 6 : 4 A 7 6
1 2 3
0.2
0.4
0.6
0.8
1
0.727
0.771
0.899
0.572
0.654
0.808
0.519
0.576
0.720
Anomaly-to-Normal Ratio
-10 dB -15 dB -20 dB
AUC
1 2 3
0.2
0.4
0.6
0.8
1
0.726
0.793
0.864
0.570
0.702
0.766
0.516
0.623
0.681
RE SNP BU
8
6
n rz P g
n rz W Y Puw
n r n o
n icIK U
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n W Y P IK 9A8 , 00 6
n IKz Ea K O CA , 00 6
n rzSic TO 8 , 00 6
n m] z O CA +20, . 6
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
n D B AD
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:
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(cont’d)
Known domain New domain
Dom
1
Dom
2
Dom
3
Dom
4
Dom
5
Dom
6
Dom
7
Dom
8
Dom
9
Dom
10
Adapt.
time
C8
0.937 0.983 0.981 0.939 0.983 0.997 0.967 0.974 0.999 0.748
C8
0.862 0.967 0.963 0.940 0.995 0.995 0.969 0.989 0.993 0.874 1.5 h
0.949 0.980 0.998 0.921 0.992 0.998 0.953 0.990 0.998 0.852 30 sec
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n O i
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2
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2
2
2
(few-shot )
Unsupervised
anomaly detector
Final
decision
Normal
Anomaly
Unknown anomaly detector
Overlooked anomaly
(few-shot )
Unsupervised
anomaly detector
Final
decision
Normal
Anomaly
!
Specific anomaly detectors
Unknown anomaly detector
+
…
S1latexit sha1_base64=lZlF4kZY+C9NjM0cGB+KeGYI+yk=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/latexitlatexit sha1_base64=lZlF4kZY+C9NjM0cGB+KeGYI+yk=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/latexit
SKlatexit sha1_base64=GzfaadDxjRPvyCYjDtW0PJ/gUUk=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/latexitlatexit sha1_base64=GzfaadDxjRPvyCYjDtW0PJ/gUUk=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/latexit
Overlooked anomaly
8 4
h g e i
CE✓k
S
=
NX
n=1
ln S(x(u)
n , mk, ✓k
S) +
MX
m=1
ln
⇣
1 S(x(a)
m , mk, ✓k
S)
⌘
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g lF h g l
- i PN
h : =
a
( F 5 8
h g F
 )N
- --
0
✓K
S argmin✓K
S
FPR(✓K
S , ) s.t. K-TPR(✓K
S , ) = 1
latexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexitlatexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexitlatexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexit
1 , +0 6 9 A 6 8 :A9 6 6 A 6 :A:C A6
2- :E : , 11
I E I F 0
0 E 0 F
 min
h
score(x(K)
m , ✓)
iM
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⇡
1
N
NX
n=1
sigmoid
h
score(x(u)
n , ✓)
i
latexit sha1_base64=GVHkZGUD0aq82QvDkkdV/KhoSVY=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/latexitlatexit sha1_base64=GVHkZGUD0aq82QvDkkdV/KhoSVY=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/latexitlatexit sha1_base64=GVHkZGUD0aq82QvDkkdV/KhoSVY=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/latexit
✓K
S argmin✓K
S
FPR(✓K
S , ) s.t. K-TPR(✓K
S , ) = 1
latexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexitlatexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexitlatexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexit
S I N E
N P S S E NR
{xK
m}M
m=1latexit sha1_base64=ENb7uT9wFUJ6NIUcYlFSXVnZxxk=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/latexitlatexit sha1_base64=ENb7uT9wFUJ6NIUcYlFSXVnZxxk=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/latexitlatexit sha1_base64=ENb7uT9wFUJ6NIUcYlFSXVnZxxk=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/latexit
p(x|y = K)latexit sha1_base64=RCIJYcli5PRopg4zqef5Xc9ua0Q=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/latexitlatexit sha1_base64=RCIJYcli5PRopg4zqef5Xc9ua0Q=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/latexitlatexit sha1_base64=RCIJYcli5PRopg4zqef5Xc9ua0Q=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/latexit
N [ N R S P KI
K-TPR(✓K
S , ) =
Z
H [score(x, ✓) ] p(x|y = K)dx
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1 , +0 7 9 A 8 :A9 A :A:C A
2- :E : , 11
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1
Overlooked
anomaly
Normal
training data
VAE
DV
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mKlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexitlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexit
x(K)
nlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=AAACkHichVHNLgNRFP6Mv6qfFhuJjWgIm+ZUJNRGsRE2/gYJ2syMi0nnLzPTRk36Al6AxIrEQjyAB7DxAhYeQSxJbCycTicRRJ2be+93v3u+c++XozqG7vlET01Sc0trW3usI97Z1d2TSPb2bXp2ydWErNmG7W6riicM3RKyr/uG2HZcoZiqIbbU4kLtfqssXE+3rQ2/4og9Uzm09ANdU3ym8ruqGRxXC1Y+GFserxaSKUpTGEO/QSYCKUSxYifvsIt92NBQggkBCz5jAwo8HjvIgOAwt4eAOZeRHt4LVBFnbYmzBGcozBZ5PeTTTsRafK7V9EK1xq8YPF1WDmGEHumGXumBbumZPv6sFYQ1an+p8K7WtcIpJE4H1t//VZm8+zj6UjVQqJzd2JOPA0yHXnT25oRMzaVWr18+OXtdn1kbCUbpil7Y3yU90T07tMpv2vWqWLtAnBuU+dmO30CeSGfTtDqZys1HnYphEMMY43ZMIYdFrEDmZ12c4xJXUr+UlWaluXqq1BRp+vEtpKVPlhSVJg==/latexitlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=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/latexit
EV
latexit sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=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 sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=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
p(x|y = K) VAE(mK)
{x(K)
n }N
n=1 ⇠ p(x|y = K)latexit sha1_base64=OeOFWFhG3xUrP+2/9X8ac+szoeU=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 sha1_base64=OeOFWFhG3xUrP+2/9X8ac+szoeU=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 sha1_base64=OeOFWFhG3xUrP+2/9X8ac+szoeU=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
2
Overlooked
anomaly
Normal
training data
VAE
Normal model
Anomaly
score
calc.
Other registered parameters
✓K
Slatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=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/latexitlatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=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/latexit
{✓1
S, ..., ✓K 1
S }latexit sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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 sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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
DV
latexit sha1_base64=fxoBzb4iaar9HERD/tFhQpDsnl4=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/latexitlatexit sha1_base64=fxoBzb4iaar9HERD/tFhQpDsnl4=AAACj3ichVHNLkNBFP56/VX9VW0kNo2GWDWnIlEW0mDBrkWRUHLvNbjp/XPvtEk1XsALWNioxEI8gAew8QIWHkEsSWwsnN7eRBCcycx88835zsyXo7mm4Uuix4jS1t7R2RXtjvX09vUPxAcT675T8XRR1B3T8TY11RemYYuiNKQpNl1PqJZmig2tvNC836gKzzcce03WXFGy1APb2Dd0VTJV2rZUeairZn3xZGd9N56iNAWR/AkyIUghjLwTv8U29uBARwUWBGxIxiZU+Dy2kAHBZa6EOnMeIyO4FzhBjLUVzhKcoTJb5vWAT1sha/O5WdMP1Dq/YvL0WJnEGD3QNb3QPd3QE73/Wqse1Gj+pca71tIKd3fgdHj17V+VxbvE4afqD4XG2X97kthHNvBisDc3YJou9Vb96vHZy+rsylh9nC7pmf016JHu2KFdfdWvCmLlHDFuUOZ7O36C4mR6Jk2FqVRuPuxUFCMYxQS3Yxo5LCGPIj97hDNcoKEklKwyp+RaqUok1AzhSyjLH/xflOg=/latexit
mKlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexitlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexit
x(u)
nlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=AAACkHichVG7SgNBFD1ZXzG+omkEGzEosQk3IvhojNqIVXxEA4mG3XWii/tidxOMS37AH1CwUrAQP8APsPEHLPwEsVSwsfBmsyAq6h1m5syZe+7M4Sq2rrke0WNEamvv6OyKdsd6evv6B+KDQ1uuVXVUkVct3XIKiuwKXTNF3tM8XRRsR8iGoott5XC5eb9dE46rWeamV7fFjiHvm1pFU2WPqd2SYvhHjbK566eqk41yPElpCmL0J8iEIIkwclb8FiXswYKKKgwImPAY65Dh8igiA4LN3A585hxGWnAv0ECMtVXOEpwhM3vI6z6fiiFr8rlZ0w3UKr+i83RYOYpxeqBreqF7uqEnev+1lh/UaP6lzrvS0gq7PHAyvPH2r8rg3cPBp+oPhcLZf3vyUMFs4EVjb3bANF2qrfq149OXjfn1cX+CLumZ/V3QI92xQ7P2ql6tifVzxLhBme/t+AnyU+m5NK1NJ7NLYaeiGMEYUtyOGWSxghzy/KyDM1zgUkpIc9KCtNhKlSKhJoEvIa1+AO9+lVA=/latexitlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=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/latexit
Elatexit sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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 sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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
x(K)
nlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=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/latexitlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=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/latexit
EV
latexit sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=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 sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=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
Dlatexit sha1_base64=Pkuk8LFsaH5+wIAmpapWSh3/ONA=AAACjXichVHLSsNQED2Nr1ofrboR3BSL4qpMRXwhIiro0ldVqFKSeKuheZHcFmrxB9yLC0FRcCF+gB/gxh9w4SeISwU3LpymAVGxTsi9556ZM8m5o7mm4Uuip4jS1NzS2hZtj3V0dnXHEz29m75T8nSR1R3T8bY11RemYYusNKQptl1PqJZmii2tuFDLb5WF5xuOvSErrti11H3bKBi6KpnK7ViqPNBVs7p4lE+kKE1BJH+DTAhSCGPFSdxhB3twoKMECwI2JGMTKnx+csiA4DK3iypzHiMjyAscIcbaElcJrlCZLfK6z6dcyNp8rvX0A7XOXzH59ViZxBA90g290gPd0jN9/NmrGvSo/UuFd62uFW4+fty//v6vyuJd4uBL1UChcXVjTxIFTAZeDPbmBkzNpV7vXz48fV2fXhuqDtMVvbC/S3qie3Zol9/061WxdoYYDyjzcxy/QXY0PZWm1bHU3Hw4qSgGMIgRHscE5rCMFWSDCz3BOS6UhDKuzCiz9VIlEmr68C2UpU8qGpQg/latexitlatexit sha1_base64=Pkuk8LFsaH5+wIAmpapWSh3/ONA=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
Overlooked
anomaly
Normal
training data
VAE
Normal model
Anomaly
score
calc.
Threshold
calc.
Other registered parameters
✓K
Slatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=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/latexitlatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=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/latexit
{✓1
S, ..., ✓K 1
S }latexit sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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 sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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
DV
latexit sha1_base64=fxoBzb4iaar9HERD/tFhQpDsnl4=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/latexitlatexit sha1_base64=fxoBzb4iaar9HERD/tFhQpDsnl4=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/latexit
mKlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexitlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=AAACinichVHNLgNRGD3GfynFRmLTaCpWzVcklI1gIbGpUm3SNs3MuJiYv8xMm1TTF7C0sWBDYiEewAPYeAELjyCWJDYWvk4nERr1Tebec8/9zjdzchRb11yP6LlL6u7p7esfGAwNDYdHRiNj43uuVXFUkVUt3XLyiuwKXTNF1tM8XeRtR8iGoouccrzevM9VheNqlrnr1WxRMuRDUzvQVNljKl9UjLrRKG+VIzFKkF/RdpAMQAxBpa3IPYrYhwUVFRgQMOEx1iHD5aeAJAg2cyXUmXMYaf69QAMh1la4S3CHzOwxr4d8KgSsyefmTNdXq/wVnV+HlVHE6Ylu6Y0e6Y5e6PPPWXV/RvNfarwrLa2wy6Onkzsf/6oM3j0cfas6KBTu7uzJwwGWfC8ae7N9pulSbc2vnpy/7Sxn4vUZuqZX9ndFz/TADs3qu3qzLTIXCHFAyd9xtIPsXCKVoO2F2OpakNQApjCNWY5jEavYRBpZP4YzXOBSCkvzUkpaabVKXYFmAj9K2vgCGPOSyg==/latexit
x(u)
nlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=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/latexitlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=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/latexit
Elatexit sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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 sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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
x(K)
nlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=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/latexitlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=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/latexit
EV
latexit sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=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 sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=AAACj3ichVHNLkNBFP56/VX9VW0kNo2GWDWnIlEW0hAJuxZFQsm91+Cm98+90ybVeAEvYGGjEgvxAB7AxgtYeASxJLGxcHp7E0FwJjPzzTfnOzNfjuaahi+JHiNKW3tHZ1e0O9bT29c/EB9MrPtOxdNFUXdMx9vUVF+Yhi2K0pCm2HQ9oVqaKTa08kLzfqMqPN9w7DVZc0XJUg9sY9/QVclUadtS5aGumvXFk5313XiK0hRE8ifIhCCFMPJO/Bbb2IMDHRVYELAhGZtQ4fPYQgYEl7kS6sx5jIzgXuAEMdZWOEtwhspsmdcDPm2FrM3nZk0/UOv8isnTY2USY/RA1/RC93RDT/T+a616UKP5lxrvWksr3N2B0+HVt39VFu8Sh5+qPxQaZ//tSWIf2cCLwd7cgGm61Fv1q8dnL6uzK2P1cbqkZ/bXoEe6Y4d29VW/KoiVc8S4QZnv7fgJipPpmTQVplK5+bBTUYxgFBPcjmnksIQ8ivzsEc5wgYaSULLKnJJrpSqRUDOEL6EsfwD+gZTp/latexit
Dlatexit sha1_base64=Pkuk8LFsaH5+wIAmpapWSh3/ONA=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 sha1_base64=Pkuk8LFsaH5+wIAmpapWSh3/ONA=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
 min
h
score(x(K)
m , ✓)
iM
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Overlooked
anomaly
Normal
training data
VAE
Normal model
Anomaly
score
calc.
Threshold
calc.
SNIPER
Other registered parameters
Iterative training
Update
✓K
Slatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=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/latexitlatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=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/latexit
{✓1
S, ..., ✓K 1
S }latexit sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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 sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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
DV
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mKlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexitlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexit
x(u)
nlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=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/latexitlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=AAACkHichVG7SgNBFD1ZXzG+omkEGzEosQk3IvhojNqIVXxEA4mG3XWii/tidxOMS37AH1CwUrAQP8APsPEHLPwEsVSwsfBmsyAq6h1m5syZe+7M4Sq2rrke0WNEamvv6OyKdsd6evv6B+KDQ1uuVXVUkVct3XIKiuwKXTNF3tM8XRRsR8iGoott5XC5eb9dE46rWeamV7fFjiHvm1pFU2WPqd2SYvhHjbK566eqk41yPElpCmL0J8iEIIkwclb8FiXswYKKKgwImPAY65Dh8igiA4LN3A585hxGWnAv0ECMtVXOEpwhM3vI6z6fiiFr8rlZ0w3UKr+i83RYOYpxeqBreqF7uqEnev+1lh/UaP6lzrvS0gq7PHAyvPH2r8rg3cPBp+oPhcLZf3vyUMFs4EVjb3bANF2qrfq149OXjfn1cX+CLumZ/V3QI92xQ7P2ql6tifVzxLhBme/t+AnyU+m5NK1NJ7NLYaeiGMEYUtyOGWSxghzy/KyDM1zgUkpIc9KCtNhKlSKhJoEvIa1+AO9+lVA=/latexit
Elatexit sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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 sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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
x(K)
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EV
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音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用
音響信号に対する異常音検知技術と応用

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音響信号に対する異常音検知技術と応用

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Yellow areas denote anomalous areas. Table 1: KLD between oracle PDFs and estimated PDFs. D(pa(x)kpb(x)) denotes the KLD between pa(x) and pb(x). Cost-function D(p(x)kq✓(x)) D(U(x)kq✓(x)) J RE ✓ 1.395 0.913 J SNP ✓ 0.222 0.333 J BU ✓ 0.403 0.083 n
  • 65. 2/2 -3 -2 -1 0 1 2 3 0 1 2 3 4 5 Anomalyscore x1 = 0.0latexit sha1_base64=l6BfYdy4qHCm7z8FfoaSKYRXs6E=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/latexitlatexit sha1_base64=l6BfYdy4qHCm7z8FfoaSKYRXs6E=AAACi3ichVG7SgNBFD1Z3/EVtRFsFkPEKtyI4AMFUQRLk7gmEiXsrqMu7ovdTVCDP2BrYaEWChbiB/gBNv6AhZ8glgo2Ft5sFkRFvcPMnDlzz505XM01DT8geoxJTc0trW3tHfHOru6e3kRf/6rvVDxdKLpjOl5RU31hGrZQAiMwRdH1hGpppihouwv1+0JVeL7h2CvBvis2LHXbNrYMXQ2YWtsrZ+RZmdJUTiR5DUP+CTIRSCKKZSdxi3VswoGOCiwI2AgYm1Dh8yghA4LL3AZqzHmMjPBe4BBx1lY4S3CGyuwur9t8KkWszed6TT9U6/yKydNjpYwUPdA1vdA93dATvf9aqxbWqP9ln3etoRVuufdoMP/2r8riPcDOp+oPhcbZf3sKsIXJ0IvB3tyQqbvUG/WrBycv+elcqjZCl/TM/i7oke7YoV191a+yIneKODco870dP4Eylp5KU3Y8OTcfdaodQxjGKLdjAnNYwjIUftbCMc5wLvVI49K0NNNIlWKRZgBfQlr8AMseka0=/latexit x2latexit sha1_base64=CsC6TXnBtOG/TFQREwqdYhtS7Wk=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 sha1_base64=CsC6TXnBtOG/TFQREwqdYhtS7Wk=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
  • 66. _ Rop Leu n n a _ g N / . n y sd C y vt n T n y r i cR 1 l n U 00 xeu op n h 1. S n 4 B6 7 6 : 4 A 7 6
  • 67. 1 2 3 0.2 0.4 0.6 0.8 1 0.727 0.771 0.899 0.572 0.654 0.808 0.519 0.576 0.720 Anomaly-to-Normal Ratio -10 dB -15 dB -20 dB AUC 1 2 3 0.2 0.4 0.6 0.8 1 0.726 0.793 0.864 0.570 0.702 0.766 0.516 0.623 0.681 RE SNP BU 8 6
  • 68. n rz P g n rz W Y Puw n r n o n icIK U n rzP a [ TO CA ,+++ 1 6 n s a hrz TK O CA 0 6 n W Y P IK 9A8 , 00 6 n IKz Ea K O CA , 00 6 n rzSic TO 8 , 00 6 n m] z O CA +20, . 6
  • 74. n D B AD n U GP U n P G n n t n c U n t e n n P
  • 75. n n p y e n s r a n e Pp p e U Pe C a n e r e p3Gi R eC b U 3Gi ea
  • 76. A B +(1 : + . ) ) 2+1 (1 : ,+ 0 12 +++ 2 2+1 . +++ 2 AdaBNAdaBN AdaBNAdaBN AdaBNAdaBN
  • 77. BA: (cont’d) ( ( + ( , 1 02 ++ ((( +( ( )+ AdaBN AdaBN AdaBN
  • 78. Cd n S n 1 B n 0 n N 7 n 0 A4U 1 A n 0 n N B AS 9 B 9 n 0 A R n C N A 0 A 0 : - : ( )
  • 79. (cont’d) Known domain New domain Dom 1 Dom 2 Dom 3 Dom 4 Dom 5 Dom 6 Dom 7 Dom 8 Dom 9 Dom 10 Adapt. time C8 0.937 0.983 0.981 0.939 0.983 0.997 0.967 0.974 0.999 0.748 C8 0.862 0.967 0.963 0.940 0.995 0.995 0.969 0.989 0.993 0.874 1.5 h 0.949 0.980 0.998 0.921 0.992 0.998 0.953 0.990 0.998 0.852 30 sec D 34 34 %% 0 9 . 01
  • 80. n O i n W YO si n m[n n w c Uh Tu n z O U S PC , + 0 n r g Uc IS PC , 2 . n W YOo aU E 8 9 + . n ] U ] E PC , + . n h IS PC , A 9 + . n K U I PC , 1 +.
  • 83. (few-shot ) Unsupervised anomaly detector Final decision Normal Anomaly ! Specific anomaly detectors Unknown anomaly detector + … S1latexit sha1_base64=lZlF4kZY+C9NjM0cGB+KeGYI+yk=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/latexitlatexit sha1_base64=lZlF4kZY+C9NjM0cGB+KeGYI+yk=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/latexit SKlatexit sha1_base64=GzfaadDxjRPvyCYjDtW0PJ/gUUk=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/latexitlatexit sha1_base64=GzfaadDxjRPvyCYjDtW0PJ/gUUk=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/latexit Overlooked anomaly 8 4
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  • 85. 0 ✓K S argmin✓K S FPR(✓K S , ) s.t. K-TPR(✓K S , ) = 1 latexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexitlatexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexitlatexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexit 1 , +0 6 9 A 6 8 :A9 6 6 A 6 :A:C A6 2- :E : , 11 I E I F 0
  • 86. 0 E 0 F min h score(x(K) m , ✓) iM m=1latexit sha1_base64=oGgGXwkVf9iTriMTDHFakC3vG1Y=AAAC1XichVFNaxNBGH66ftX1I7G9CF4GQyWFEiZFaC0Wil4EEZrW2EA2XXa3k2Tozu6yOwmty3oSD148evCk4KH0B/QHePEPeOjBqyIeK3jx4JvNgmixfYeZeeaZ93lnHl438mWiOT+cMM6cPXf+wuRF89LlK1dL5WtTT5JwEHui6YV+GLdcJxG+DERTS+2LVhQLR7m+2HC374/uN4YiTmQYPNa7kegopxfIrvQcTZRdblhRX7K7zFJuuJMqGWSm5YuubptjJvHCWGSsarkq3clstZlWH85mc8zSfaGdWWZasez1dcdOmVqus2zzkV2u8BrPgx0H9QJUUMRqWD6AhS2E8DCAgkAATdiHg4RGG3VwRMR1kBIXE5L5vUAGk7QDyhKU4RC7TWuPTu2CDeg8qpnkao9e8WnGpGSY4Z/4Hj/iH/k+/8Z//bdWmtcY/WWXdnesFZFdenl9/eepKkW7Rv+P6gSFS9kne9LoYjH3IslblDMjl964/vDp66P1pbWZ9BZ/x7+Tv7f8kH8gh8Hwh/e+IdbewKQG1f9tx3HQnK/dqfHG7crKvaJTk7iBm6hSOxawggdYRZOePcBnfMFXo2U8M54bL8apxkShmcZfYbz6DfiMr0Q=/latexitlatexit sha1_base64=oGgGXwkVf9iTriMTDHFakC3vG1Y=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/latexitlatexit sha1_base64=oGgGXwkVf9iTriMTDHFakC3vG1Y=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/latexit ⇡ 1 N NX n=1 sigmoid h score(x(u) n , ✓) i latexit sha1_base64=GVHkZGUD0aq82QvDkkdV/KhoSVY=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/latexitlatexit sha1_base64=GVHkZGUD0aq82QvDkkdV/KhoSVY=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/latexitlatexit sha1_base64=GVHkZGUD0aq82QvDkkdV/KhoSVY=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/latexit ✓K S argmin✓K S FPR(✓K S , ) s.t. K-TPR(✓K S , ) = 1 latexit sha1_base64=OguablK6jSHEJY6SCc6prD9xDtk=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/latexitlatexit 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  • 89. 2 Overlooked anomaly Normal training data VAE Normal model Anomaly score calc. 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  • 90. Overlooked anomaly Normal training data VAE Normal model Anomaly score calc. Threshold calc. 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  • 91. Overlooked anomaly Normal training data VAE Normal model Anomaly score calc. Threshold calc. 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