1 A Taste of Data Mining. 2 Definition “Data mining is the analysis of data to establish relationships and identify patterns.” practice.findlaw.com/glossary.html.

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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.