A Taste of Data Mining

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A Taste of Data Mining
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Definition

• Data mining is the analysis of data to establish
  relationships and identify patterns.practice.fin
  dlaw.com/glossary.html.
• Learning from data.

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Examples of Learning Problems

• Digitized Image ? Zip Code
• Based on clinical and demographic variables,
  identify the risk factors for prostate cancer
• Predict whether a person who has had one heart
  attack will be hospitalized again for another.

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Kth-Nearest Neighbor
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Linear Decision Boundary
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Quadratic Decision Boundary
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Beneath the blur A look at independent component
analysis with respect to image analysis

• Galen Papkov
• Rice University
• January 1, 2021

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Outline

• Biology
• Gray vs. White Matter
• T1 vs. T2
• How does Magnetic Resonance Imaging work?
• Theory behind ICA
• Cocktail party
• Nakai et al.s (2004) paper

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Biology

• Gray matter consists of cell bodies whereas white
  matter is made up of nerve fibers
• (http//www.drkoop.com/imagepages/18117.htm)

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Biology (cont.)

• T2 effect occurs when protons are subjected to a
  magnetic field
• T2 time is the time to max dephasing
• T1 effect is due to the return of the high state
  protons to the low energy state
• T1 time is the time to return to equilibrium
• (http//www.es.oersted.dtu.dk/masc/T1_T2.htm)

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How Does MRI work?

• Protons have magnetic properties
• The properties allow for resonance
• process of energy absorption and subsequent
  relaxation
• Process
• apply an external magnetic field to excite them
  (i.e. absorb energy)
• Remove magnetic field so protons return to
  equilibrium, thereby creating a signal containing
  information of the resonanced area
• (http//www.es.oersted.dtu.dk/masc/resonance.htm)

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Cocktail Party Problem

• Scenario
• Place a microphone in the center of a cocktail
  party
• Observe what the microphone recorded
• Compare to human brain

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Independent Component Analysis (ICA)

• Goal to find a linear transformation W
  (separating matrix) of x (data) that yields an
  approximation of the underlying signals y which
  are as independent as possible
• xAs (A is the mixing matrix)
• syWx (WA-1)
• W is approximated via an optimization method
  (e.g. gradient ascent)

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Application of ICA to MR imaging for enhancing
the contrast of gray and white matter (Nakai et
al., 2004)

• Purpose To use ICA to improve image quality and
  information deduction from MR images
• Wanted to use ICA to enhance image quality
  instead of for tissue classification
• Subjects 10 normal, 3 brain tumors, 1 multiple
  sclerosis
• Method
• Obtain MR images
• Normalize and take the average of the images
• Apply ICA

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Normal MR and IC images vs. Average of the
Normalized Images
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Observations w.r.t. ICA transformation for normal
subjects

• IC images after whitening have removed
  (minimized) noise
• Observe the complete removal of free water

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Tumor Case 1 (oligodendroglioma)
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Tumor Case 1 (cont.)

• Hazy in location of tumor in original images
• Less cloudy, but can see involvement of tumor in
  IC images

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Tumor Case 2 (glioblastoma)
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Tumor Case 2 (cont.)

• Post-radiotherapy and surgery
• Can clearly see where the tumor was
• CE image shows residual tumor the best

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Multiple Sclerosis
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Multiple Sclerosis (cont.)

• IC1 shows active lesions
• IC2 shows active and inactive lesions
• Gray matter intact

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Discussion

• IC images had smaller variances than original
  images (per F-test, plt0.001)
• Sharper/more enhanced images
• Can remove free water, determine residual tumor
  or tumor involvement (via disruption of normal
  matter)
• Explored increasing the number of components

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Future Research

• Explore ICAs usefulness with respect to tumors
• Neutral intensity
• Tumor involvement in gray and white matter
• Separate edema from solid part of tumor
• May help in the removal of active lesions for MS
  patients
• Preprocessing method to classify and segment the
  structure of the brain

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References

• Hastie, T., Tibshirani, R., Friedman, J.
  (2001). The Elements of Statistical Learning
  Data mining, inference, and prediction.
  Springer-Verlag, NY.
• Nakai, T., Muraki, S., Bagarinao, E., Miki, Y.,
  Takehara, Y., Matsuo, K., Kato, C., Sakahara, H.,
  Isoda, H. (2004). Application of independent
  component analysis to magnetic resonance imaging
  for enhancing the contrast of gray and white
  matter. NeuroImage, 21(1), 251-260.
• Stone, J. (2002). Independent component
  analysis an introduction. Trends in Cognitive
  Sciences, 6(2), 59-64.