Exploring Principal Component Analysis

Samantha Garcia, 11.02.2026

A series of applications that explore principal component analysis in 2D and 3D.

Inhaltsverzeichnis

  1. What is PCA?
    1. Introduction
    2. What is PCA?
    3. PCA Color Projection
    4. PCA Color Projection (complicated version)
  2. Exploring PCA in 2D
    1. Principal Component Analysis
    2. Circles PCA in 2D
    3. Absolute Value PCA in 2D
    4. Cubic PCA in 2D
    5. Linear PCA in 2D
  3. Exploring PCA in 3D
    1. Principal Component Anlaysis 3d
    2. Groups PCA in 3D
    3. Circle PCA in 3D
    4. Line PCA in 3D
  4. Other ML Concepts
    1. The 5 Queens Problem
    2. Reinforcement Learning
  5. ANNs
    1. Book access
    2. What the Heck are Artificial Neural Networks?
    3. Activity!
  6. About Me
    1. Contact Info and Bio
    2. Other useful tutorials, books, or lessons

1.

What is PCA?

  • 1. Introduction
  • 2. What is PCA?
  • 3. PCA Color Projection
  • 4. PCA Color Projection (complicated version)

1.1.

Introduction

Access this link using the bit.ly link: [br][br][b][size=200]https://bit.ly/ggb26PCA[br][br][/size][/b]
– Samantha Garcia

1.2.

–

1.3.

–

1.4.

–

2.

Exploring PCA in 2D

  • 1. Principal Component Analysis
  • 2. Circles PCA in 2D
  • 3. Absolute Value PCA in 2D
  • 4. Cubic PCA in 2D
  • 5. Linear PCA in 2D

2.1.

Principal Component Analysis

Move the points around to see what the top principal components are for the given inputs. The horizontal axis represents x1 and the vertical axis represents x2. [br][br]Click "Explore PCA" to see the top 2 principal components and explore other possible components by moving the vector around. [br][br]Check "Show rotation" to rotate the points so the component is horizontal and input can be reduced to one dimension.
– Samantha Garcia

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Exploring PCA in 3D

  • 1. Principal Component Anlaysis 3d
  • 2. Groups PCA in 3D
  • 3. Circle PCA in 3D
  • 4. Line PCA in 3D

3.1.

Principal Component Anlaysis 3d

Move the points around to see what the top principal components are for the given inputs. Points can move anywhere within the 3D box. The three axis represent x1, x2, and x3. [br][br]Click "Explore PCA" to see the top 3 principal components and explore other possible components by moving the vectors around. You can also snap to the principal components by checking the corresponding boxes.[br][br]The value of "n" represents the number of principal components that the points will get projected onto. If n = 1, points are projected onto a line. If n = 2, the points are projected onto a plane. A maximum of two principal components may be selected when n = 2.
Use this icon to switch to 2D perspective
Use this icon to switch to 3D perspective. A slider can be used to rotate the view.
Use this icon to switch to 2 principal component plane when n = 2 is selected.
– Samantha Garcia

3.2.

–

3.3.

–

3.4.

–

4.

Other ML Concepts

  • 1. The 5 Queens Problem
  • 2. Reinforcement Learning

4.1.

The 5 Queens Problem

The 5 Queens Problem
The 5 Queens Problem originates from the 8 Queens Problem that asks the question of how 8 queens can be placed on an 8x8 chess board without any of them being able to attack each other. This derivation uses 5 queens on a 5x5 chessboard. In Chess, a queen can attack other pieces if they are in the same row, column, or diagonal as the queen. (Learn more about the n-non attacking queens problem [url=https://medium.com/@miodragpetkovic_24196/problem-of-n-non-attacking-queens-i-98ea37f282a0]here[/url]).[br][br]Your goal is to find as many solutions to the 5 queens problem on the board below. Drag and drop the queens to a square on the 5x5 board. As you are solving, think about what algorithms you are using to help solve the problem.[br][br]You can use the "Show Attacks" checkbox to show the ways queens can attack each other. Check Solution to see if your answer is a solution and see what solutions you have found so far. [br][br]For a 5x5 board with 5 queens, there are 10 possible solutions. Can you find them all? [br][br]
– Samantha Garcia

4.2.

–

5.

ANNs

  • 1. Book access
  • 2. What the Heck are Artificial Neural Networks?
  • 3. Activity!

5.1.

Book access

This section is a small excerpt from last year's presentation on ANNs. To access the full book, go here: [url=https://edushare.ing/GGBANN]https://edushare.ing/GGBANN[/url]
– Samantha Garcia

5.2.

–

5.3.

–

6.

About Me

  • 1. Contact Info and Bio
  • 2. Other useful tutorials, books, or lessons

6.1.

Contact Info and Bio

Samantha Garcia M.Ed. C&I, BSEE, is a former AP Computer Science teacher, mathematics teacher, and robotics coach. She also served as department head for mathematics at an online private school. She worked with GeoGebra as an author on the US Content project. Now, she is part of the NSF data science traineeship program at FAU pursuing a second master's degree in computer engineering. She is passionate about technology in education. Samantha has also worked with Middle and High School teachers in the area of curriculum planning and course design. She has also assisted with LMS development. [br][br][b]X:[/b] [url=https://twitter.com/cruzteach]@CruzTeach[br][/url][b]LinkedIn: [/b][url=https://www.linkedin.com/in/samantha-garcia-597202181/]https://www.linkedin.com/in/samantha-garcia-597202181/[br][/url][b]E-mail: [/b]scruz10@me.com
– Samantha Garcia

6.2.

–

Information