Singular Value Decomposition and Machine Learning

March 21, 2019July 2, 2019Leave a comment

For this project, I used Singular Value Decomposition (SVD) to analyze two collections of facial images, and to prepare audio data for machine learning algorithms to identify music genres and artists.

The full paper describing this project is here.

For the first part, I analyzed two sets of faces from the Yale Face Database. The first set included 2,414 images of human faces which were cropped to roughly the same size and position for each face. The second set included 167 images of human faces which were uncropped. I used SVD on each set of images. I then compared a sample image with an increasing number of principal modes.

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Spectral Filtering of Ultrasound Images

March 21, 2019July 2, 2019Leave a comment

For my first project of applied math, I used spectral filtering of noisy, simulated ultrasound images to locate a marble swallowed by a dog. I analyzed a series of 20 three dimensional images of the dog’s digestive system with 64x64x64 voxels. In order to remove noise, I first averaged all 20 images in the frequency domain to locate a peak frequency profile, and then spectrally filtered each of the images in the frequency domain, using a gaussian filter around the peak frequency profile. I was able to locate the marble as a peak within each of the 20 filtered images.

The full paper describing this project is here.

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Monte Carlo Simulation

March 20, 2019March 25, 2019Leave a comment

My first project with the CERN ATLAS Group was a training exercise to build my own Monte Carlo simulation. The Monte Carlo simulation is built on the assumption that a highly energetic particle will decay into two particles. The first particle will scatter by an angle theta and an angle phi relative to the initial trajectory of the parent particle. The angles are governed by probability distributions p(theta)=1/(1+theta) and p(phi)=1/(1+ phi). Each angle is determined stochastically. The first particle will then have an energy which is a fraction z of the initial energy E. From these values we can determine the trajectory of the second particle based on relativistic energy and momentum conservation. The first and second particles then decay in the same manner. The simulation assumes that once a particle reaches an energy Ecrit, it will no longer decay. This value is initially determined in the simulation.

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The Fun Begins

March 18, 2019March 25, 2019Leave a comment

This blog documents my journey from a 13-year career in Patent Law to a career in Data Science. I am presently studying for a Master of Science in Physics at the University of Washington. I have been a part time student since January of 2018. Next quarter, I will be transitioning to a full-time student to accelerate my completion of my M.S. For summer quarter, I will be working on my capstone project. I intend to complete my studies in August of 2019.

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