PCA with smileys and faces – An interactive and visual explanation

MICCAI 2024 MEC Submission4 Authors

Keywords: PCA, Principal Component Analysis, Interactive examples, Visual explanation

TL;DR: This project - implemented as two Jupyter notebooks - explains Principal Component Analysis (PCA) conceptually, mathematically and via Python code using visual and interactive examples.

Abstract:

In many areas and across multiple disciplines, large and especially high-dimensional data sets are used that often need to be analysed or visualised. Since it is hard to visualise data that goes beyond 3D, this often requires what is known as “dimensional reduction” - a process of reducing the dimension of the data while minimising the loss of information. One of the arguably most simple and widely used dimensional reduction algorithms is Principal Component Analysis (PCA for short). Principal component analysis is used in lots of applications including data compression, feature extraction or data visualisation. It is therefore useful to have a low-threshold introduction to the topic of PCA which is where this project comes in.

This project intuitively explains PCA using visual and interactive examples, implemented as Jupyter notebooks. \
With the first notebook, one can learn how PCA is performed - conceptually, mathematically and in Python code - and experience it with the interactive example of a smiley face in 2D. \
The second notebook builds on that and transfers the knowlegde to a more complex example: a face in 3D. \
Together, the two Jupyter notebooks offer an opportunity to deeply understand the basics of PCA in different settings.

Both Jupyter notebooks are provided publically via Google colab:

Notebook 1 - Smileys: \
https://colab.research.google.com/drive/1HVipazHa0WX8I1kVSUfW_ouQryTmugOJ?usp=sharing \
Notebook 2 - Faces (also refers to notebook 1): \
https://colab.research.google.com/drive/16oMHRt5kj-X-2sBOE5ziw43CgdvJ6mm6?usp=sharing
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The project can also be found on GitHub: https://github.com/annikakrause/PCA_with_smileys

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Please note: The original Jupyter notebooks were converted to one PDF file for submission.
The notebooks contain interactive outputs that cannot be reproduced in the PDF file.
We highly recommend reading the Jupyter notebooks on Google colab.

Website: https://colab.research.google.com/drive/1HVipazHa0WX8I1kVSUfW_ouQryTmugOJ?usp=sharing; https://colab.research.google.com/drive/16oMHRt5kj-X-2sBOE5ziw43CgdvJ6mm6?usp=sharing

Submission Number: 4