Oct 17 - Oct 31 Journal

Concept Maps: 

Finishing off my Concept Map on k-means  algorithm, I explained more about k-means to the rest of my group while we all shared information about what we learned. I created my Concept Map video on the k-means algorithm (pasted below) while the group and I discussed how centrality worked in data graphing (pictured below). While we were originally planning on focussing in on centrality for our next concept map, our visit to Caltech changed the course of our plans as centrality was not as focussed upon. Will had figured out parts of the centrality concepts though, so he taught us how betweenness centrality, closeness centrality, and degree centrality would be used to analyze nodes in the data graphs. The centrality established that the higher the centrality value, the more "central" that point is. If you imagine the data graph to be a social network, the node with the highest centrality is the most popular person.



After visiting Caltech on Thursday, the focus on data graphs shifted from centrality to an analysis of the friendship paradox and how math can be used to reason and logically explain certain seemingly nuanced questions. The friendship paradox asks if your friends on average have more friends than you. Prior to the mathematical proving, we debated whether or not we would have the same or less friends than our friends (no one said we have more!) and explored how complicated the situation seems. Drawing out an arbitrary data graph to represent our friend group, Dr. Hassibi proved how actually we have less friends than our friends do and this is further explored in the MIT video attached below. The proof compares the average edges (friendships) the node (you) have and compare that with the average edges of all other nodes (your friends). The math simplifies to the number of friends you have added with another value equaling the number of friends your friends on average have. This constant means that people always have less friends than their friends on average.


Research:

Outside the research into the concept map topics, the group and I collected data for our side project on clustering students based on a series of random questions. We shared the form and got our teachers to assign them in class with me getting Mrs. Lintons' classes on board. Since launching the form, we have collected over 200 responses and anticipate clustering the data. This would likely be done, as explored by Robert, by converting our responses to numerical values with Yes as 1 and No as -1 (already done) and then inputting the data into a clustering algorithm. We are still collecting data though we feel that over 200 responses would be enough for this smaller, side project. An example of what our data looks like is pictured below.



Paper Airplanes: 

For the less computer science related, my work in the Paper Airplanes Project also continued. After finishing the labs, I started and completed my Introduction and my Background. Discussing with Elizabeth, I was able to convey what information was necessary though differentiating the paper airplane articles in the background was a harder task. As many articles overlapped and covered the same information, I spent some time cutting down the applicable articles to which articles I wanted to use. Seeing this report quickly coming together, I am very excited to see what my final product will be like.




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