A Comparison of DFT and DWT Based Similarity Search
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7/29/2019 A Comparison of DFT and DWT Based Similarity Search
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Yi-Leh Wu Divyakant Agrawal Amr El Abbadi
Department of Computer ScienceUniversity of California, Santa Barbara
ABSTRACT
1. INTRODUCTION
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CIKM 2000, McLean, VA USA ACM 2000 1-58113-320-0/00/11 . . .$5.00
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2. BACKGROUND
2.1 Query Processing in Time-series Databases
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stockclosingpriceinUD$
time in days
real stock data
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reconstructfromcoef.#5
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reconstructfromcoef.#1
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reconstructfromcoef.#2
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reconstructfromcoef.#3
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reconstructfromcoef.#4
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reconstructfromcoef.#6
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reconstructfromcoef.#7
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reconstructfromcoef.#8
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originaldata
+ + ++
+++++ + ....
=
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normalizedstockdata
time in days
original datareconstruct from 8 coef.
reconstruct from 64 coef.
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normalizedstockdata
time in days
original datareconstruct from first 8 DFT coef.
reconstruct from first 8 DFT coef. with conjugate property
2.2 Discrete Wavelet Transform
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reconstructfromcoef.#1
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reconstructfromcoef.#2
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reconstructfromcoef.#3
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reconstructfromcoef.#4
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reconstructfromcoef.#6
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reconstructfromcoef.#7
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reconstructfromcoef.#8
+ + ++
+++++ + ....
=
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originaldata
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normalizedstockdata
time in days
original datareconstruct from 8 coef.
reconstruct from 64 coef.
3. WHY WAVELETS?
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standarddeviation
coefficient 0 to 127
DFT coefficient (real part)DFT coefficient (imaginary part)
DWT coefficient
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0.01
0.1
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energypercentage(%)
coefficient 0 to 127
average energy of indivisual DFT coefficientaverage energy of indivisual DWT coefficient
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energypercentage(%)
# of coefficients
accumulate energy of DFT coefficientsaccumulate energy of DWT coefficients
accumulate energy of DFT coefficients with mirror effect
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1 2 3 4 5 6 7 8 9 1 0
energypercentage(%)
# of coefficients
accumulate energy of DFT coefficientsaccumulate energy of DWT coefficients
accumulate energy of DFT coefficients with mirror effect
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4. EXPERIMENTS
4.1 Approximation Errors after Transforms
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approximationerror(%)
storage space (# of floting point numbers)
DFTDFT (with mirror effect)
DWT
4.2 Matching Errors after Transforms
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malizedstockdata
time in days
stock ABRX from day 20
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re
lativeerror(%)
storage space (# of floting point numbers)
Query with ABRX (set #45) data starting date 20
DFTDFT (with mirror effect)
DWT (first)
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relativeerror(%)
storage space (# of floting point numbers)
DFTDFT (with mirror effect)
DWT
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4.3 Precision of Epsilon Query with Trans-forms
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precision
epsilon distance
DFT (first 4 coef.)DFT (first 4 coef. with mirror effect)
DWT (first 8 coef.)
5. CONCLUSION
6. REFERENCES
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Appendix A: Mathematics for Discrete FourierTransform (DFT)
Appendix B: Minimizing Thresholding Error
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