Happy New Year!
2018 has been a wild ride-- especially with the research group. We began not knowing a single thing about machine learning (much less anything related to any algorithms)-- but that was soon replaced by lectures, research, paper airplanes, and lots of inside jokes. We started the year by outlining some ground rules and basics for research. I thought that was pretty interesting, and the entire class worked together as a group. After the initial bonding, we were separated into our individual research groups.
Research!
I started out my research journey by learning about the Amazon Mechanical Turk, a platform upon which people can work small, menial task for small amounts of rewards. Armed with a better understanding of how the real-world marketplace worked for implementing my ideas and inspirations, I was able to delve into the next topic: paper airplanes. The paper airplane project was my least favorite part of first semester, if I'm going to be really honest. It frankly wasn't as bad as I had initially made it seem, but my lack of paper-airplane folding skills were evidence throughout the entire process. I learned to delegate tasks and became quite good at timing airplane flight times.
Are you seeing what you're seeing? Yep, it's us flying our planes.
We had our first trip to Caltech-- which was to watch some SURF presentation by undergraduate students at Caltech over the summer. I still have a pretty lasting impression of the presentation that discussed garage energy saving research, the multi-dimensional clustering methods using VR, and the "predict action based on your previous movements" project. They're all very cool and I think I want to draw inspiration from them in my second semester project. Our first meetings with Prof. Hassibi was incredibly rewarding-- we learned about different forms of clustering and regression models. They were tough eggs to crack, but we were able to crack the egg of Mystery up and scramble it around until it made sense to us.
My proudest moment was when I figured out the friendship paradox:
We finally then got to play around with datasets! The iris data set and Titanic data sets got our feet wet with the different applications and methods we could engage in in order to find and predict different features of a given sample data. I thought that was really cool. I struggled a bit though, since I'm not very familiar with coding and StackOverflow became my best friend. Love ya, pal.
As a group, we ventured into different the different facets of Machine Learning-- for the rest of the semester we studied the friendship paradox, investigated matrix factorization, explored graphs and relationships, and I even found out that matrix factorization could help you separate backgrounds and foregrounds from a video! Math really works in amazing ways. Here's my understanding of that factorization, Singular Value Decomposition (SVD):
In this step, you split the video into frames.
You then flatten the 2D image into a 1D vector, based on the general colorscale of the original picture.
Next, you put all of these vectors for each frame next to each other.
Finally, you can decompose this matrix composed of all of the vectors from above using SVD.This creates three matrices: U, S, and V. From this, you can find a two images-- the background and the foreground. The process of SVD creates a lower rank matrix which is the background. You can extract the foreground by finding the difference between the original matrix and the lower rank matrix.
Our year ended with the finalization of the airplane project, and I can't say I was too miserable to say goodbye. I worked long and hard and toiled blood, sweat, and tears for that paper. I'm pretty proud of it and its presentation, looking back on it. I'm really proud of my work-- and I'm looking for a better semester.
Scribble2Equation
We chose to create a program that would translate a user's entry of scribbles or curves into an equation or a set of equations because of its implications towards a crucial integration between art and mathematic disciplines. The goal of the research is to produce an algorithm that could cross-test different regression and curve-fitting models and report to the user the graph(s) that best correst to the image they inscribed onto the application interface. This project will enable us to garner a more object orientation towards our current understanding of mathematical models, and potentially may be used in various applications: paths trekked by robots, artist renditions, or maybe even future explorations of mathematics and its horizons.
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