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A Taste of Data Mining

A Taste of Data Mining. Definition. “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. Digitized Image  Zip Code

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A Taste of Data Mining

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  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. • Learning from data.

  3. 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.

  4. Kth-Nearest Neighbor

  5. Linear Decision Boundary

  6. Quadratic Decision Boundary

  7. Beneath the blur: A look at independent component analysis with respect to image analysis Galen Papkov Rice University April 2, 2014

  8. 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

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

  10. 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)

  11. 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)

  12. Cocktail Party Problem • Scenario: • Place a microphone in the center of a cocktail party • Observe what the microphone recorded • Compare to human brain

  13. 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)

  14. 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

  15. Normal MR and IC images vs. Average of the Normalized Images

  16. Observations w.r.t. ICA transformation for normal subjects • IC images after whitening have removed (minimized) “noise” • Observe the complete removal of free water

  17. Tumor Case 1 (oligodendroglioma)

  18. Tumor Case 1 (cont.) • Hazy in location of tumor in original images • Less cloudy, but can see involvement of tumor in IC images

  19. Tumor Case 2 (glioblastoma)

  20. Tumor Case 2 (cont.) • Post-radiotherapy and surgery • Can clearly see where the tumor was • CE image shows residual tumor the best

  21. Multiple Sclerosis

  22. Multiple Sclerosis (cont.) • IC1 shows active lesions • IC2 shows active and inactive lesions • Gray matter intact

  23. 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

  24. 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

  25. 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.

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