Transcript Document

A Taste of Data Mining
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Definition
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“Data mining is the analysis of data to establish
relationships and identify patterns.”
practice.findlaw.com/glossary.html.
Learning from data.
Examples of Learning Problems
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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.
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
July 15, 2015
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Outline
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Biology
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How does Magnetic Resonance Imaging
work?
Theory behind ICA
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Gray vs. White Matter
T1 vs. T2
Cocktail party
Nakai et al.’s (2004) paper
Biology
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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.)
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T2 effect occurs when protons are subjected to
a magnetic field
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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
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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?
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Protons have magnetic properties
The properties allow for resonance
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process of energy absorption and subsequent
relaxation
Process:
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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
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Scenario:
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Place a microphone in the center of a cocktail
party
Observe what the microphone recorded
Compare to human brain
Independent Component
Analysis (ICA)
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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
x=As (A is the mixing matrix)
s»y=Wx (W»A-1)
W is approximated via an optimization method (e.g.
gradient ascent)
Application of ICA to MR imaging for
enhancing the contrast of gray and white
matter (Nakai et al., 2004)
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Purpose: To use ICA to improve image quality and
information deduction from MR images
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Subjects: 10 normal, 3 brain tumors, 1 multiple sclerosis
Method:
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Wanted to use ICA to enhance image quality instead of for tissue
classification
Obtain MR images
Normalize and take the average of the images
Apply ICA
Normal MR and IC images vs. Average
of the Normalized Images
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Observations w.r.t. ICA
transformation for normal subjects
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IC images after whitening have removed
(minimized) “noise”
Observe the complete removal of free water
Tumor Case 1 (oligodendroglioma)
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Tumor Case 1 (cont.)
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Hazy in location of tumor in original images
Less cloudy, but can see involvement of tumor
in IC images
Tumor Case 2 (glioblastoma)
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Tumor Case 2 (cont.)
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Post-radiotherapy and surgery
Can clearly see where the tumor was
CE image shows residual tumor the best
Multiple Sclerosis
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Multiple Sclerosis (cont.)
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IC1 shows active lesions
IC2 shows active and inactive lesions
Gray matter intact
Discussion
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IC images had smaller variances than original
images (per F-test, p<0.001)
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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
Future Research
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Explore ICA’s usefulness with respect to tumors
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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
References
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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.