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Transcript of 1 A Taste of Data Mining. 2 Definition “Data mining is the analysis of data to establish...
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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.findlaw.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
April 19, 2023
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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
x=As (A is the mixing matrix)
s»y=Wx (W»A-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:
1. Obtain MR images
2. Normalize and take the average of the images
3. 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, p<0.001) 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 ICA’s 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.