Mathematical Model Behind PCA algorithm, My High School Final Paper in Mathematics

Hey folks,

I'm really excited to share with you something I've been working on for a past few weeks. The paper is about mathematical model underlying PCA algorithm and it's done in online LaTeX editor, ShareLaTeX.

Paper cover In Serbia, in order to graduate from high school (in USA that would be preparatory school I guess), among some other exams, you're obliged to write a final paper (graduation work) about a topic that's related to one of the subjects you studied at school. Although it's usually just a formality and it's generally not taken seriously, I, who had been exploring and studying ML and Deep Learning online (mostly at Coursera, but on Brilliant as well) during the last year, decided to put an effort to collect all the proofs and theorems I had gathered throughout the year and put it together to form a purposeful whole. Paper is broken down into a few sections: Problem defining, Mathematical prerequisites, Construction of the model, Conclusion and use in ML. My goal was to write it so that every high school student with decent math background can understand and follow.

PCA algorithm is an unsupervised learning algorithm used for data dimensionality reduction and it's often applied before the actual supervised learning algorithms such as Artificial Neural Networks. The goal of the PCA is to significantly decrease the number of dimensions while retaining as much information given in the original data as possible. This becomes very important for the efficiency of the actual learning algorithms, especially when we talk about ANN's because of their complex architecture and vast number of calculations.

In a way, this paper also represents the summary of my work and dedication to mathematics over the last four years. Words cannot express how much gratitude I owe to Brilliant and this incredible community for my improvement in mathematics. Discovering Brilliant was for sure a milestone for me and I could've never written this paper without knowledge and deep understanding I gained here.

So, here's the link, I hope you will have fun reading it and maybe learn something new! I want to hear your impressions, critiques and suggestions in the comment section.

Cheers!

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

I never would have been doing this in high school! I didn't learn about PCA until grad school. I'm glad the internet is enabling this accelerated learning.

Ryan Peach - 2 years, 11 months ago

This is very impressive. Good job on the hard work, and congratulations on completing high school. Maybe you can add a small abstract of your thesis with this note for the uninitiated?

Agnishom Chattopadhyay - 2 years, 11 months ago

I'm glad you like it. I added a few lines to briefly describe PCA and its importance in modern-day ML.

Uros Stojkovic - 2 years, 11 months ago

Sounds really interesting. I never would’ve written something so complex at such a young age. Looks like you’re the type who can apply for a writer position at essaypro and become one of their best writers in no time. A lot of other students need big, bright minds like yours. Perhaps you should consider giving it a shot?

Leo Bull - 1 year, 10 months ago

Great job! I wish I could read the full paper. Because I fond of reading science papers. And it’s funny I hate to write essays))) Fortunately, there is an honest essay writing rating https://essaycheckup.com. I advice to use it each student who wants to find professional academic writer.

Alex Serov - 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$