SSA

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SSA????????????

• K. Demachi, Sergei Rybalko, Zhu Haitao
• demachi_at_nuclear.jp
• Professional School of Nuclear Engineering,
• Graduate School of Engineering, The University of
  Tokyo

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Application of SSA for Medical-Technology
(Irradiation therapy)
Tumor Movement Chaser for Irradiation Therapy
Tumor in Lung moves in wide area

breathing
all
blowing
(Shirato H, et al. Lancet 3531331-32, 1999)
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Concept of SSA prediction of tumor movement
X-ray roentgen chase the Movement of gold marker
near the lung tumor
Gold Marker
tumor
Now, the therapy X-ray is irradiated only when
the lung tumor enters the beam area.
X-ray roentgen
Patient
X-ray source
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• SSA(Singular Spectral Analysis) (1)

? N-M1 Matrix (M1) are derived from N
Time-series
Measured Data
xt-M1
xt
xt-NM

xt-N1
time
t-M1
t-NM
t
t-N1
? N-M1 matrices are combined to one matrix
(N-M1M)
N time-series
?The mean-value of each line is subtracted (
Center-shifted)
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• SSA(Singular Spectral Analysis) (2)

?Transverse matrix is operated ? Symmetric
matrix Y (MM)
?Eigen value analysis for matrix Y
?Matrix VMr from eigen vectors of biggest r
eigen values
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• SSA(Singular Spectral Analysis) (3)

? is satisfied for

? xt1 is separated to xt1 L and Q
Future to be predicted
Measured past
Time
xt2
xt
xt1
?xt1 is obtained as
The future time-series can be predicted by
repeating calculation ??
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SSA analysis of movement of skin on chest
SSA?????(?) gt FFT(??????)?????(?)
8 seconds
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SSA analysis of movement of skin on chest
SSA?????(?) gt FFT(??????)?????(?)
8 seconds
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SSA analysis of movement of skin on chest
SSA?????(?) gt FFT(??????)?????(?)
8 seconds
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Future task

• Accuracy
• Long time prediction
• 3-dimension code
• Collaboration with MPS
• Experiments

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OTHER EXAMPLES OFPREDICTION OFTIME-SERIES DATA
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Verification 1 (Mackey-Glass equation)
MG eq. shows the chaotic phenomena.
Prediction after 3020 step
Time-series of Mackey-Glass equation
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Verification1(Mackey-Glass eq.)
N3000?M160?r30
Mackey-Glass
Predicted
3020 step
Good agreement of original Mackey-Glass
time-series and the predicted
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Verification 2 (Atmosphere temperature)
Maximum temperature in Melboun (Australia,
19801990)
N3000?M160?r30
Prediction after 1988
Measured
Prediction
Time Series Data Library, http//
www-personal.buseco.monash.edu.au/hyndman/TSDL/
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Verification 3 (Rank of star shining)
N300?M160?r30
Measured
Measured data to be predicted
Prediction
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Verification 4 (Stock Price)
Prediction from N2000?2500?3000
SP500 index( 19801992)
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Verification 4 (Stock Price)
M160?r30
N2500
N3000
N2000
Original
Original to be compared
Prediction